Gamblers Fallacy - Definition & Examples LF

Hey all, so from just perusing some of the top video makers on youtube for this game and the servers I play on it's come to my attention a lot of players don't actually know/understand the odds of getting the character you want from banners. So I've done this sporadically on a few of PayneBlades videos (shoutout to him for putting up with my shit) but I figured I'd make a post here and hopefully shed some light to some people on the actual numbers behind summoning. The goal of this is so that people can better understand their odds and make smarter decisions on when to summon. So there aren't so many "I can't believe I got shafted, this is BS!" comments all the time.

I'm going to show the following points from a statistical POV:

How many summons do you need to pull the banner UR.
- How many shino coins you need to do this.
How many summons do you need to pull one of the EF Banner URs
- How many shino coins you need to do this.
What are your odds of pulling the Banner UR when you get a UR?
How to figure out your chance of getting the banner UR in X shino coins

There is a TL;DR at the bottom that summarizes the main stats, so feel free to skip to that if you don't want to read through this math.

NOTE: There are currently no normal double UR Banners so I don't know their rates and thus cannot calculate that. I can update this post when a normal double UR banner comes.

How many summons do you need statistically to get the banner UR:
Total odds of getting the banner character = odds of getting 3* banner + odds of getting 4* banner
= .047% + .660% = .707% (This means on each summon you have a .707% chance of pulling the banner UR in 3* or 4* form in other words you will succeed .707 times out of 100. Do note I'm not saying the chance of pulling the 4* is .707% just that the chance of either event happening sums to .707%)
.707% / 100 = .00707 (Divide by 100 to remove the %)
1 / .00707 = 141.442 ~ 142 (Can't have half a summon)
142 - 1 = 141 (141 to 1 is the odds ratio. This means for every one success you will have 141 failures.)
Now that we have the total number (142) let's see how many shino coins that is:
142 * 250 = 35500 shino coins
This means statistically you'll need 35500 shino coins to get the feature unit on the banner. Obviously there is a .707% chance you can get the banner unit on any single summon. So some of you may summon the banner UR from their first pull, but the chance of not summoning the banner unit each summon is:
1 - .00707 = .99293 * 100 = 99.293%
So every time you summon you have 99.293% chance of NOT summoning the banner unit.

How many Summons do you need to get the banner UR on an EF banner:
Total odds of getting one of the URs = odds of 3* + odds of 4*
= .1% + 1.4% = 1.5% ( This is 2.12x compared to a standard banner. Almost 4.5 times as much if we compared getting either)
1.5 / 100 = .015
1 / .015 = 66.667 ~ 67 (can't have partial summon)
67 - 1 = 66 ( 66 to 1 is the odds ratio. Every success will contain 66 failures)
67 * 250 = 16750 shino coins
This is 47% (less than half) the cost of a normal banner. So as you can see it's a very smart idea to wait for the EF banner if you aren't a whale. As I said above I don't know the rates for a double UR banner but I would assume they're slightly worse than a normal UR banner because more units in the pool is usually a reduced rate. Even if that assumption is incorrect with a double UR banner you could likely purchase one (maybe both? I'm not sure how the shop works) from the shinobi exchange and then get the shards from FG/Abyss and then summon the unit on the corresponding EF banner.

What are your odds of pulling the Banner UR when you get a UR?
In EF banners it's 50% (Super easy, only two units both have equal rates so it's split right down the middle)
Normal Banner:
Total chance of pulling a UR (4* or 3*) is 3%, as we saw above the chance of pulling the banner UR is 0.707%
.707 / 3 = 0.235667 * 100 = 23.56%
So whenever you pull a UR there is a 23.56% chance it is the banner UR. Compared to EF where it's 50% you can again see EF banners give just over twice the chance of getting the UR you want.

How to figure out your chance of getting the banner UR in X shino coins
So this is (in my opinion) the best one. This is a way for anyone to see what their odds of getting the banner UR is with the amount of Shino coins they currently have.
Chance of getting banner UR at least once = 1 - chance of not getting banner UR
This makes sense because in percentages things need to add up to 100 (or one if you want to look at just the raw number and not the %). If if you know the odds of some event happening then the compliment (in other words the opposite of that event) have the remaining odds needed to sum up to 100%.
For example if you're watching the Super Bowl and the announcer says "The Chiefs have a 98% chance to win the game right now" it means the chance of them losing the game is 2% (1 - .98 = .02, .02 * 100 = 2%)
So we need to calculate the chance of not getting a banner UR in X (your number of summons) tries. This is actually easier than it sounds because the chance of not getting a banner UR is the SAME every single time you summon (another word for this is independent events. Meaning whatever happened on the previous try has no effect on the current try)
It just changes out equation to:
chance of getting banner UR at least once = 1 - (chance of not getting banner UR)^{number of summons}
**chance of getting banner UR at least once = 1 - (.9923)**^{number of summons}
Now that the equation is all laid out here are the steps:

Calculate number of summons you have = number of shino coins / 250 (round DOWN. Can't have a partial summon)
Calculate (.9923)^{number of summons} (As we saw above chance of not getting banner UR is .9923)
Calculate chance of getting banner UR = 1 - your answer to #2
(optional) multiply answer to #3 by 100 to get the % chance

An example:

I have 10,000 shino coins. 10,000 / 250 = 40
(.9923)⁴⁰ = .734039 (You can google .9923^40 to have it calculate the answer for you)
1 - .734039 = .26961
.26961 * 100 = 26.961% chance of pulling the banner UR.

Here are the equations needed to calculate getting 1 of the EF characters and getting either of the EF characters:

chance of getting one EF UR at least once = 1 - (.985)^{number of summons}
chance of getting either EF UR at least once = 1 - (.97)^{number of summons}

TL;DR:
It's very low odds to summon the banner unit on a normal banner. If you're not a Whale you should NOT summon on every banner. You should save resources as much as possible to give yourself the best chance to get the banner unit. EF Banners are a way better chance EVEN if one of the units is not desirable.

TL;DR Stats:
(All include the 4* or 3* chance added together)

Normal Banner stats
- You have a .707% to summon the banner UR on a normal banner summons each time you summon. (This is the chance of the 3* or 4* summed.)
- If you were to pull the Banner UR there is a 6% chance it's the 4* version.
- You have a 99.293% chance to NOT summon the banner UR on a normal banner summons each time you summon.
- The odds ratio for summoning the banner UR is 141 to 1 (Meaning for each success you will have 141 failures)
- 142 summons is 35500 shino coins. Meaning you have to spend that much before it becomes a "shaft" anything under that and you've not met the odds ratio so it may be unlucky compared to others but it's not uncommon from a straight odds perspective.
EF Banner Stats
- You have a 1.5% chance to summon one of the banner URs on an EF banner.
- The odds ratio for summoning one of the banner URs on an EF banner is 66 to 1 (meaning for each success you will have 66 failures)
- 67 summons is 16750 shino coins. Meaning you have to spend that much before the banner has shafted you. (Not here I didn't calculate summoning both meaning if you summoned the unit you didn't want you got a coin flip the wrong way.
Odds of pulling Banner UR when you pull a UR
- For EF it's 50% chance. When you pull a UR there's a coin flip between which it will be.
- Normal Banners you have a 23.56% chance to get the banner unit when you summon a UR
What is my % chance of getting the banner unit when summoning with X shino coins
- Shino coins / 250 = number of summons
- chance of getting banner UR at least once = 1 - (.9923)^{number of summons}
- chance of getting one EF UR at least once = 1 - (.985)^{number of summons}
- chance of getting either EF UR at least once = 1 - (.97)^{number of summons}

Common misconceptions:

"But pedantic programer I got the banner unit in one single. So this math doesn't apply to me"
- No it still does. You just achieved that .707% chance on your first try. If 30,000 people all summon once on a banner there is a pretty much guaranteed chance (.9999999 to like the 100th place) that at least one of them will get the banner unit on their first summon.
"But pp I didn't get the banner unit in 75k coins so this isn't true"
- This is the exact opposite of the previous answer. It's RNG so while your chance of getting the banner unit with 75k coins is high (90.2%) there's still the chance you don't get it. You got shafted. That sucks pray to RNGesus
"I spent 40k, I should get him/her anytime now right?"
- Wrong, this is pretty much the definition of gamblers fallacy and your previous 40k summons have absolutely 0 effect on the next 40k summons. A lot of gacha games have implemented spark systems to alleviate this. So after X amount of coins spent you will be guaranteed the banner unit. I hope tribes implements one but until then there is not magic cure to guarantee you'll get the unit.

Defending shell guy and roasting a dream stan

You should know about the tricks gacha games use to get you addicted/make you spend money!

I administrate a small gacha community myself and feel like these are information that need to be shared. I'm not telling you that you shouldn't or can't spend money on Genshin Impact, but the least you can do is being aware of these things.
Whether you are already caught in the trap or not, simply knowing about these tricks, traps and fallacies will help you. Games use them to lure you in, keep you engaged and tempt you to spend money. I'll try to keep these points as short and condensed as I can.

0. Am I genuinely having fun?

Since this one is not really a trap and thus something of an outlier I marked it as 0., but it's a great question to keep in mind: "Do I still have genuinely fun playing this game, or does it feel like a chore? Is this worth my limited time?" You should regularly ask yourself that question.

1. The monthly pass (Blessing of the Welkin Moon) has a great price-performance ratio and is cheap so it can't hurt... can it?

The monthly passes in games are more dangerous than you think:

You get part of your purchase only on a daily basis to make you log in every day to not waste the gems you bought. This is to condition you to make the game your daily routine.
Using a cheap thing you can buy makes you set up a payment option and makes you accustomed with the process of buying. This reduces the resistance in case you have the urge for an impulse purchase.
Just because the price-performance ratio is better than the other available options doesn't make $4.99/5,50€ automatically worth it. You're still spending money on virtual things.

2. It's free to play and I enjoy(ed) it, so spending some money can't hurt.

While technically not wrong, be aware of the consequences this can have. Similar to the points above it might also be a trigger to incentivize for further purchases. Especially considering the next point:

3. Guilt-tripping the player into playing after they spent money

The game doesn't even have to do much for this since it usually happens by itself. Once you paid money you feel like you now have to play, even when you're not even really having fun.

4. The daily routine of work and chores

Just like with the monthly pass, by rewarding daily engagement with the game (daily quests/battle pass/rotating dungeons) you get conditioned to make the game part of your daily schedule/life. Once logging in and playing becomes a habit it can be difficult to stop, even if you don't really enjoy it and are literally just doing in-game work/chores.

5. The first time is free - veiling the distribution of currencies/gems

Also known as the honeymoon phase. You get a lot of free stuff in the beginning, tempting you to roll and get a taste of what rolling feels like - especially if you're lucky and get a rare characteitem. By slowly decreasing the distribution of these currencies you feel tempted to spend money to get more of that initial high you had. This hits especially bad when new content is shown/announced while you are out of gems.

6. Overwhelming the player with a lot of different currencies/gems

Genesis Crystals, Primogems, Intertwined Fate, Acquaint Fate, Starglitter, Stardust, there are so many (more or less) premium currencies that it's almost confusing - and not by accident.

Multiple currencies are used to make the player lose track of the different values. Buying something should make the player also think they got "a lot of different things" when it's just real money in different forms.
By sneaking in multiple currencies, the value of money is lost along the way. Example: Real money -> Primogems -> Intertwined Fate - This blurs the link between money and Intertwined Fate.

7. The carrot and the stick - New content and changing the meta

"Now that I have the best/meta character I will never need to spend money again." is sadly a trap a lot of people fall for, but what is currently considered "the best" will definitely change.
This is an investment into something that will not last, and even worse is that since you already spent a lot of money in the past you feel pressured to get the new "best" thing to not lose your place on top of the player-base.

8. "It's okay, I only spent $___, some other people spent waaay more."

If you're telling yourself something like this then you already walked further into the gacha trap than you might think. Denial in the form of rationalization is a crucial and dangerous sign for gambling addiction.

9. Gambler's Fallacy and Sunk Cost Fallacy - A dangerous combination

Well known classics, but I still felt like including them.
Gambler's Fallacy: "Gambler's fallacy refers to the erroneous thinking that a certain event is more or less likely, given a previous series of events."
Sunk Cost Fallacy: "Individuals commit the sunk cost fallacy when they continue a behavior or endeavor as a result of previously invested resources (time, money or effort)."
While already dangerous on their own, in combination these two reach a whole different level. Even with the pity system, just because you were unlucky a lot doesn't mean that you are guaranteed to become more lucky in the future. This in combination with spending a lot of money without getting what you want can tempt you to spend even more.
"I already spent $200 and didn't get what I want. If I stop now those $200 will be wasted!"
This is a highly dangerous train of thought!

10. The Sunk Cost Fallacy strikes again

You don't have to spend actual money to fall for this fallacy. If the only thing that keeps you playing is the amount of time you already spent, the items you own and the characters you unlocked, then maybe you should reevaluate your decision. "If it's not fun, why bother?"

There are a lot more techniques that are used to trick people, from flashy pull animations to making you aware and jealous of other people's characters/pulls (Why do you think phone players are incentivized to take a screenshot of their pulls and share it?), but I wanted to keep it to the most common/obvious ones.
Edit: If you're still curious and want to know even more tricks and traps, Dokuganryu linked a great and informative video. Definitely worth a watch if you have the time.

I genuinely hope everybody is enjoying Genshin Impact, but keep in mind how this company makes their money.

You are all mad

SPOILER: Why the infinite monkey theorem is wrong.

Hello all, I have revisited the infinite monkey theorem and have been giving it much thought as of late. I have come to the conclusion that the infinite monkey theorem is false. Upon sharing this information with many people online they have all simply made like monkeys and threw their feces at my face saying I'm just an ignorant idiot (Apart from a select few). So I have decided to share my thoughts on Reddit in hopes to gather a larger consensus.
Firstly I will start with presenting the theorem; The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times.
Ignoring the fact that a real monkey would just slam a rock on the typewriter and take a shit on it, the actual point is not the monkey, but the random generation of letters eventually producing verbatim, deliberate works of art. Now to be completely clear, I do accept that it is entirely possible for this to occur. It is entirely possible for a magical immortal monkey to physically type out such works given enough time. However, the issue is the term "Almost surely" as if to imply that it must occur.
To start off we must first understand the concept of infinity. Fundamentally it is impossible to think of a string of words or numbers that goes on for infinity, as it is so large that even our brains would not have enough storage space to memorize and account for every number or letter. This is the same in terms of time. Infinity is not just a large value, it is a boundless value. However there can be different types of infinity. For example, any whole number can theoretically have an infinite value, as well as any combination of whole numbers such as 11111 reoccurring and 122222 reoccurring and 133333 reoccurring, and so on to an infinite set of infinite numbers. This can also apply to decimal numbers such as 0.111111 reoccurring, and so on. Similarly this can apply to letters, such as one A followed by an infinite string of B's, one A followed by an infinite string of C's, and so on.
With this in mind I would like to assert that the monkey, given an infinite amount of time, has the ability to string together any infinite combination of possibilities. For example, the monkey could simply type the letter S for an infinite amount of time or any combination of letters which exclude any deliberate piece of writing. It is also possible for a different monkey to type out a string of letters, as I did mention earlier, containing hamlet.
The reason we must accept that it is possible for an outcome to be an infinite string of S, is due to the gamblers fallacy. The probability of any given coin flip does not change simply because it has been tails 12 times in a row. The theoretical probability that S is typed an infinite amount of times draws closer to 0 with every tap of the key, but never actually reaches 0. This is why in probability, the term "almost surely" is used. Even though the mathematical value of a probable outcome is considered to be 0, it does not mean it is impossible. In saying this, it is equally possible that the monkey types an infinite string of G's or B's or any other combination of valueless letters. They all have a mathematical probability of 0.
So how do people argue that the theorem is still correct? Well they assert that when stringing together any infinite combination of 'finite' strings such as the work of hamlet, followed by the complete transcript of the transformers movies, as well as each version of the bible on hand, etc increases the strings value, approaching to a 1 (but again never reaching it). This is to say that it is argued that it is more impossibly probable for any given string to contain hamlet than it is to not contain hamlet. That is to say, there are more infinite sets of hamlet strings than there are non hamlet strings. And when you put it into perspective and think about it in this fashion, it becomes blatantly false.
Finite works, no matter how many, are finite, and any infinite combination of finite works are also finite. In theory you could also have every finite string of letters followed by an infinite string, but it is less likely for any deliberate string to occur than it is for a random string, if not at least the same in terms of probability. For example, it is more probable for a string of letters to contain "zpt" than something like the word "indubitably", meaning it is more probable for a string to contain gibberish than any legible string of words. Another example is that the English language heavily relies on certain letters, the letter E for example appears 11.1607% of the time in the oxford english dictionary. Where as the letter Q only occurs at a percentage of 0.1962%. This makes the letter E 56 times more common than the letter Q. Another example is by the oxford university press who complied a list of the most common words used which analysed over a billion words. "The" is by far the most commonly used word.
If we are to assume that a monkey is to type out all great works of writing in English, then we can assume that the monkey will be heavily relying on typing the letter E and the word "the". Again, the probability is astronomically low, but not impossible. The argument however, is that it is more likely for random letter generator to generate all finite works of writing, than infinite strings of letters. Well, if we are to do some simple math we discover that 100/26 is equal to 3.84615384615. Meaning that each letter has a 3.84615384615% chance to occur. If we revisit the occurrence of the letter E in the English language, we discover that likelihood of producing the letter E at random is far lower than what is required to produce every word. This is again, not to say that there doesn't exist a realm where the letter E is produced at random 11.1607% of the time, and where the letter Q occurs only 0.1962% of the time etc. But that is is far less likely than simply typing any given letter at random, even in the realm of infinities.
Simply stating that an infinite string of "S" to be irrational and invalidating that string on the basis of probability is absurd when the probability of the letter S being typed is far greater than what is required within our English vocabulary. Furthermore, there are an infinite string of letters which can be taken as gibberish which do not contain an 'irrational number'. There are an infinite amount infinite gibberish where hamlet simply doesn't exist. People will say infinity is to hard for people to grasp and that is why they cannot understand hamlet existing within the infinite, but i would say it is the opposite. They are so fixated on the infinite containing the finite, that they forget what infinite truly means.
If this still doesn't convince my readers so far lets then pick apart the argument and demonstrate why it is fundamentally flawed. The argument asserts that: there are an uncountable infinite set of strings which do not end in such a repetition (such as zptzptzptzpt...) these correspond to the irrational numbers. We can then separate these into two uncountable infinite subsets. Those which contain hamlet, and those which do not. However the 'largest' subset are those which do contain hamlet, as well as any other combination of written work.
Well, the basis of this argument relies on what we call irrational numbers. And as such irrational numbers are less likely to be picked than normal numbers. And somehow, it is normal for any given random string to contain hamlet and irrational for it not to. If we actually look at what an irrational number means, we get this definition: In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
So if it to be considered a normal number, and not a rational number, it must be expressed as the ratio of two integers. An integer is a number that can be written without a fractional component (aka a whole number). Well, since we are dealing with infinity, any combination of finite work will eventually come to an end in the span of infinity, and thus must have an infinite string attached to the end. This means that while containing finite works approaches us towards 1, it will actually never reach it, meaning there are no strings which are integers, which is to say there are no rational strings, which is to say there are no 'normal' strings, which is to say the probability of the monkey typing a normal number is not 1.
Taking all this into account it is impossible for a string containing hamlet to exist if there is a string which only contains gibberish such a "zptzptzptzpt". Given there are infinite strings which do not contain hamlet, and that hamlet is not a requirement to exist within the string. The equation we actually are looking at is hamlet+∞. And it is far less likely for this to exist than simply ∞. Regardless, the term "almost surely" does not apply, as the monkey will not almost surely produce hamlet.
Who knew infinity wasn't rational.

Building a translation mapping of my trauma responses

PSA: For those of you who want to do math on rolls, here are some resources to get a footing on how to actually do it so you don't end up saying we're 77x more likely to die drowning than get a roll we want

You're Not Getting Auto-Farming, Our Brains Suck, and They Know This: Breaking down the business aspect of mobile games we don't like to acknowledge or talk about.

The subject of auto-farming comes up once or twice a week in this Reddit and every time it is greeted by the exact same two people:

Person 1 makes the argument that they do not have the time to invest as heavily into the game, therefore the less that they are able to look at their phone, the more productive they feel they would be in other aspects of the game such as PvP content. They make the argument that many people quit because of a lack of auto-farming.
Person 2 makes the argument that auto-farming is detrimental to the health of the game and will result in less engagement, therefore more players quitting. Less time spent actively engaged with the game coupled with a quicker depletion of crystals will result in less overall phone time spent on the game.

Both Person 1 and Person 2 are correct, and have valid points to make. However what we rarely talk about are the plain and simple facts that we don't like to acknowledge when we are playing a game, especially one with the Freemium model that so many mobile games have today.

Com2Us is a business, first and foremost
Com2Us will make decisions based on maximizing revenue
Com2Us, despite poor customer service and the general perception of not caring about their player base, did not earn 2 billion dollars in revenue by sitting around with their thumb stuck up their ass

So let's break down the arguments made by both Person 1 and Person 2. Instead of analyzing these from our feelings based on our personal relationship with Summoners War, we are going to instead analyze these from the perspective of a game developer and a business owner. But before we do this, we need to recognize Summoners War for the game that it is, rather than the game we expect it to be.
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The Freemium Game Model, the Sunk Cost Fallacy, Skinner Box Mechanics, and the Feeling Of Getting What What We're Owed.
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The Freemium Game
A quick Google search tells you what a Freemium game is better than most could summarize. "The freemium model offers users the core product — the game — for free and then optionally charges them for premium content such as in-game currency, extra content, or customizations." We are all aware of this and separate ourselves into different factions based on this accordingly - Free To Play players and Pay To Win players (F2P+P2W respectively.) What's interesting about these two factions is how they can so vastly differentiate themselves and the gymnastics we do to convince ourselves what faction it is that we belong to.
By definition, a F2P player will have spent $0 on this game. A P2W player will have spent at minimum $1 to play this game. How many times have you read someone say "F2P btw.. But I only get the $5 package to keep my account secure". If a player has purchased $5 every 15 days from this game for a period of 5 years, this equals roughly $600 spent on this game. Does that sound F2P to you?
Another very common argument is that you are not a P2W player if you only buy certain packs. The transcendence pack every Christmas, that's it. A 750 crystal pack when you were off sick from work and wanted to spend the day farming. Does this sound like F2P to you?
The point I am trying to make within the Freemium Game Model is that we are all capable of making mental gymnastics work in our favor of convincing ourselves that we view this game differently than how we actually play it. Which is a perfect time to talk about the way that mobile game developers and businesses such as Com2Us manipulate our trains of thought using extremely common tactics used in every business from getting ourselves a Starbucks coffee in the morning, to walking into a casino and dropping $1,000 at the slot machine.
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The Sunk Cost Fallacy
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Individuals commit the sunk cost fallacy when they continue a behavior or endeavor as a result of previously invested resources (time, money or effort)
Does this sound familiar? To put it plainly; the more time and money you put into something, the more you feel it owes you. For this point, I like to liken hitting the replay button in the dungeons akin to pulling the lever of a casino slot machine. You sit down at the machine, pull the lever, watch the lights go by. You either get a payout (rare), you get something meager not worth the value of your pull ($1 back on a $5 pull for example), or you get nothing. This is exactly what we are doing with the dungeons. We are pulling the lever (the replay button) and hoping for a big payout (a legendary rune) and scoffing at the meager payouts we deem invaluable (runes that we need to sell) or get frustrated that we receive nothing (unknown scrolls)
The only difference is that a slot machine can pay you out nothing, however a dungeon run cannot. So unknown scrolls and rune craft stones are put in their place to simulate the mechanics of a slot machine adapted for a mobile game.
Now that we've likened dungeon runs to the slot machine, I'd like you to consider how you may behave sitting behind a slot machine. Do you walk from one slot machine to the other and try your luck at different ones over and over? Likely not. You are more likely to sit at the same slot machine and pull the same lever because you have invested your time, resources and money into this slot machine already. This tricks our brains into thinking that the machine is more likely to pay out to us when in fact your odds would be just as good sitting at any other machine. The longer we sit at this machine without a payout, the more frustrated we get, and the harder it is to move away from it. So you keep trying, over and over.
"The effect becomes a fallacy if it's pushing you to do things that are making you unhappy or worse off. "
Sound familiar?
But hold on, Person 2, because this isn't just proving your point. It is also diminishing the main argument that you pose stating that the health of a game is directly tied to whether or not auto-farming exists on that platform, and cite other games that feature auto-farming to have died. Person 1, you likely have heard Person 2 claim that Com2Us has had other games that feature auto-farming die off despite being exact replicas of Summoners War. And why is that? Well, you can blame the Sunk Cost Fallacy for that as well.
Imagine walking into the casino and you begin to make your way over to the slot machine you have been pulling for the past five years. But wait, there's a BRAND NEW, shiny, sparkly, up to date, modernized slot machine sitting dead center in the middle of the casino. It pulls for you! It has better graphics! It has a drink dispenser! It appears to be better in every single way!
.. Good luck pulling everyone off of the slot machine they have spent the last five years pulling, never having quite obtained the payout they were hoping for. This is the manipulation that game developers like Com2Us have over us and that they are well aware of. "Oh, you want to go try something new? lol you'll be back. You've spent too much time here to leave now."
The Sunk Cost Fallacy works both ways. On one hand, it's unfair that one demographic doesn't feel that they get something they perceive as a QoL update that would enhance their experience. On the other hand, the other demographic can't really use it as too strong a basis for their arguments either based on the fact we've ALL sunk time into Summoners War. Other games didn't necessarily die because they didn't have auto-farming - it's just as likely they died due to not being able to pry enough people off their slot machine of choice.
Summoners War is one of the longest running and most successful mobile games in existence. It hasn't survived through dumb luck. It survived because it knew how our minds worked, it exploited that, and now they've got us in their clutches - just like casinos do to the millions of people on this planet who suffer from gambling addictions.
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Skinner Box Mechanics - Why Our Brains Suck, and the Chemical Reason Com2Us Won't Implement Auto-Farm
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https://www.youtube.com/watch?v=tWtvrPTbQ_c
I won't outline the whole history of Skinner Box Mechanics, but I'll summarize as best as I can

Researchers found that they could condition animals based on having pigeons peck at a button inside of a box. Each time they pecked the button, they would receive food, or, a reward
Researchers found that this conditioning, called Operant Conditioning, could work on humans
Researchers found that simply rewarding someone every time they perform an action, is not the best way to get someone to continually do that action. If you provide a reward to the person a random number of times or every number of minutes, these methods are far more effective at getting someone to repeat an action.
Researchers know that we are well aware of this, and we keep doing it anyway.

I can't say much more on this topic because it is completely black and white.
We are not getting auto-farming because Com2Us is aware that the more they can get us to press a button and reward us some of the time is far more effective than giving us the ability to farm 10x the amount with 10x less effort. It is not a matter of how we think we might feel. It is a matter of how our brains are wired to feel.
-
In summary:
Giving us the ability to auto-farm would be completely counter-productive to Com2Us' business model, their bottom line, and the science behind the Sunk Cost Fallacy as well as Skinner Box Mechanics. Our brains are wired to press the replay button over and over, even when we don't feel like doing it, for the chance at a reward that we don't know will ever appear. Com2Us exploits this, just as casino owners exploit this of their gamblers.
Person 1 and Person 2 both have good points to make about having and not having auto-farming. The unfortunate reality is that it doesn't matter what Person 1 or Person 2 thinks, because neither of these have a basis in the conversation as to why Com2Us operates the way that it does. Com2Us will make their business decisions on what will generate the most revenue, not what will affect one majority of the player base over the other - Com2Us would rather have 1,000 players spending $20,000 a year, than have 100,000 players spending $20 a year.
It is up to the individual to be aware of these mechanics and choose accordingly if you are able to view the game for what it is and if you would like to continue playing. If you are living under the illusion that they might implement full auto-farming one day and keep pressing replay because you hope it will come to fruition, I hope this has helped you understand why it is not coming and can help you decide accordingly if this game is harmful to you, or a fun part of your daily routine.

***EDIT***
Yes I saw the most recent developer note. Welp.

Playing Golden Sun: The Lost Age - Part 6

Too busy celebrating Caillou's cancellation to play (nah, just kidding, studies are the culprit) but I can squeeze some time out now to continue the game a bit! Just finished the Gabomba Statue dungeon, so I'll take a look around Kibombo and see if anything's changed before revisiting places where I can use Piers' Frost (for now, I remember the Madra Catacombs and the Kibombo Mountains).
-Seems like everything's peaceful again around here, but to be honest I'm not optimistic at all about Akafubu's leadership being anything but pathetic. Who knows, maybe if I keep coming back to Kibombo I'll be able to see character growth. Is there a teleporting Psynergy in this game?
-Speaking of Akafubu, his dad's already singing his praises, but Akafubu's only beating himself up for leaving the room so quickly - not quite sure if he's doing it out of greed or something else, tbh.
-All the warriors were farm boys? Sounds pretty horrible for the town's economy and sustainability, but what do I know? It's literally like the military draft, I guess. Also, the weapon and armor shopkeepers talk about deadly poison and 'maaaaagic' being infused in the warriors' spears, but all the war paint in the world isn't gonna help you against a fireball, bud.
-Speaking of weapons and armor... Jenna (ironically) nabs the Frost Wand for herself, and that's it for weapons. As for Armor, Piers gets an Iron Helm and some Gauntlets. After some item shuffling (and seriously, what are these Game Tickets even used for?) I clear up enough inventory space so that Jenna can get some Gauntlets too. Item lady's got some daaark thoughts.
-...I should've guessed that monsters were eaten in this world, tbh. Thinking about it, how do people even separate normal animals from monsters here? What's the difference between, say, a wolf animal and the something-Wolf enemy from all the way back around the Kandorean Temple? Or the Emu monster and the actual emu? Food for thought... and for the stomach.
-Ooooh, some guy's talking about there being treasure west of the river... but he also thinks that nobody in Kibombo's ever found it. Well, mister, I guess they just didn't have superpowers. A woman in another house says that they're blocking the way across the river, and that you'd need a ship, which is convenient for us - we've got the Black Gem and we've got Piers, so we'll probably be able to get his ship soon enough unless anything goes wrong. West from Southern Gondowan (pretty sure that's where we are right now?) is the Eastern See, which is sorta confusing - supposedly, there's two continents in the middle of that sea. Guessing we'll go there soon enough. Found a Lucky Medal in a jar in the same house, which is nice. It seems like the villagers are starting to be more positive towards Akafubu, so we'll see.
-That 'being nice to people training' thing sounds hilarious. I want to watch that.
-Huh, I thought there'd be something on the furthest south point of the cliff you need to use Frost to get to. Well, going up a screen.
-...Wait, this is the exact same place where we recruited Piers - we just jumped on a roof instead of using the ice pillar. Whoops.
-Well, the Gabomba Statue's still open, so... yeah, I might as well try the dungeon the Great Gabomba opened last time.
-Gabomba Catacombs... hmm. The grass here reminds me of the one in Pokemon where wild Pokemon could attack you. There's also a crater-thing in the ground that won't budge even after I try all the field Psynergy I've got. I also run into a couple of Red Demons... which reminds me that someone commented to try and kill them with a Jupiter Djinn to get an item, so I'll try that. I think this is the first time I'm actually using the Defend command in this game, wow.
-Well... holy cow, that was a lot of XP. But no item dropped, so... unless anything interesting happens, I won't update anything until I get an item drop from the demons.
-Having to constantly re-set the one Jupiter attacking Djinn you have is a bit of a pain. Really wish there was a way to make fleeing more reliable too.
-jeeeeesus fucking christ, these salamanders' psynergy spells are stupid strong. or maybe Sheba's just stupid fragile.
-Jeeeeeeeesus, the Vital Moon left Piers at O N E HP.
-Pretty sure I've killed more than 16 Red Demons with Blitz already...
-Yep, this has officially entered gambler's fallacy territory.
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-Staff of Anubis, huh? All right - holy crap, that took longer than I expected. Oh my god. I spent waaay too much time running away and failing and then running away and succeeding and then healing up with Felix, but everyone's level 20 now. The new staff is a power boost... but not exactly a big one, haha. Would I do it if I knew? Probably not. But here we are, and at least I've finally got it. Don't think I can do anything right now in the Gabomba Catacombs, so let's get out.
-Oh my god, the innkeeper's wife is offering BBQ Monster Steak. That sounds sick - in both senses of the word. The warriors seem like good guys now that, you know, there's no raids and storming-cities and sneaking-into-sacred-rituals-shenanigans going on. A short rest, and it's time to leave Kibombo.
-Into the Kibombo mountains! I remember seeing a Djinni in here - let's see if Frost can help us.
-Oh my fucking god
-The Sarcophagus unleash literally summons a literal sarcophagus that crushes the pixie flat like a pancake. That's hilarious, 100% worth it, I now regret nothing.
-Oh, a Growth plant! It's annoying to have to switch to another class to use the Psynergy, tbh, but them's the breaks. I save before interacting with the Djinni, and thank goodness, because it leaps into a fight. After a few spells traded, Sheba whacks the Djinni into submission. I guess Waft must've been impressed with that, because it goes straight into Sheba right after that. With that, she class changes from a Magician to a Mage - nice!
-Felix levels up to 21, and I decide to go to Naribwe. Let's see what to do next with the fortune teller... and besides, I'd also like to see what else the people living there have to say. I run into a Wyvern Chick on the way - and man, I used to be so scared of them, wow. ~~I still am~~.
-Seems like some soldiers came through Naribwe asking for Piers... that doesn't bode well. Don't think the Kibombo knew his name, so I'm not quite sure who they might be. Otherwise, a guy's got updated dialogue, but still thinks that Kibombo's a dangerous place at the moment - I suppose the signal flare and the messengers haven't gotten to Naribwe just yet.
-...Holy shit, the innkeeper's husband dropped a bomb: it's Isaac! Isaac's trying to get to Piers! Not expected, holy crap - urgggggh, how did Felix miss them? And why do Isaac and company want to talk with Piers, anyways? Does it have something to do with the Lemurian boat Babi took from the country and gave to Isaac...? Huh. Food for thought.
-Seems like the girl that mentioned Magma Rock to Felix also mentioned it to another traveller, who headed in that direction. Might that be Isaac? But she didn't mention a group, so... not sure. Another kid mentions a man trying to get to Kibombo - I think that one might've been Piers, actually. So I guess that we're actually ahead of Isaac's group right now... huh. Usually the playable characters are the ones doing the pursuing, so this is a nice change of pace.
-Seems like the fortune teller's been predicting some pretty apocalyptic things. "The power of nature would rekindle the advance of civilization," huh? Interesting. The lady gets philosophical afterwards, asking whether a peaceful or advanced world would be better.
-...Wait, what? The old man in the backyard we broke into to nab the Unicorn Ring mentions that a 'big brute' came by looking for, of all people, Menardi? How many freaking people have been to this village? Pretty sure Saturos died with Menardi when they fell into the hole on top of Venus Lighthouse, but... hmm.
-Awww, the Kibombo are trying so hard, but I guess it's been a while since they've had to communicate like that, huh? Doesn't seem like anyone in Naribwe really understands what they're doing - though the fortune teller did tell them that the Kibombo's warlike ways are over, so let's see what ends up happening. The priest mentions a freezing cold region called Tundaria, all the way down in the south. I'll keep it in mind too.
-Time to have a reading or two. Setting down Sheba's Staff of Anubis leads the fortune teller to say that "beyond the weapon I've set down lies a terrible foe," and that my next foe awaits in the misty sea. I have to gather the "pieces of the weapon" (whatever that means), or drown in defeat. Next, I set down Piers' Chainmail: to the north, beneath the sacred icon, the one I seek awaits. Pretty sure that means in the Gabomba Catacombs, but I don't think I can progress there just yet (I should know, I spent way too long running around that floor). Setting down an Elixir tells me a similar thing to the staff: that I must forge a weapon to defeat a mortal enemy, and to seek out the pieces. I feel a fetch quest incoming. I try to set down the bag with the Jupiter Star, but I "can't remove it", so that's that, I guess.
-Well, that was a very informative diversion. Glad I stopped by here, it's given quite a lot of things to consider and watch out for. Time to move on! I think next was... Gondowan Cliffs?
-Right, Gondowan Cliffs. Pretty twisty area. There was a puddle somewhere...
-Found it. I use Frost and use the pillar to go from the right to the left. There's only one drop, and to the right of the cliff below is a Healing Fungus that I picked up. Kinda like the Laughing Fungus I've got right now, actually - I think I got that one here too. There's another puddle near the other entrance, but I backtrack after following the path because I'm pretty sure it's little more than a shortcut.
-Back to Madra! For... the fourth time, I think. Let's check out what the folks around here are saying, and then venture into the catacombs.
-I see they've fully covered up the catacombs entrance behind the graveyard. I should probably do the catacombs before I leave Madra so I don't potentially miss anything good. The guards are in high spirits, and inform us that the mayor's returned! Let's see how the guy's holding up.
-Quite a few people are talking about the boat in Alhafra: they mostly think that it should be ignored or destroyed, which seems kinda short-sighted, but hey. An old man in front of the vendor stands is instead thinking about ~~Lemurland Lulu~~ Lemuria.
-...There's a woman with a portrait asking for Menardi. Let's just say 'no' for now, haha... um. She can detect the Mind Read Psynergy, so she's an adept, but she doesn't accept us telling her that Menardi's dead, so... hmm. Well, at least Felix has told her the truth; hopefully none of these decisions come back to bite me on the ass later.
--Oh, so the Shin guy - the item vendor's boyfriend - is the guy that was being an ass to Piers and got some Frost Psynergy demonstrations for his trouble, huh. Not sure what to say other than 'don't be rude', haha.
-Well, the other vendors are still thinking about the first raid. Seems like the armor vendor doesn't think that there was an alliance because they attacked from different sides - and to be honest, given that Briggs' ship got wrecked on the right of Madra, it would've been hard to coordinate with the Kibombo even without their warlike attitude. Coincidence sounds kind of fishy, though... was there somebody pulling the strings?
-Some girl in the cave house is talking about a business scheme that's gonna use Isaac's power. Whatever that is, it doesn't sound very good. The guy in the house is thinking the same thing; to be honest, I do like that there's all sorts of varied reactions. This greedy fuck wants to parade Isaac around like a circus animal to get some money, and I could sadly see that happening in real life, given what people have been shown as circus freaks in the past. But more importantly - Isaac's group was here, huh? Was it before or after going to Naribwe?
-One of the sailors, Isaac... The guy even mentions the Lemurian ship he was given. Doesn't seem like those guys in that house see him as very trustworthy. A kid below the house I was just in actually clarifies - seems like they're looking for Lemuria. Did they mention that in the first game? I don't remember - but they're probably going there on Babi's orders, either way.
-A woman in the church is fearful of the future, pointing out the ocean warming up and the fish dying. Seems like nature's going to shit - kinda fits in with what the fortune teller supposedly said earlier, according to the lady in Naribwe. The people in the house next to the church are instead talking about the Kibombo; seems like they think they'll attack again. Hm. Can't blame them.
-The lady in the house with the Djinni's talking about mushrooms from the Gondowan Cliffs now, which certainly catches my attention: I smell a sidequest. I've got the option to hand him something... so I'll save first. Uh, the Laughing Fungus has the description 'a rare and suspicious mushroom', so I'm guessing that's the 'bad ending' to this sidequest? I'll save, hand it over, and probably reload.
-Ah, so it's not quite right. Well, that's better than him eating it and keeling over dead with his face in a puddle of his own vomit. It was returned to Jenna's inventory, so... huh. Well, let's hand in the Healing Fungus then.
-Seems like this is it. Glad to be of help to the old man: everyone deserves some comfort in their lives. They're going upstairs... and yep, they're fetching the Mars Djinni. Seems like they had it as a pet - which brings up a question. Non-Adepts can see and interact with Djinni, but can they actually use their unleashed powers or gain something from them? Regardless of the answer, Jenna gets Char for herself, and everyone's happy: I get a Djinni, and this old couple can have some tasty mushrooms for dinner.
-Going down to the prison before going to the mayor's house, and it seems like the mayor got fed up with the greedy bureocracy in Alhafra, which... 100% fairs, yeah. He wants to get people back there himself to fix the boat - I'm guessing we'll help him in that endeavor sometime. More confirmation that Isaac's party showed off their Psynergy: seems like one of them even took the time to explain what it was. Whoever it was, I'm guessing it wasn't Garet, haha.
-Ahaha, some people in the prison are trying to freeze the puddle. Glad to see they're taking it better than the guy in the cave house behind the stalls, anyways: this seems benign (and tbh, I'd definitely try too). Seems like Shin's trying to better himself - I'm glad. Time to go to the mayor's house, I guess - I'll pop into the inn to mind-read the people there after coming back from the Madra Catacombs.
-Oh, everyone's coming out for this one, nice. Everything worked out fine in the end, woop! Sheba calls attention to the girl outside (which doesn't surprise me, considering her mutterings about Menardi and her standoffish behaviour) and is swiftly ignored. Seems like Piers wants to go to Lemuria, just like Isaac - oh god, they're gonna be chasing after us trying to get information, aren't they? Do they even know that Felix and company are with Piers now?
-Awwwww, Piers is saying that he thinks we're all good people now! That's great, haha. ~~Is he counting Kraden?~~ I really hope that these guys get some dialogue, because I think there's a hell of a lot of potential dynamics that could be explored. I'd love some interactions between Sheba and Jenna, for example. Seems like Piers has decided to lend us his ship so that we can get to Lemuria... nice. The group promises to visit, and the conversation's over. I just have to highlight the old lady's thoughts, though: she thinks Piers would've been eaten by monsters if he'd been alone. Lots of faith.
-The mayor stops us when we leave to give us the gift he'd promised: a Cyclone Chip. Interesting name. I'd totally forgotten about the gift, tbh: you're all right, mayor :)
-...uh oh, "Felix...?" and random evil music? Seems like this girl knows us.
-Goddamn, Sheba - blunt as shit. "Isaac killed them. They're probably at the bottom of the sea by now." OOOOF
-Seems like the party wants to protect Isaac, which is very sweet and noble, but Menardi's sister is smart enough to figure out who he is anyways, which sucks. Kraden suddenly pipes up with "How do you know that Felix didn't kill your sister?", which is proooooobably not the best thing to say unless you want Felix to die. Is that it, Kraden? Do you want Felix to die? Menardi's sister calls him out on his bullshit (but seriously, what the hell, Kraden?) and says that even at double power, Felix'd still get stomped, which... fairs. She also says that "the lives he hold dear hangs in the balance," which... hmm.
-All right, so Menardi's sister is gonna try and seek out Isaac while Felix's group lights up Jupiter Lighthouse. She mentions "we" - is the big brute mentioned earlier that was also looking for Menardi with her? She refers to herself as Karst. Cool name.
-"Wow. And I thought Saturos and Menardi had issues." I LOVE YOU SHEBA
-The group's actually intelligent (shocker in an RPG, I know) and discusses the ramifications of their conversation. They catch on to the fact that Karst said 'we', and discuss the possibility of warning Isaac before dismissing it; and I can see why, since their goals are literally opposing each others'. Besides, Isaac's already seeking us out, and Karst is seeking him out... if she saw us fraternizing with the 'enemy', I don't think she'd exactly be merciful.
-Heh, Sheba calls Isaac and Jenna an item. How long ago was the Sol Sanctum incident, anyways? "...Stupid Sheba..." Jenna mutters. I love these two - they've already gotten so comfortable around each other that they can joke about silly stuff like this. It's great. Kraden also brings up that if a confrontation came, they'd squash us... but I dunno, iirc I finished the game with everyone at level 30 or 29 and Felix is already level 21. A bit more time... and we'd at least be able to fell Ivan, hahaha. Time to venture into the Madra Catacombs before they close for good!
-We progress a bit (the enemies are so puny now, and I'm still not over bees being here) until we reach a door: "Look upon me with eyes of truth", the tablet next to it reads. Using Sheba's Reveal Psynergy, the tablet turns into a button - pressing it opens the gates, and we enter into the ruins. I see a chest on the left and a chest to the right, but can't reach them quite yet. A bit of running around, however, and we get to the chest: it holds an Apple! The jars next to it have nothing, though.
-You know, I never noticed before, but the monsters have higher or lower-pitched death cries: for example, the Drone Bee's is higher-pitched than the Mini-Goblin's. I see an open door, but let's try to get as much business on the outside done as we can. Some Lash action allows us to use the Frost pillar to get above the open door - but there's an open door there too.. I backtrack and check if I missed anything, but going to the left only leads to the Tremor Bit chest I opened a while ago.
-Ground floor entrance: quite a few staircases and doors. The right staircase leads to a room with nothing but an empty box and a destroyed bed. Jenna levels up to 21 after a fight with a couple of Trolls. The left staircase is blocked, huh. The left room has a lot of jars and barrels, but none of them have anything - I do see a chest behind some rocks, though. The right room has a staircase that leads down to a room with a locked door and another staircase that eventually leads to the chest from earlier: it has a Lucky Medal, which Jenna pockets with gusto. Finally, the central hallway has a table cracked in half by a large stone and a seat (a throne?) worn down by the passage of time. Creepy stuff, honestly - what the hell happened here?
-Frost and Lash combined allow us to get to the top level. Going down allows Felix to nab a Mist Potion from the chest that we saw in the start. Restoring 300 HP to everyone is no joke... this could definitely be useful. Entering the first floor's entrance, we can go through the left door now. There's a bedroom inside, along with a bookshelf with a chest. Move doesn't work, but Tremor does - the chest drops below. It's not in the left room, but it is in the room down the central hallway. A Ruin Key... I think this is for the door on the right room's staircase that goes down.
-The Ruin Key works, and there's (what I think is) the final secret of the catacombs - a summon tablet! Moloch's power is ours. Time to test the summon out and then retreat out of here.
-...It's kinda ugly-cute, haha. And with that, we're out of the Madra Catacombs! Time to go to the inn and see what's going on there.
-The innkeeper reassures our party that the fish he uses are fine - his thoughts confirm that, luckily. A lady that works in the inn mentions that someone was asking for a weapon - a trident, she clarifies - that 'he' could use to slay a sea monster. Interesting. Pretty sure the fortune teller told Felix that he'd have to find a special weapon to fight a sea enemy with, too. The merchant up in there (and how long are those two staying, anyways? Like - woah) theorizes that an undersea volcano's responsible for the rising temperatures and the tidal wave. We're probably gonna explore it somehow, watch, haha. Seems like that's pretty much it for the dialogue in Madra, though, so I pay for a night and then prepare to leave.
-Oh, shoot, the Cyclone Chip, I nearly forgot about it. Seems like it gives another Field Psynergy (we're running out of inventory spaaaaaaace). I give it to Jenna: she's got quite a bit of PP, so she should have something other than Lash.
-We leave Madra, but someone calls out after us. It's, uh... one man and two purple aliens. Seems like they know Isaac.
-Oh - OH! Vault; that's where we recruited Ivan, right? And we fought bandits that were trying to steal something from Hammet (Hammett?) and his wife (Lady Lanaya or Layana, don't remember). They want to fight - and holy shit the battle themeeeeeeeeeeeeeeeeeeeeeeeeee I'm dying
-It's so good
-Why are the bandits still purple, though. Like, is that their actual skin colour
-Wow, what a throwback. The bandits are down in a couple of turns, and flee. Kraden says something like "Will you stop trying to get your revenge on Isaac?" after they've gone off-screen, which is... something. But they drop Golden Boots, and holy shit do those make your Agility go up the wazoo. After some consideration, I give them to Piers: the Agility boost would be a bit superfluous, and I do like the idea of Felix being a slow and steady healer. Time to get to Piers' boat! ...Where was it again?
-Oh my god, it's a Wild Wolf. I haven't seen them in foreverrrrr!
-Right, found it - East Indra Shore! There's a puddle, which I freeze and use to get to the cliff: there's a Cookie inside the box, nice! Now it's time to get to the boat itself - when we do so, Piers says that we have to get to the energy chamber below. There's nothing in the barrels and nothing in the crow's nest, so might as well follow. The interior's pretty cozy, huh. A Barrel's got an Elixir, but none of the others have anything, so time to proceed.
-...An Aqua Jelly. There's monsters in here? Ooof. The monster goes down in a few hits, and... dissolves into a puddle of water. Interesting. I check down the stairs to make sure I'm not missing anything, but the way is blocked by some crates, so we can't go anywhere else. Piers levels up to 21 after we defeat the second Aqua Jelly and celebrates by solidifying its remains into ice so that we can get a Potion. Going down.
-Holy crap, that's a lot of Aqua Jellies. There's a lot in the adjacent room, too - what in the world happened here? Some more shenanigans ensue, and we manage to get through to the other side and push the crate down in the hallway for a shortcut. Gotta say, though, this has a pretty horrendous layout for an actual ship that people would use.
-More Jellies and some pipes. You know, all this Frost usage is making me wonder where's the equivalent Fire power. Venus has Move and Growth, Jupiter has Whirlwind and Mercury has Frost, but Mars has... nothing. Some fireballs to light tinder up, or an explosion to blow up big rocks? Oooh, or summoning lava. While I'm at it, I clear out some inventory space by giving Felix a Cookie and Piers an Apple. A box has an Antidote - exciting stuff. No other barrels and boxes that I check have anything though, so I freeze the last Aqua Jelly and move on.
-I pass a few rooms and go into the first Aqua Jelly-filled room we saw, the one with the chest. The barrel's got an Oil Drop (Briggs!!!!!).
-...I didn't save before this
-I didn't know there was a boss. Welp.
-All right. Aqua Hydra, bring it on. I start off by using some Djinn to bolster my attack and defense, while reducing the Aqua Hydra's defense as well. The Raging Flood it uses in retaliation nearly one-shot Sheba, but what's new? I really wish I had some multi-target healing Psynergy right now, though. Ugh.
-Well, Sheba and Jenna are dead thanks to Raging Flood spam, and the only revival Djinni I had was Jenna, so it looks like it's The Boys' Time. The hydra thankfully wastes quite a few turns using Triple Chomp against Piers and dealing single-digit damage, and after a few very tense rounds, one final Ramses summon finishes the enemy off. Phewwwwwww.
-...Well, that chest is now underwater. But at least we can now continue!
-We go down into a really weird chamber that doesn't really vibe with the rest of the ship: some Douse usage opens the door. Piers sets the Black Orb... and everything starts shining - and we're sailing! Piers tells Felix to take the tiller, which Google informs me is "a horizontal bar fitted to the head of a boat's rudder post and used for steering". Jenna wants to go to Lalivero, and Tolbi, and Vale - which I definitely wouldn't be opposed to. Gods, having complete and utter freedom must feel very nice for Sheba, Jenna and especially Felix after so long being trapped with Saturos and Menardi. Piers agrees, and Felix too, but Kraden decides to be ~~the rational one~~ a party-pooper. And with that... holy shit, I'm controlling the ship. Or I guess you could say... holy ship!
-I make a quick stop in the beach near Alhafra to revive Sheba and Jenna (you just have to press A next to the beach, I think, which is pretty convenient). A small fee of 820 coins later, and everyone's ready to go - but it's pretty late here, and I think I've gotten quite a bit done today. It's been a lot of fun, and I can't wait to explore the sea and see (heh) what stuff lies in wait for us.
Everyone's Level 21 except Sheba - she's Level 20. We've got 3 Venus, 4 Mars, 4 Jupiter and 5 Mercury Djinn, and Felix is a Knight, Jenna is a Hex (interesting name), Sheba is a Mage and Piers is a Commander. That Aqua Hydra seriously caught me off guard - thank goodness I just about managed to win. Apart from that, though, this session's been more about plot development and exploration than about combat, which isn't necessarily a bad thing. And now that we have a ship... well, I guess we have to find the parts to make the weapon we need, according to the fortune teller, so hopefully I'm able to find some next time I play.

[Spoilers C2E104] Bring out your dead! Speculations on death going into C2E105

Death is one of my favourite parts of Actual Play media, because it's so completely different from death in other shows. It's unplanned. It's a little random, always. And it's as much a surprise to the actor as it is to the audience. And yet, it still packs the thematic punch we associate with a planned and foreshadowed death in a television show or comic. So, in the spirit of morbid fun, I'd like to analyze the likelihood of death for each character going into this week's (probable) boss fight, and speculate on the potential consequences of non-permanent death for each character now.
This is meant to be for fun. I do not actually want any PC to permanently die. I certainly do not want any of them to be replaced. I was trying to pick my favourite M9 member and couldn't because they're all my favourite! But just as death was a major driver of character growth and character relationship growth in C1, it could be a major driver in C2 as well. What would interesting, character-driving death look like at this point in the campaign? Whose story arc would benefit most from a non-permanent death now? Who is actually most in danger during the combat that is to come? Let's investigate:
Veth

Likelihood Rank: ~~Low~~ Medium(edited up to Medium after a good point by u/Syegfryed) . As a ranged rogue, Veth is probably the safest in this combat if she sticks to her usual playstyle. Distance keeps her out of the range of some reflected spells, and high DEX and evasion will keep her safe from the worst of them anyway. She'll be fine.
Consequences: Severe. Veth received a speech from her husband about the importance of not dying right before leaving for this very adventure. Her loyalty to the party has kept her here so far, but might not survive another near-death experience now that her body has been restored. It would be interesting, but as someone who is very fond of Veth, I cannot condone it.

Caduceus

Likelihood Rank: Med-high. Wholly on the basis that Caduceus' run of luck on this island has been just atrocious. If we leave the Gambler's Fallacy aside, he's probably a Low risk, since he acts at distance and has high WIS.
Consequences: Interesting. Caduceus has been having a bad time on this island, but it's all been a mechanical bad time, rather than a character bad time. In his character arc, though, he's in a weird place. The last 'quest' for him has ended, but it's not entirely clear what the next one will be. Last time he died he got a vision that pointed him in the direction of a really interesting arc - perhaps that's what would happen again.

Jester

Likelihood Rank: Med-Low. Jester, an offensive spellcaster, will likely take a backseat here. Morkoth spell-reflection has that effect on people. So she'll likely be out of the line of fire. Add in her high WIS and she's pretty safe.
Consequences: Extremely Interesting. Though she's fairly safe, probability has its little quirks sometimes. If she did die, the consequences for her would be huge. It would magnify the degree to which she feels the Traveler has betrayed her by sending her here immensely. Would massively alter the tone of Travelercon. Jester is already worried that the Traveler might not care as much about her well-being as he says, per their last conversation. If she died against Vokodo, that would only cement the worry.

Beau

Likelihood Rank: Medium. This fight will be very melee-heavy, and Beau is the most delicate of the melee fighters. Good WIS makes her less susceptible to mind-control, though.
Consequences: Not quite interesting yet? Beau is also at an interesting turning point in her arc, as her recent playlist implies. She's still recovering from the disastrous interaction with her family and the hag, and struggling to maintain a sense of self-worth. She really is willing to sacrifice herself for the party, and that could be very interesting in this context. But she's also dealing with having feelings for two people at once (probably?). Death can help to clarify complicated feelings, but I think both of these threads could stand to be closer to resolution before a death puts them into hard focus. Beau's is a really interesting arc, but my intuition is that it's not quite cooked yet.

Caleb

Likelihood Rank: Medium-Low. Lowest WIS of the pure spellcasters, but voted 'Most Likely to Disintegrate Himself' by Exandria Magazine 2020. Spellcasters are safer than melee in this fight, but depending on how Matt handles Vokodo's targeting of the spell reflection, he's definitely the most likely to accidentally Disintegrate himself.
Consequences: Low-ish. Caleb's arc right now is not in a period of high tension. The high tension was about 20 episodes ago, during the Rexxentrum sequence. Caleb has a pretty solid sense of why he's doing this (to help Jester) and has much less complicated feelings about the Traveler than the rest of the party. His reaction to a lot of stuff on this island has been much simpler for that reason. He clearly doesn't like it, but it doesn't strongly connect to anything he cares about beyond the way it connects to the party.

Yasha

Likelihood Rank: Low. Tanks ftw. Could be mind controlled, though. All Yasha deaths are likely to be non-permanent. But it's also not the sort of thing that would happen easily to begin with.
Consequences: Interesting. Yasha has been behaving in a distinctly self-sacrificing way since returning to the party. This is a natural consequence of her story so far, of course. The party have had ample hints that she doesn't think highly of her life compared to others (cf. the pit fight) but have yet to really confront that. If Yasha died here, it would be an interesting call to action for the rest of the party. Beau is dealing with at least some amount of feelings for Yasha, and Caleb and Yasha have recently had some interesting heart-to-hearts. I think Yasha non-perma-dying would be an interesting catalyst for more of her group dynamic.

Fjord

Likelihood Rank: Medium. Low WIS plus melee equals a bad time with a Morkoth, but he's sturdier than Beau. And a mind-controlled paladin is mostly a peril to his friends, not himself. Look forward to that!
Consequences: Probably Not Interesting. Fjord died 5 episodes ago! What would be added that wasn't added then? Admittedly, we didn't get a lot of conversation coming off that death, since pandemic interrupted the natural flow of things, but it's hard to see how dying at Vokodo's ~~hands~~ tentacles would be more story-relevant for Fjord than death-by-Ukatoa. I do think we're owed a bit of a resolution to Fjord's earlier death, though, since the peace talks brushed that plot point away very quickly. Jester and Caduceus clearly have some Serious Thoughts on the matter, given how they acted. But there's no reason, at this point, to think it would be different.

If you like this analysis, let me know, and I'll post more like it before boss fights. I find it interesting to piece through things like this. Hopefully others do too!

Lucky Friends Rules/Bug?

Ultimate Gambling Guide for GTA Online - odds, probabilities, and optimal strategies

Since the Diamond Casino update, I have seen a large number of 12-year-olds posting Blackjack memes on this sub. As a parent, this has me very worried.
On top of that, I have seen some of the most trustworthy GTA Youtubers giving flawed gambling advice, which can have damaging impact on their gullible audiences.
So that's why I decided to write this up, to educate everyone on the subject, so there will be no more misunderstandings.
(2020 Update down at the bottom.)
If you're one of those Youtubers that wants to use this information in a video, feel free to do so. The more people (especially kids) that become educated about gambling, the better.
But then also please go back and review your own work, and delete or edit the videos that are giving out the wrong advice, like where you're saying you have "a good strategy for making money with roulette", or some other nonsense that I've heard this week. Delete that please.
Before I get into the individual games, I need to discuss a few concepts first, that will make understanding the rest a lot easier.

Expected return and variance
A game like Roulette or Slots has a fixed expected return on your bets. This is a percentage that you have no way of influencing. Say you are flipping a coin against a friend, and you both put up $1. The winner gets the pot. Since the odds are even at 50%, in the long run, you will expect to break even. Your expected return is 100% of your bet.
But imagine if you would play this coin flipping game in a casino against the house. On the "house rules" listed at the table they would probably say that you would only get 95 cents back for every win, while you are forfeiting a dollar on every loss. Would you still play?
Sounds stupid to do so, but still, everybody does it. Every bet they place on Roulette, every coin they put into a Slot machine, is based on the same concept.
Those few cents they take on every bet are their profit margin, and has paid for all the Vegas lights, the Mirage volcanoes, and the Bellagio fountains. Make no mistake - casino gambling games are not designed to make you lose, because sure, you can get lucky on a single night, but they are designed to make them win. That's the beauty of it. They can both exist at the same time.
Too many people that don't see how this works, are just destined for disaster. Just because you went on a lucky streak and won 8 games out of 10, does not mean that flipping coins is a profitable game, or that choosing tails is a winning strategy. Always be aware of the house edge, your true chances of winning, and just realize that you got lucky. There is no such thing as a strategy in flipping a coin that will give you a higher expected return, so it's just pure gambling, just like Slots and Roulette.
Most casino games are made in such a way, that your expected return is a little under 100%. This means that from every dollar bet at the tables, the casino expects to keep a few cents. For individual players, results may vary. Some will win, most will lose. But for the house, it doesn't matter. They take millions of bets each day, so for them, the expected average works out a lot sooner. In short: the house always wins.
When looking at the house edge, we're talking about the expected long-term result, based on the game's house rules. But for a player, it can take literally tens of thousands of hands or spins before you also reach this average number. Until that time, you can experience huge upswings and downswings, that are the result of nothing but short-term luck, which is called variance.
Some games and some bets have a much higher variance than others, which means your actual results will differ enormously from what you're expected to be at.
Take for example betting on red/black at the Roulette table. This is a low-variance proposition, because it has a high percentage chance of occurring, and a low payout.
Contrast this with betting single numbers in Roulette, which only win once every 38 spins on average. This bet has a much higher variance, meaning you can easily hit a dry spell, and not hit anything for 200 bets in a row, or you can see a single number hit three times in five consecutive spins. This is not a freak occurrence in high-variance bets.
Even though the expected return in both these bets is exactly the same, there's a huge difference in variance, causing massive differences in short-term results, which can go both ways. You need to be aware of this, before you decide what types of bets you are comfortable with placing.

Gamblers' Fallacy
Another thing to realize, is that each individual game, hand, or spin, is completely independent from the one(s) before it, and after it.
Gamblers tend to believe, that the chance of a certain outcome is increased, based on previous results.
The most famous example comes from the Casino de Monte Carlo, where the Roulette wheel managed to land on black 26 times in a row. Gamblers lost many millions during that streak, all frantically betting on red, believing that the odds were in favor of the wheel coming out on red, after producing so many blacks. This is not true. Each round is completely independent, and the odds are exactly the same.
You will hear people say things like a Blackjack table being "hot" or "cold", which is completely superstitious, and should be ignored. The exception was when Blackjack was being dealt from a shoe. It made card counting possible. But with the introduction of shuffle machines, and continuous shuffling like is being used in GTA, this no longer exists.
This is also why "chasing your losses" is a very bad idea. After being on a losing streak for some time, many gamblers believe that now it's their turn to start winning. So they will often increase their bet size, believing that when their predicted winning streak comes around, they will win back their losses, and more.
The reality of it, more often than not, is that people will indeed start playing higher and higher limits, until they are completely broke. Nobody is ever "due for a win". There is never a guarantee that you're about to start winning. In fact, the opposite is more likely to be true. You are, after all, in a casino.

Betting systems
Some people like to think that they have a fool-proof betting system, like the Martingale system. Simply increase or even double your bet when you lose, and keep doing that until you win. In theory, this system will always win. So that's why table limits were introduced, and where the system fails.
If you start at the Roulette table, playing red/black, with a small 750 chip wager, and just double your bet every time you lose, you only have to lose 6 times in a row, before you will be betting the table limit of 48,000, just to get that 750 chip profit.
Sure, you can go on all evening without this happening, winning 750 chips each time, but this losing streak only has to happen once, and you're bust. Any betting system like this is ill-advised, because you are hugely increasing your so-called "risk of ruin", and that's what we were trying to avoid.
And even if your starting bet is only 100 chips, after only nine straight losses, and nine doubled bets, you are betting the table limit at 50,000 chips. If you lose that bet, you're 100,000 chips in the hole, with no way to recover that with your 100 chip base wager.
So don't believe anyone that says this is the perfect system to always win in the casino. Sooner or later they will understand why they were wrong, when they're asking you for a loan.

Set your limits BEFORE you start playing
One final point before we get into the games, a general tip for people that head out to play: money management.
Just like in real life, before you go to the casino, decide on a maximum amount that you are WILLING TO LOSE.
Bet small enough, so that amount can last you through the entire evening, and you will not be tempted to run to the ATM to continue playing.
Considering GTA money, some people will be comfortable losing 1% of their GTA bank balance, some people will be comfortable with gambling away 5% of their total GTA savings. It's up to you what you can handle. Decide for yourself where it will start to hurt, and don't cross that line.
But whatever number you decide on, as soon as you lost that amount, get up and walk away. Don't chase your losses, stick to your limits, and accept that this has not been your day. There is always another game tomorrow. Always agree with yourself on a simple stop-loss rule, how much you would want to lose at most, and simply stop playing when you get there.
Same goes for winning. You can decide on a number, how much profit you would like to take away from the casino. You can go on a hot streak and be up half a million in a short period of time, but if you would continue to play longer, looking for more, chances are that you're going to lose it all back.
Most people are happy with doubling their daily casino budget, for example. Others are looking for 10 bets profit in Blackjack. Whatever you choose, when you hit that number, you can stop playing and bank your profits, or you can continue playing if you're still enjoying the games, but then only just play minimum bet sizes. Then you're just playing for fun, not for money. You've already made your profit, so simply keep it in your pocket, and don't risk losing it again.
Either way, decide on what your money management strategy will be, and STICK TO IT.

Casino games in GTA Online
Now, I'm going to dive into the games that you can find at the Diamond casino, ordered from worst to best.

6) Slots
Generally the rule is this: the less strategy a game has, the worse it is for the player. And with slots, this is definitely the case.
The only influence you have, is choosing what type of machine you're going to play. Basically, there are two types of slot machines:
-high frequency, low payout slots
-low frequency, high payout slots
In the first type, there is no huge (progressive) jackpot on offer, just your average selection of prizes that don't go up to crazy amounts.
This will result in a player having many more spins resulting in a win. The amounts that you win on the bigger prizes, will be smaller, but they do come around more often. This type of slot machine has a lower variance, which means that your money should last you longer, winning many smaller prizes along the way to keep you going.
The second type of slot machine lures you in with the temptation of a huge jackpot prize. Even though the long-term expected return on these machines is the same as the previous type, the prize distribution is hugely different. The large jackpot prize weighs heavily on the scale of expected return, but the chance of it hitting is extremely small. This results in a much higher variance on this type of machine. Usually your money will go down very fast, because the smaller prizes are less rewarding than on the other type of machine.
At the Diamond, the info screen says the player return at slots is set at 98.7%. This means that, on average, for every maximum bet of 2,500 chips, you expect to lose 32.5 chips.
This might not seem like a lot, but the danger of slots is that the game is extremely fast. You can spin about once every 6 seconds, which would result in an expected LOSS of about 20,000 chips per hour of playing.
But again, in this long-term expected number, the large jackpot awards are also factored in, and as long as you don't hit those big prizes, you'll see your money go down a lot faster.
In any case, thank heavens the max bet is only set at 2,500, or else we would see more players go bankrupt at alarming rates.
Optimal strategy for slots:
There is none. Because after betting, you have no more influence over the outcome. The only choices you have, is what type of machine you want to play at, and how much money you are going to risk. And those are all personal preference. As long as you stick to your loss limits, as discussed above, there's no harm in having a go every once in a while, hoping to get a lucky hit. Just realize that you don't have a high chance of scoring a big win, so as soon as you do, get up and walk away.

5) Roulette
Roulette is also a game where you have no influence over the outcome. There is zero skill involved. You place your bet, and that's it.
In traditional French roulette, a table has only the single-zero, but of course, for American casinos that wasn't enough of a house edge, so they simply doubled their profits by adding a second zero. The house edge was increased from 1/37 to 1/19, which is huge.
This makes playing on a double-zero roulette table by definition a sucker's play.
The payouts scale evenly, which means that a bet on a single number, and a bet on half of the numbers, and everything in between, yields the same expected return. The only difference, again, being the variance that you are willing to subject yourself to.
The player return for double-zero Roulette for all bets is 94.74%.
Except for the 5-number bet, which can only be made by placing a bet on the two top rows that contain 0, 00, 1, 2 and 3. The expected return on this bet is lower: 92.1%. This is because it only pays out 6-1. Why? Well, the number 36 isn't divisible by 5, so the greedy people that came up with double-zero Roulette had to round it off someway, and as expected, it wasn't going to be in the players' favor.Just remember that that 5-number bet is the worst bet at the table, and should be avoided. All other possible bets have the same expected return.
So it really doesn't matter how you spread your bets, if you bet only one chip, or if you litter the entire table with a bucketload of chips. Each chip you put out there, has the same expected return, so there is no strategy that will improve your long-term results.
Assuming that you're betting the maximum table amount of 50,000 chips, you will be looking at an expected loss of about 2,630 chips per spin. Considering that a round takes about 45 seconds to complete, your expected LOSS at the GTA Roulette tables will be around 200,000 chips per hour of playing.
Optimal strategy for double-zero roulette:
Stay away. Stay far away.

4) Three Card Poker
With Three Card Poker, we come across the first game where there is actually some strategy involved. You get to look at your cards, and then decide if you want to fold, and surrender your ante, or double your bet.
Additionally, you can choose to place a side bet on "Pair Plus", which offers progressive payouts.
There are some websites out there that ran all the numbers with computer simulations, and even though I would like to quote the source here, these websites are understandably littered to the max with online casino ads, so that's why I have decided against doing that.
Optimal strategy for Three Card Poker:
For this game you only have to remember one strategy rule: Always bet on any high card queen-six-four or better, and fold any high card queen-six-three or lower. That's it. Just don't forget to double check if you're not folding a straight or a flush, and you'll be fine.
This strategy will result in an expected return of 96.63%.
The Pair Plus sidebet, with the payout table that is used at the Diamond casino, gives you an expected return of 97.68%, which is actually a bit better than the main ante bet.
So by playing both wagers, you're reducing your expected losses per bet, but since you're betting more, you're also increasing your expected loss per hour.
My advice would obviously be to not play this game at all, but if you do, put as much of your bet as possible on the Pair Plus, while making our Ante bet as small as you can.
To be able to compare it to the other games at the Diamond, let's stay on that 50,000 maximum wager, meaning making your ante bet 35,000, and your pair plus bet 15,000, if the table would allow it.
This results in an expected loss of about 1,525 chips per hand, and with a round taking about 45 seconds, this adds up to an expected LOSS of around 120,000 chips per hour of playing. In comparison, if you would only play the ante bet for 50,000 per hand, you expect to lose 1,685 chips per hand, which means an expected LOSS of about 135,000 chips per hour. So the more out of that 50,000 wager you can put on the "Pair Plus" sidebet, the better.
Even though it may be fun to try out this game for a bit, since there's only one simple strategy rule to follow, you'll soon find yourself robotically grinding down your bankroll until it has vaporized. You're not missing out on anything if you skip these tables, there is no real challenge.
Just like with Roulette and Slots, if you want to try it out nonetheless, you can just bet the minimum amounts and only play for fun, so it won't matter if you win or lose.

3) Blackjack
Blackjack is the most complicated game by far. Simply because the player has to make a series of decisions, which will largely decide the outcome. Luckily, there is such a thing as an optimal strategy, which will be outlined below.
However, the strategy is also dependent on the house rules. These not only affect your expected return, but in some places also your decisions.
Here are the house rules at the Diamond casino:
-The game uses 4 standard decks, and a continuous shuffle.
-Blackjack pays 3 to 2, dealer checks for early blackjack.
-No insurance offered, no surrender.
-Dealer stands on soft 17.
-Double down on any two cards.
-Player can split only once, but doubling after split is allowed.
-Seven-Card Charlie.
Under these rules, and following the "basic strategy" chart, your expected return at Blackjack is a shade under 99.6%, which is extremely good for a casino game, that's why Blackjack should be your table game of choice.
But it comes at a price: you are going to have to memorize the relatively complicated strategy chart, or at least stick it to your monitor until you have it in your head. But in case you ever stumble into a real-life casino, you won't regret having this table memorized, so I would definitely advise you to work on that.
The strategy chart might look complicated at first, but you will be able to notice certain patterns. Your decisions are mainly based on the dealer's upcard, which is basically divided into a weak card (2 to 6), and a strong card (7 to ace).
When a dealer shows a strong card, you will be hitting more often with the risk of going bust, but when a dealer shows a weak card, you're not taking that risk, and you will be standing more, but also doubling and splitting more. You want to increase your bets when the odds are in your favor, and get out cheap when they're not.
But it also helps to take some time to think about why a certain advice is given. For example, why does it say that you always have to split two eights, even against an ace. Well, that's because two eights equals 16, which is the worst total you can have. It's better to split them up, and give yourself a chance of finding a 17, 18 or 19 with the next card. Once you see the logic in that, you'll have one less thing to memorize.
The playing advice in the basic strategy chart is a result of computer simulations that ran all possible outcomes against each other, and produced the most profitable decision for each situation. So you can't go wrong following it.
Optimal strategy for Blackjack with Seven-Card Charlie
The added house rule of Seven-Card Charlie, adds a small advantage for the player, and it does influence a few strategy decisions. For example, you might have a 14 with 6 cards, against the dealer's 5 upcard.
Normally this would be an automatic stand, but if you're only one card away from the Seven-Card Charlie, meaning an instant win for the player, regardless of the dealer's hand, it turns it into a hit.
Here's the most optimal strategy chart to follow for the Diamond Casino house rules: https://prnt.sc/olct6g
You'll see that two fives are missing from the chart, and that's because you never split them. You treat them as a regular 10. You also never split tens. Just stand on 20.
If you follow this strategy religiously, even with a maximum wager of 50,000 chips, you only expect to lose about 215 chips per hand, and with rounds taking about 30 seconds, that amounts to an expected LOSS of 26,000 chips per hour, which is only half a bet. A small price to pay for an hour of entertainment.
But since the expected return is so extremely close to 100%, you will see more positive short-term results than with other games. But obviously it can also swing the other way. Again, this is supposed to be the game where your money lasts you the longest, but always set your loss and win limits before you sit down. That rule simply always applies.

Still, even with optimal strategies applied, all these games are expected to lose you money in the long run. So betting any kind of large amounts is not advised. If you simply want to enjoy playing these games, there's nothing wrong with betting a minimal amount. Playing these games for a longer period of time will already cost you money anyway, since your daily property fees will still be charged while you're playing in the GTA casino. As long as you can play for fun, there's nothing wrong, but when you see yourself betting insane chunks of your entire bank balance to try to recoup some unfortunate losses, you're doing it wrong.
As the commercials in Britain all correctly say: when the fun stops, stop.

2) Virtual Horse Racing
Now onto the good stuff. I ran some numbers, and I believe Rockstar has made a mistake with the horse racing game. Because as it stands, and if I read the numbers correctly, this game is actually profitable for the player. You can actually make money with this, at least, until Rockstar figures out their mistake and patches it.
If anyone wants to jump into the math and double check this to make sure, please do so. I will add any corrections to this post. This is one of those "to good to be true" things, so I keep thinking that I might have overlooked something. So please verify it if you can.
The setup is this. There is a pool of 100 horses, each with their own attached payout. These are divided into 3 groups, ranked by their odds. From each group, 2 horses are randomly selected to provide a pool of six runners for you to bet on.
Now it's not an actual race you're looking at. You are looking at a raffle. This is important to realize.
Each horse gets awarded a certain number of raffle tickets. The favorites get awarded more tickets than the underdogs, and therefore, have a higher chance of winning.
If this distribution works like it does in the real-life casinos, then the raffle tickets are awarded according to the betting odds.
Example 1: imagine a race with 3 runners, all have 2/1 odds, representing a 33.3% chance of winning. (Because 2/1 means 2 AGAINST 1, so 3 total.) In this case, each horse gets one third of the raffle tickets, giving them an equal chance to win.
Example 2: imagine a race with 3 runners, one has 1/1 odds (or EVENS), representing a 50% chance of winning, and the other two horses are marked up as 3/1, with a 25% chance of winning. The favorite gets half the tickets, the other two get a quarter of the tickets each.
A ticket is drawn, and you'll have a winner.
It doesn't matter in this game which horse you bet on, because the expected return is always the same: 100% or break-even, for the above examples.
Now, what happens if the percentages don't exactly add up to 100%?
They must add up to 100%, because there will always be a winner. And only one winner.
So when this is the case, the actual winning chances of the horses are adjusted to meet the 100% requirement, using their payout odds to determine the scale.
So, if the represented percentages add up to more than 100%, the actual winning chances of the runners will be DECREASED, resulting in all bets becoming losing propositions for the players.
Example: In a 6-horse race, all runners are listed at 4/1, representing a 20% chance. Only with six runners that amounts to 120%. So all chances are scaled down by 1/6th, to end up at 100%.
This means your horse's chances are reduced from 20% to 16.67%, turning it into a losing bet: 5 times you will lose your bet, and 1 time you will win, but only get 4 bets back in this instance, instead of 5. A losing bet in the long run.
This is the type of odds that you find in regular casinos, with fields as large as 15 runners to bet on, where the assumed winning chances always add up to more than 100%, therefore are decreased for all runners, resulting in a house edge.

But in GTA Online's Inside Track, there are other scenarios, because of the small field, and the way that they are put together.
In some cases, the represented percentages when added up, are LESS than 100%, meaning that the actual winning chances of all runners, are INCREASED.
This creates profitable bets for the players, because in the long run, you're expecting to win more money than you lose. This is a gambler's dream, pure and simple.
So, according to the in-game information, the three groups of horses are divided as follows:
-Favorites: EVENS to 5-1
-Outsiders: 6-1 to 15-1
-Underdogs: 16-1 to 30-1

Let's take the two most extreme examples to show what's happening.
The worst possible field to bet on: two runners at EVENS, two runners at 6-1, and two runners at 16-1.
EVENS represents a 50% chance, 6-1 is 14.29%, and 16-1 is 5.88%. Add those up and you land on a total of 140.34%.
This means that the actual winning chances of the horses are decreased by 28.75% (to get that 140% down to 100%), which makes betting on this field extremely unwise.
A horse at EVENS will only come in as a winner 35.63% of the time, instead of 50%,
a horse at 6-1 will only win 10.18% of the time,
and an underdog at 16-1 will only win 4.19% of the time.

The expected return on a bet on any of the horses in this field is only 71.26%, so a maximum bet of 10,000 chips on any of these horses holds an expected LOSS of 2,875 chips.
These returns are the same, because the winning chances are scaled equally, according to the payout numbers. So it really doesn't matter which horse you bet on, in the long run, you expect the same results.
But as explained before, it does influence variance, and therefore your short-term result, which can swing both ways.

But now, the best possible field to bet on: two runners at 5-1, two runners at 15-1, and two runners at 30-1.
Odds at 5-1 represents a winning chance of 16.67%, 15-1 odds means 6.25% chance, and 30-1 odds means a 3.23% chance of winning. Add these six horses together, and you only get 52.285%.
This means that, to get from 52% to 100%, the actual winning chances of these horses will be almost doubled! Multiplied by 1.91 to be exact.
So the 5-1 favorites will now win 31.88% of the time, instead of 16.67%,
the 15-1 runners will win 11.95% of the time,
and the underdogs at 30-1 odds will still win 6.17% of the time.
When betting on this field, the expected return on your bet is 191.25%!
This means that a max bet of 10,000 chips will result in an expected PROFIT of 9,125 chips.
This is printing money, if there ever was such a thing.
Optimal strategy for Virtual Horse racing
So all you have to do, is only bet high on the games where you have an expected positive return, and bet the absolute minimum on the games where your expected return is negative. Or back out of the racing game to refresh the field.
If you don't have a way to quickly add up all the percentages, and until somebody shows up here with a neatly formatted table, just use a few general rules of thumb:
-Always bet the maximum on a race with favorites at 2/1 and 3/1 or higher in it.
-Simply skip all races with two favorites at EVENS in it, and at EVENS and 2/1. Or bet the minimum, if you can't skip or refresh the field.
-To decide if you should play races with other favorite combinations EVENS and 3/1, EVENS and 4/1, EVENS and 5/1, or two favorites at 2/1, the payouts on the other four runners determine whether or not it's profitable to play them. The results of betting on these fields vary from an expected 1,330 chip loss (worst-case) to an expected 1,680 chip win (best-case), with a max bet of 10,000 chips.
But if you're not looking for another strategy chart, you might just want to skip these borderline cases, and just cherry pick the best ones, which are easy to recognize, and with which you can never go wrong.
It's difficult to put a number on an expected win-rate, because it all depends on which fields you get presented with, but it's not unreasonable to state that you can maintain a steady win-rate of around 200,000 chips per hour, with about 50 seconds per race.
Remember, you're not trying to win every race. You're trying to win the most money per hour. So don't sweat it when you bet on a 4/1 favorite, and lose a couple of races in a row. It will still be more profitable in the long run. You have the math on your side.
To reduce negative variance, always bet on the favorite, when betting on profitable fields. We're not gambling anymore, we're grinding out a steady profit. We want to keep the swings to a minimum.
I contacted Rockstar support to verify if this is indeed how it works, but the only reply I got after 6 weeks is that they were "looking into it".
User u/Garsant made a useful Excel-worksheet, available for you to download, where you can quickly type in the payouts on the horses, to see if it produces a profitable bet or not. You can find it in his post here: https://www.reddit.com/gtaonline/comments/ekp8na/gta_online_inside_track_odd_calculato

1) Wheel of Fortune
The number one profitable casino game in GTA Online is obviously the Wheel of Fortune, because it costs you nothing to play.
Unfortunately, you only get one free spin per day, but it holds great value, so make sure you do it.
With a chance to win a super car, vehicle discounts, expensive mystery prizes (which also can be vehicles), and a lot of cash and chips, the expected return on a single spin is around $100,000 in value.
So don't forget your daily spin, it's definitely worth your time.

2020 Update:
As of the Diamond Casino Heist update, the Inside Track horse racing is confirmed to still be as profitable as outlined above.The only thing that seems to be changed, is that you can't refresh the field anymore by backing out of the screen. This does affect your hourly rate in a negative way, but does not change the fact that this game has a huge positive expected return, and should be your go-to when you're trying to take money from the house, without having Lester's nagging voice in your ear. That should also be worth something.

And with that, I conclude my 5,000 word essay on gambling in GTA. Questions, comments, feel free to add your input to this guide.

Cliffs:
-Gambling games should only be played for fun, not for big money. You should expect to lose in the long run. The house always wins.
-A casino game doesn't have a memory, and betting systems don't work.
-Set your limits before you start, how much you are willing to lose or win, and then walk away when you get there.
-Don't play slots, roulette, or three card poker.
-Only play blackjack following a basic strategy chart (https://prnt.sc/olct6g).
-Inside Track betting can be played profitably, if you only bet on fields WITHOUT a heavy favorite.
-Wheel of Fortune is always your best bet, because it's a free bet.

The probability of rolling for multiple units, and a look at the midseason roll % changes

In a previous post I used a simulation to determine the probabilities of rolling for single units. Afterwards, DeepDiveLM made me aware of a far smarter approach using Markov chains that they use in their interactive calculator. The Markov chain allows one to directly calculate the probabilities without needing to simulate games, and it's much faster. Ever since, I've been puzzling over how to do something similar with rolling for multiple units. I have a working implementation now and I wanted to share it with everyone.
You can find the exact code I used to generate every graph in this post here. Some of them take a while to run, so it might time out on repl.it, but you can comment out the slow ones (Mech and Shredder) at the bottom. Maybe some day I can turn this into an interactive version for non-coders. Until then, if someone wants to take this and do it themselves, go right ahead.
THE MATH CONCEPT AND CODE, SKIP BELOW IF YOU DON'T CARE
A Markov chain describes the probability of a system changing states, assuming the probability of the future state depends only on the current state. In TFT's case, that perfectly describes the unit shops, where "state" refers to the numbers of each unit owned. The probability of finding a specific unit in a shop slot is calculated from the number of available units and the total pool, combined with the probabilities of finding the unit tier at a given player level. The probability has nothing to do with how many times we've rolled up until now, and all that matters is the current state (don't fall victim to the gambler's fallacy!).
Markov chains can be described mathematically using matrices. In TFT's case the index (i, j) (the notation for row, column) represents the probability of going from i units to j units. If we are are considering just one shop slot, then we only have to consider the probabilities of staying at the current number of a unit (i, i) and the probability of finding one unit (i, i + 1). Since we either find the unit or we don't, those two matrix values must sum to 1. We can also fill out the matrix to find i + 2 units, by filling out the matrix indices (i + 1, i + 1) and (i + 1, i + 2), and so on until we have accounted for the number of a unit we are looking for.
That matrix gives us the probability of finding a specific unit in a single shop slot. Thanks to the properties of matrix multiplication, the Nth power of that matrix gives us the probability of finding a unit in N shop slots. For example, if we want to see 3 shops, then we raise our matrix to the power of 15. Afterwards, (i, j) describes the probability of going from i units to j units. And that's about it. Some addition, division, and a matrix power are all that's needed to exactly calculate TFT roll probabilities for one unit, accurately accounting for the existing pool and the the lessening probability of finding each successive unit.
Ok great, but how do we handle rolling for multiple units? As a simple approximation, we could determine the probability of finding each unit separately, then ask what is the probability finding at least one or all. While that's a pretty good approximation, the odds of finding all of the units are ever so slightly higher than this would suggest, because buying up one unit can improve the odds of finding the others (if they are the same tier). The key to a more accurate calculation is realizing (i, j) refers to the abstract concept of going from state i to state j. There's no reason that i and j need to refer to the same unit. They could refer to different combinations of units. So, we expand our matrix to encompass every combination of the units we are looking for. If we want to find 3 of one unit and 3 of another, now we need a 12x12 matrix, where each index represents a different unit combination (0 + 0, 0 + 1, 0 + 2, 0 + 3, 1 + 0, 1 + 1, 1 + 2, 1 + 3, 2 + 0, etc...). The matrix must also be filled out for the odds of going from one combination of unit numbers to +1 of every unit. If we want to find 3 of 3 different units, that's a 64x64 matrix. It does get a little crazy if we aren't careful (I don't have 300 GB of RAM lying around to calculate rolling for nine 3* units), but it works well enough for the interesting TFT cases.
After taking the power of the matrix, the matrix contains the probability of finding every different combination of units. We can query the indices representing all of the combinations of at least 1 unit, or requiring 1 specific unit and finding 2 of 3 others, etc. The probabilities are "disjoint" (ie, mutually exclusive, as we can't have both 1 and 2 of the same unit) and so the final probability is the sum of these cases. (A thanks to zyonsis for helping me think through this part!)
END MATH, BEGIN DATA
Some caveats to these graphs:

I have not accounted for Mercenary upgrades taking the place of units.
I also have not accounted for bench space.
In game, it's impossible to know what units are in someone's shop, so there might be more of a unit removed from the pool than you realize.
Don't forget that you need money to buy all of these units. The probabilities are only part of a much larger story.

As before, to give you a sense of the variance between games, most of my graphs show the probability distribution and not the cumulative probability.
CASE 1: HYPERROLLING 1-COST UNITS (e.g. Shredder)
Shredder got nerfed while I was making this, so maybe this is a historical footnote now, but the takeaways are useful for future hyperroll comps.
Here I have calculated the probabilities of finding 3* 1-costs while purchasing four different units (Xayah, Jarvan, Fiora, Caitlyn), contingent on finding 3* Xayah. For good measure, we take into account some parameters for a good scenario that pushes us towards Shredder:

We have 3 each of Jarvan, Fiora, Caitlyn already. There are also another 3 of each taken.
We have 5 of Xayah which is why we're rolling for this comp in the first place
Everyone likes Xayah so another 6 are gone (plus the 5 we own)
60 other 1-cost units are taken out of the pool (roughly 2 2* units per player, plus whatever's hiding in shops)

Surprising result: If you are rolling for a comp that requires a specific 3* unit, the odds of finding that unit and more are almost identical (assuming, of course, that you can afford everything). The consistency of finding that one unit is low: finding 4 Xayahs in this case will require >46 gold worth of shops in 75% of your games! But regardless of when you roll, you'll find 3* and 0 to 2 other 3* units with almost equal probabilities. The takeaway here is always roll for multiple 3* units if you can afford it. Leveling to 5 will generally require 10-20 additional shops to hit your 1-cost units (20-40 gold).
CASE 2: THE MECH
Again I've been foiled, since I set this up contingent on Kai'Sa who will be removed from the game in 2 weeks. I hope it is useful nonetheless.
What are the odds of finding a win condition of 3* Kai'Sa + a level 7 or level 8 Mech? Here I assume we are uncontested (no holding hands during quarantine, please). There are 30 other 2-costs, 15 3-costs, and 8 4-costs already taken. We start with 3 Kai'Sa, 3 Annie, 3 Rumble, and 1 Fizz (here we only 2* the fish).
Getting 3* Kai'Sa and level 8 mech is difficult, requiring up to 66 shops in 75% of your games at level 6. What really struck me is that the difference between level 7 and level 6 is pretty small. For the level 7 mech, the difference is only 3-9 shops. Of course, this doesn't consider that staying at 6 will get you the Kai'Sa sooner, but if you need an immediate power spike then leveling to 7 is hardly detrimental for finishing the mech. Rolling at 8 is doomed though.
CASE 3: FINDING A 4-COST CARRY
Suppose you have 1 each of 3 different 4-costs. Can you find a 2*? For simplicity, we're assuming the entire pool is available.
If you roll for 3 different units, you are almost twice as likely to hit at least one than if you tunneled for a specific unit. That means, even at level 6, you can reasonably hit a 2* 4-cost by rolling down 50 gold (assuming you start with 1 of each). At level 7, you will hit one in almost 75% of your games, even taking into account the money you need to buy the units.
CASE 3b: TUNNEL VISION ON A 4-COST CARRY
How often will we miss an alternative 2* 4-cost if we tunnel on the unit we already have 1 of? This graph is different from the previous ones. It shows the probability of finding 3 of another specific 4-cost and not finding 2 of the unit you were rolling for (at level 8). If you roll down 40 gold worth of shops, you have a ~25% chance of missing another specific 2* 4-cost when you started with 0 (and now consider there are 10 4-costs in the midseason update!). For consistent results, you should definitely look out for pivots while you roll because there's a very good chance of another opportunity presenting itself. You will probably pass by 3 of another 4-cost before you find 2 of one you are looking for.
CASE 4: FINISHING A COMP AT LEVEL 8 VS LEVEL 9
Suppose we have 2 of a 4-cost carry. To finish our comp, we want to get it to 2* and find one or two specific legendary units. Should we level to 9 or roll at 8?
For an easier comparison between level 8 and 9, here I'm showing the cumulative probability instead of the distribution (top graphs). Looking for both legendaries more than doubles the number of shops we need to hit. Plotting shop equivalences in terms of probabilities (bottom) gives a better picture of whether we should level or roll. With legendary units in the picture, a level 9 shop is worth 2-2.5 level 8 shops. So, if leveling to 9 leaves you with at least 1/3 of the gold you would spend rolling (don't forget about the cost of buying the units), you will have better odds at level 9.
THE MIDSEASON UPDATE
[edit] COMMENT PER Riot_Mort HIMSELF: Only the level 4 changes are shipping. You can disregard most of this, but I'll leave it up.
The midseason update is adding 1 unit of each tier. To compensate, Riot changed the shop percentages at each level. Let's compare the before and after. (Assuming 0 units removed from the pool, as we just want a sense of the before-and-after.)
1-cost: At levels 4 and 5, the changes will be hardly perceptible for a 2* unit, but hyperrolling for a 3* is significantly worse. This will probably put the final nail in the coffin for hyperrolling unless a new 3* 1-cost emerges as grotesquely overpowered. Even if it does, slow rolling at 5 will almost certainly better. The roll changes SERIOUSLY HURT your chances for upgrading a 1-cost at level 6 and 7. I'm not sure I like this change, since it makes it hard to pivot into comps that require 1-cost units (looking at you, Cybernetics).
2-cost: The changes do their stated job. The odds are about as close to identical as they can get with the extra units.
3-cost: Hitting 3* is a little easier at level 7 and quite a bit harder at level 8. Maybe we will see the return of slow rolling at 7 for 3* 3-costs. What I really don't like is the distribution changes at level 4. We will see a lot more people highrolling a 2* 3-cost before Krugs, especially on the reroll galaxy. Bear in mind the probability can be misleading because the axes are all normalized. For a less biased view, here are the cumulative probabilities. The probability of going from 1 to 3 of a 3-cost has gone from 5.6% to 9.9% in 10 shops, almost double! Although it still won't be common, 2* 3-costs this early feel really unfair to players on the receiving end. Maybe it's ok, but I think this is the riskiest change in the roll percentages. Maybe Riot decided that is the tradeoff for slashing hyperroll.
4-cost: Finding your specific 2* 4-cost is a little harder at level 7, and a little easier at level 8. Nothing dramatic. It's a nice little boost to fast-8 comps.
5-cost: Getting a 2* legendary is a little harder. Getting a 3* legendary is now even more ridiculous.
That's all for now. Happy rolling!

Ultimate Gambling Guide for GTA Online - odds, probabilities, and optimal strategies

This is not mine, the creator of this is u/enderpiet

Since the Diamond Casino update, I have seen a large number of 12-year-olds posting Blackjack memes on this sub. As a parent, this has me very worried.
On top of that, I have seen some of the most trustworthy GTA Youtubers giving flawed gambling advice, which can have damaging impact on their gullible audiences.
So that's why I decided to write this up, to educate everyone on the subject, so there will be no more misunderstandings.
(2020 Update down at the bottom.)
If you're one of those Youtubers that wants to use this information in a video, feel free to do so. The more people (especially kids) that become educated about gambling, the better.
But then also please go back and review your own work, and delete or edit the videos that are giving out the wrong advice, like where you're saying you have "a good strategy for making money with roulette", or some other nonsense that I've heard this week. Delete that please.
Before I get into the individual games, I need to discuss a few concepts first, that will make understanding the rest a lot easier.
Expected return and variance
A game like Roulette or Slots has a fixed expected return on your bets. This is a percentage that you have no way of influencing. Say you are flipping a coin against a friend, and you both put up $1. The winner gets the pot. Since the odds are even at 50%, in the long run, you will expect to break even. Your expected return is 100% of your bet.
But imagine if you would play this coin flipping game in a casino against the house. On the "house rules" listed at the table they would probably say that you would only get 95 cents back for every win, while you are forfeiting a dollar on every loss. Would you still play?
Sounds stupid to do so, but still, everybody does it. Every bet they place on Roulette, every coin they put into a Slot machine, is based on the same concept.
Those few cents they take on every bet are their profit margin, and has paid for all the Vegas lights, the Mirage volcanoes, and the Bellagio fountains. Make no mistake - casino gambling games are not designed to make you lose, because sure, you can get lucky on a single night, but they are designed to make them win. That's the beauty of it. They can both exist at the same time.
Too many people that don't see how this works, are just destined for disaster. Just because you went on a lucky streak and won 8 games out of 10, does not mean that flipping coins is a profitable game, or that choosing tails is a winning strategy. Always be aware of the house edge, your true chances of winning, and just realize that you got lucky. There is no such thing as a strategy in flipping a coin that will give you a higher expected return, so it's just pure gambling, just like Slots and Roulette.
Most casino games are made in such a way, that your expected return is a little under 100%. This means that from every dollar bet at the tables, the casino expects to keep a few cents. For individual players, results may vary. Some will win, most will lose. But for the house, it doesn't matter. They take millions of bets each day, so for them, the expected average works out a lot sooner. In short: the house always wins.
When looking at the house edge, we're talking about the expected long-term result, based on the game's house rules. But for a player, it can take literally tens of thousands of hands or spins before you also reach this average number. Until that time, you can experience huge upswings and downswings, that are the result of nothing but short-term luck, which is called variance.
Some games and some bets have a much higher variance than others, which means your actual results will differ enormously from what you're expected to be at.
Take for example betting on red/black at the Roulette table. This is a low-variance proposition, because it has a high percentage chance of occurring, and a low payout.
Contrast this with betting single numbers in Roulette, which only win once every 38 spins on average. This bet has a much higher variance, meaning you can easily hit a dry spell, and not hit anything for 200 bets in a row, or you can see a single number hit three times in five consecutive spins. This is not a freak occurrence in high-variance bets.
Even though the expected return in both these bets is exactly the same, there's a huge difference in variance, causing massive differences in short-term results, which can go both ways. You need to be aware of this, before you decide what types of bets you are comfortable with placing.
Gamblers' Fallacy
Another thing to realize, is that each individual game, hand, or spin, is completely independent from the one(s) before it, and after it.
Gamblers tend to believe, that the chance of a certain outcome is increased, based on previous results.
The most famous example comes from the Casino de Monte Carlo, where the Roulette wheel managed to land on black 26 times in a row. Gamblers lost many millions during that streak, all frantically betting on red, believing that the odds were in favor of the wheel coming out on red, after producing so many blacks. This is not true. Each round is completely independent, and the odds are exactly the same.
You will hear people say things like a Blackjack table being "hot" or "cold", which is completely superstitious, and should be ignored. The exception was when Blackjack was being dealt from a shoe. It made card counting possible. But with the introduction of shuffle machines, and continuous shuffling like is being used in GTA, this no longer exists.
This is also why "chasing your losses" is a very bad idea. After being on a losing streak for some time, many gamblers believe that now it's their turn to start winning. So they will often increase their bet size, believing that when their predicted winning streak comes around, they will win back their losses, and more.
The reality of it, more often than not, is that people will indeed start playing higher and higher limits, until they are completely broke. Nobody is ever "due for a win". There is never a guarantee that you're about to start winning. In fact, the opposite is more likely to be true. You are, after all, in a casino.
Betting systems
Some people like to think that they have a fool-proof betting system, like the Martingale system. Simply increase or even double your bet when you lose, and keep doing that until you win. In theory, this system will always win. So that's why table limits were introduced, and where the system fails.
If you start at the Roulette table, playing red/black, with a small 750 chip wager, and just double your bet every time you lose, you only have to lose 6 times in a row, before you will be betting the table limit of 48,000, just to get that 750 chip profit.
Sure, you can go on all evening without this happening, winning 750 chips each time, but this losing streak only has to happen once, and you're bust. Any betting system like this is ill-advised, because you are hugely increasing your so-called "risk of ruin", and that's what we were trying to avoid.
And even if your starting bet is only 100 chips, after only nine straight losses, and nine doubled bets, you are betting the table limit at 50,000 chips. If you lose that bet, you're 100,000 chips in the hole, with no way to recover that with your 100 chip base wager.
So don't believe anyone that says this is the perfect system to always win in the casino. Sooner or later they will understand why they were wrong, when they're asking you for a loan.
Set your limits BEFORE you start playing
One final point before we get into the games, a general tip for people that head out to play: money management.
Just like in real life, before you go to the casino, decide on a maximum amount that you are WILLING TO LOSE.
Bet small enough, so that amount can last you through the entire evening, and you will not be tempted to run to the ATM to continue playing.
Considering GTA money, some people will be comfortable losing 1% of their GTA bank balance, some people will be comfortable with gambling away 5% of their total GTA savings. It's up to you what you can handle. Decide for yourself where it will start to hurt, and don't cross that line.
But whatever number you decide on, as soon as you lost that amount, get up and walk away. Don't chase your losses, stick to your limits, and accept that this has not been your day. There is always another game tomorrow. Always agree with yourself on a simple stop-loss rule, how much you would want to lose at most, and simply stop playing when you get there.
Same goes for winning. You can decide on a number, how much profit you would like to take away from the casino. You can go on a hot streak and be up half a million in a short period of time, but if you would continue to play longer, looking for more, chances are that you're going to lose it all back.
Most people are happy with doubling their daily casino budget, for example. Others are looking for 10 bets profit in Blackjack. Whatever you choose, when you hit that number, you can stop playing and bank your profits, or you can continue playing if you're still enjoying the games, but then only just play minimum bet sizes. Then you're just playing for fun, not for money. You've already made your profit, so simply keep it in your pocket, and don't risk losing it again.
Either way, decide on what your money management strategy will be, and STICK TO IT.
Casino games in GTA Online
Now, I'm going to dive into the games that you can find at the Diamond casino, ordered from worst to best.
6) Slots
Generally the rule is this: the less strategy a game has, the worse it is for the player. And with slots, this is definitely the case.
The only influence you have, is choosing what type of machine you're going to play. Basically, there are two types of slot machines:
-high frequency, low payout slots
-low frequency, high payout slots
In the first type, there is no huge (progressive) jackpot on offer, just your average selection of prizes that don't go up to crazy amounts.
This will result in a player having many more spins resulting in a win. The amounts that you win on the bigger prizes, will be smaller, but they do come around more often. This type of slot machine has a lower variance, which means that your money should last you longer, winning many smaller prizes along the way to keep you going.
The second type of slot machine lures you in with the temptation of a huge jackpot prize. Even though the long-term expected return on these machines is the same as the previous type, the prize distribution is hugely different. The large jackpot prize weighs heavily on the scale of expected return, but the chance of it hitting is extremely small. This results in a much higher variance on this type of machine. Usually your money will go down very fast, because the smaller prizes are less rewarding than on the other type of machine.
At the Diamond, the info screen says the player return at slots is set at 98.7%. This means that, on average, for every maximum bet of 2,500 chips, you expect to lose 32.5 chips.
This might not seem like a lot, but the danger of slots is that the game is extremely fast. You can spin about once every 6 seconds, which would result in an expected LOSS of about 20,000 chips per hour of playing.
But again, in this long-term expected number, the large jackpot awards are also factored in, and as long as you don't hit those big prizes, you'll see your money go down a lot faster.
In any case, thank heavens the max bet is only set at 2,500, or else we would see more players go bankrupt at alarming rates.
Optimal strategy for slots:
There is none. Because after betting, you have no more influence over the outcome. The only choices you have, is what type of machine you want to play at, and how much money you are going to risk. And those are all personal preference. As long as you stick to your loss limits, as discussed above, there's no harm in having a go every once in a while, hoping to get a lucky hit. Just realize that you don't have a high chance of scoring a big win, so as soon as you do, get up and walk away.
5) Roulette
Roulette is also a game where you have no influence over the outcome. There is zero skill involved. You place your bet, and that's it.
In traditional French roulette, a table has only the single-zero, but of course, for American casinos that wasn't enough of a house edge, so they simply doubled their profits by adding a second zero. The house edge was increased from 1/37 to 1/19, which is huge.
This makes playing on a double-zero roulette table by definition a sucker's play.
The payouts scale evenly, which means that a bet on a single number, and a bet on half of the numbers, and everything in between, yields the same expected return. The only difference, again, being the variance that you are willing to subject yourself to.
The player return for double-zero Roulette for all bets is 94.74%.
Except for the 5-number bet, which can only be made by placing a bet on the two top rows that contain 0, 00, 1, 2 and 3. The expected return on this bet is lower: 92.1%. This is because it only pays out 6-1. Why? Well, the number 36 isn't divisible by 5, so the greedy people that came up with double-zero Roulette had to round it off someway, and as expected, it wasn't going to be in the players' favor.Just remember that that 5-number bet is the worst bet at the table, and should be avoided. All other possible bets have the same expected return.
So it really doesn't matter how you spread your bets, if you bet only one chip, or if you litter the entire table with a bucketload of chips. Each chip you put out there, has the same expected return, so there is no strategy that will improve your long-term results.
Assuming that you're betting the maximum table amount of 50,000 chips, you will be looking at an expected loss of about 2,630 chips per spin. Considering that a round takes about 45 seconds to complete, your expected LOSS at the GTA Roulette tables will be around 200,000 chips per hour of playing.
Optimal strategy for double-zero roulette:
Stay away. Stay far away.
4) Three Card Poker
With Three Card Poker, we come across the first game where there is actually some strategy involved. You get to look at your cards, and then decide if you want to fold, and surrender your ante, or double your bet.
Additionally, you can choose to place a side bet on "Pair Plus", which offers progressive payouts.
There are some websites out there that ran all the numbers with computer simulations, and even though I would like to quote the source here, these websites are understandably littered to the max with online casino ads, so that's why I have decided against doing that.
Optimal strategy for Three Card Poker:
For this game you only have to remember one strategy rule: Always bet on any high card queen-six-four or better, and fold any high card queen-six-three or lower. That's it. Just don't forget to double check if you're not folding a straight or a flush, and you'll be fine.
This strategy will result in an expected return of 96.63%.
The Pair Plus sidebet, with the payout table that is used at the Diamond casino, gives you an expected return of 97.68%, which is actually a bit better than the main ante bet.
So by playing both wagers, you're reducing your expected losses per bet, but since you're betting more, you're also increasing your expected loss per hour.
My advice would obviously be to not play this game at all, but if you do, put as much of your bet as possible on the Pair Plus, while making our Ante bet as small as you can.
To be able to compare it to the other games at the Diamond, let's stay on that 50,000 maximum wager, meaning making your ante bet 35,000, and your pair plus bet 15,000, if the table would allow it.
This results in an expected loss of about 1,525 chips per hand, and with a round taking about 45 seconds, this adds up to an expected LOSS of around 120,000 chips per hour of playing. In comparison, if you would only play the ante bet for 50,000 per hand, you expect to lose 1,685 chips per hand, which means an expected LOSS of about 135,000 chips per hour. So the more out of that 50,000 wager you can put on the "Pair Plus" sidebet, the better.
Even though it may be fun to try out this game for a bit, since there's only one simple strategy rule to follow, you'll soon find yourself robotically grinding down your bankroll until it has vaporized. You're not missing out on anything if you skip these tables, there is no real challenge.
Just like with Roulette and Slots, if you want to try it out nonetheless, you can just bet the minimum amounts and only play for fun, so it won't matter if you win or lose.
3) Blackjack
Blackjack is the most complicated game by far. Simply because the player has to make a series of decisions, which will largely decide the outcome. Luckily, there is such a thing as an optimal strategy, which will be outlined below.
However, the strategy is also dependent on the house rules. These not only affect your expected return, but in some places also your decisions.
Here are the house rules at the Diamond casino:
-The game uses 4 standard decks, and a continuous shuffle.
-Blackjack pays 3 to 2, dealer checks for early blackjack.
-No insurance offered, no surrender.
-Dealer stands on soft 17.
-Double down on any two cards.
-Player can split only once, but doubling after split is allowed.
-Seven-Card Charlie.
Under these rules, and following the "basic strategy" chart, your expected return at Blackjack is a shade under 99.6%, which is extremely good for a casino game, that's why Blackjack should be your table game of choice.
But it comes at a price: you are going to have to memorize the relatively complicated strategy chart, or at least stick it to your monitor until you have it in your head. But in case you ever stumble into a real-life casino, you won't regret having this table memorized, so I would definitely advise you to work on that.
The strategy chart might look complicated at first, but you will be able to notice certain patterns. Your decisions are mainly based on the dealer's upcard, which is basically divided into a weak card (2 to 6), and a strong card (7 to ace).
When a dealer shows a strong card, you will be hitting more often with the risk of going bust, but when a dealer shows a weak card, you're not taking that risk, and you will be standing more, but also doubling and splitting more. You want to increase your bets when the odds are in your favor, and get out cheap when they're not.
But it also helps to take some time to think about why a certain advice is given. For example, why does it say that you always have to split two eights, even against an ace. Well, that's because two eights equals 16, which is the worst total you can have. It's better to split them up, and give yourself a chance of finding a 17, 18 or 19 with the next card. Once you see the logic in that, you'll have one less thing to memorize.
The playing advice in the basic strategy chart is a result of computer simulations that ran all possible outcomes against each other, and produced the most profitable decision for each situation. So you can't go wrong following it.
Optimal strategy for Blackjack with Seven-Card Charlie
The added house rule of Seven-Card Charlie, adds a small advantage for the player, and it does influence a few strategy decisions. For example, you might have a 14 with 6 cards, against the dealer's 5 upcard.
Normally this would be an automatic stand, but if you're only one card away from the Seven-Card Charlie, meaning an instant win for the player, regardless of the dealer's hand, it turns it into a hit.
Here's the most optimal strategy chart to follow for the Diamond Casino house rules:https://prnt.sc/olct6g
You'll see that two fives are missing from the chart, and that's because you never split them. You treat them as a regular 10. You also never split tens. Just stand on 20.
If you follow this strategy religiously, even with a maximum wager of 50,000 chips, you only expect to lose about 215 chips per hand, and with rounds taking about 30 seconds, that amounts to an expected LOSS of 26,000 chips per hour, which is only half a bet. A small price to pay for an hour of entertainment.
But since the expected return is so extremely close to 100%, you will see more positive short-term results than with other games. But obviously it can also swing the other way. Again, this is supposed to be the game where your money lasts you the longest, but always set your loss and win limits before you sit down. That rule simply always applies.
Still, even with optimal strategies applied, all these games are expected to lose you money in the long run. So betting any kind of large amounts is not advised. If you simply want to enjoy playing these games, there's nothing wrong with betting a minimal amount. Playing these games for a longer period of time will already cost you money anyway, since your daily property fees will still be charged while you're playing in the GTA casino. As long as you can play for fun, there's nothing wrong, but when you see yourself betting insane chunks of your entire bank balance to try to recoup some unfortunate losses, you're doing it wrong.
As the commercials in Britain all correctly say: when the fun stops, stop.
2) Virtual Horse Racing
Now onto the good stuff. I ran some numbers, and I believe Rockstar has made a mistake with the horse racing game. Because as it stands, and if I read the numbers correctly, this game is actually profitable for the player. You can actually make money with this, at least, until Rockstar figures out their mistake and patches it.
If anyone wants to jump into the math and double check this to make sure, please do so. I will add any corrections to this post. This is one of those "to good to be true" things, so I keep thinking that I might have overlooked something. So please verify it if you can.
The setup is this. There is a pool of 100 horses, each with their own attached payout. These are divided into 3 groups, ranked by their odds. From each group, 2 horses are randomly selected to provide a pool of six runners for you to bet on.
Now it's not an actual race you're looking at. You are looking at a raffle. This is important to realize.
Each horse gets awarded a certain number of raffle tickets. The favorites get awarded more tickets than the underdogs, and therefore, have a higher chance of winning.
If this distribution works like it does in the real-life casinos, then the raffle tickets are awarded according to the betting odds.
Example 1: imagine a race with 3 runners, all have 2/1 odds, representing a 33.3% chance of winning. (Because 2/1 means 2 AGAINST 1, so 3 total.) In this case, each horse gets one third of the raffle tickets, giving them an equal chance to win.
Example 2: imagine a race with 3 runners, one has 1/1 odds (or EVENS), representing a 50% chance of winning, and the other two horses are marked up as 3/1, with a 25% chance of winning. The favorite gets half the tickets, the other two get a quarter of the tickets each.
A ticket is drawn, and you'll have a winner.
It doesn't matter in this game which horse you bet on, because the expected return is always the same: 100% or break-even, for the above examples.
Now, what happens if the percentages don't exactly add up to 100%?
They must add up to 100%, because there will always be a winner. And only one winner.
So when this is the case, the actual winning chances of the horses are adjusted to meet the 100% requirement, using their payout odds to determine the scale.
So, if the represented percentages add up to more than 100%, the actual winning chances of the runners will be DECREASED, resulting in all bets becoming losing propositions for the players.
Example: In a 6-horse race, all runners are listed at 4/1, representing a 20% chance. Only with six runners that amounts to 120%. So all chances are scaled down by 1/6th, to end up at 100%.
This means your horse's chances are reduced from 20% to 16.67%, turning it into a losing bet: 5 times you will lose your bet, and 1 time you will win, but only get 4 bets back in this instance, instead of 5. A losing bet in the long run.
This is the type of odds that you find in regular casinos, with fields as large as 15 runners to bet on, where the assumed winning chances always add up to more than 100%, therefore are decreased for all runners, resulting in a house edge.
But in GTA Online's Inside Track, there are other scenarios, because of the small field, and the way that they are put together.
In some cases, the represented percentages when added up, are LESS than 100%, meaning that the actual winning chances of all runners, are INCREASED.
This creates profitable bets for the players, because in the long run, you're expecting to win more money than you lose. This is a gambler's dream, pure and simple.
So, according to the in-game information, the three groups of horses are divided as follows:
-Favorites: EVENS to 5-1
-Outsiders: 6-1 to 15-1
-Underdogs: 16-1 to 30-1
Let's take the two most extreme examples to show what's happening.
The worst possible field to bet on: two runners at EVENS, two runners at 6-1, and two runners at 16-1.
EVENS represents a 50% chance, 6-1 is 14.29%, and 16-1 is 5.88%. Add those up and you land on a total of 140.34%.
This means that the actual winning chances of the horses are decreased by 28.75% (to get that 140% down to 100%), which makes betting on this field extremely unwise.
A horse at EVENS will only come in as a winner 35.63% of the time, instead of 50%,
a horse at 6-1 will only win 10.18% of the time,
and an underdog at 16-1 will only win 4.19% of the time.
The expected return on a bet on any of the horses in this field is only 71.26%, so a maximum bet of 10,000 chips on any of these horses holds an expected LOSS of 2,875 chips.
These returns are the same, because the winning chances are scaled equally, according to the payout numbers. So it really doesn't matter which horse you bet on, in the long run, you expect the same results.
But as explained before, it does influence variance, and therefore your short-term result, which can swing both ways.
But now, the best possible field to bet on: two runners at 5-1, two runners at 15-1, and two runners at 30-1.
Odds at 5-1 represents a winning chance of 16.67%, 15-1 odds means 6.25% chance, and 30-1 odds means a 3.23% chance of winning. Add these six horses together, and you only get 52.285%.
This means that, to get from 52% to 100%, the actual winning chances of these horses will be almost doubled! Multiplied by 1.91 to be exact.
So the 5-1 favorites will now win 31.88% of the time, instead of 16.67%,
the 15-1 runners will win 11.95% of the time,
and the underdogs at 30-1 odds will still win 6.17% of the time.
When betting on this field, the expected return on your bet is 191.25%!
This means that a max bet of 10,000 chips will result in an expected PROFIT of 9,125 chips.
This is printing money, if there ever was such a thing.
Optimal strategy for Virtual Horse racing
So all you have to do, is only bet high on the games where you have an expected positive return, and bet the absolute minimum on the games where your expected return is negative. Or back out of the racing game to refresh the field.
If you don't have a way to quickly add up all the percentages, and until somebody shows up here with a neatly formatted table, just use a few general rules of thumb:
-Always bet the maximum on a race with favorites at 2/1 and 3/1 or higher in it.
-Simply skip all races with two favorites at EVENS in it, and at EVENS and 2/1. Or bet the minimum, if you can't skip or refresh the field.
-To decide if you should play races with other favorite combinations EVENS and 3/1, EVENS and 4/1, EVENS and 5/1, or two favorites at 2/1, the payouts on the other four runners determine whether or not it's profitable to play them. The results of betting on these fields vary from an expected 1,330 chip loss (worst-case) to an expected 1,680 chip win (best-case), with a max bet of 10,000 chips.
But if you're not looking for another strategy chart, you might just want to skip these borderline cases, and just cherry pick the best ones, which are easy to recognize, and with which you can never go wrong.
It's difficult to put a number on an expected win-rate, because it all depends on which fields you get presented with, but it's not unreasonable to state that you can maintain a steady win-rate of around 200,000 chips per hour, with about 50 seconds per race.
Remember, you're not trying to win every race. You're trying to win the most money per hour. So don't sweat it when you bet on a 4/1 favorite, and lose a couple of races in a row. It will still be more profitable in the long run. You have the math on your side.
To reduce negative variance, always bet on the favorite, when betting on profitable fields. We're not gambling anymore, we're grinding out a steady profit. We want to keep the swings to a minimum.
I contacted Rockstar support to verify if this is indeed how it works, but the only reply I got after 6 weeks is that they were "looking into it".
User u/Garsant made a useful Excel-worksheet, available for you to download, where you can quickly type in the payouts on the horses, to see if it produces a profitable bet or not. You can find it in his post here: https://www.reddit.com/gtaonline/comments/ekp8na/gta_online_inside_track_odd_calculato
1) Wheel of Fortune
The number one profitable casino game in GTA Online is obviously the Wheel of Fortune, because it costs you nothing to play.
Unfortunately, you only get one free spin per day, but it holds great value, so make sure you do it.
With a chance to win a super car, vehicle discounts, expensive mystery prizes (which also can be vehicles), and a lot of cash and chips, the expected return on a single spin is around $100,000 in value.
So don't forget your daily spin, it's definitely worth your time.
2020 Update:
As of the Diamond Casino Heist update, the Inside Track horse racing is confirmed to still be as profitable as outlined above.The only thing that seems to be changed, is that you can't refresh the field anymore by backing out of the screen. This does affect your hourly rate in a negative way, but does not change the fact that this game has a huge positive expected return, and should be your go-to when you're trying to take money from the house, without having Lester's nagging voice in your ear. That should also be worth something.
And with that, I conclude my 5,000 word essay on gambling in GTA. Questions, comments, feel free to add your input to this guide.
Cliffs:
-Gambling games should only be played for fun, not for big money. You should expect to lose in the long run. The house always wins.
-A casino game doesn't have a memory, and betting systems don't work.
-Set your limits before you start, how much you are willing to lose or win, and then walk away when you get there.
-Don't play slots, roulette, or three card poker.
-Only play blackjack following a basic strategy chart (https://prnt.sc/olct6g).
-Inside Track betting can be played profitably, if you only bet on fields WITHOUT a heavy favorite.
-Wheel of Fortune is always your best bet, because it's a free bet.

gambler's fallacy definition video

Other Examples of Gambler’s Fallacy. The definition of Gambler’s Fallacy has evolved to include other rationalizations that can be made by gamblers who are likely addicted to the games that they play. While we want to focus on the game of blackjack, we will use that game in most of the examples that we provide. A person plays online blackjack. They notice that they have won seven sessions ... The Gambler’s Fallacy is very real and a large reason for why casinos make money, because many people are superstitious and as a result commit the fallacy. Randomize decisions. One method to take emotions out of your decision-making is by randomizing your decisions based on naturally-occuring random number generators, such as the flip of a coin, or the position of the second hand of a watch ... Welcome to Gambler’s Fallacy. By definition, the gambler’s fallacy is the “erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future”. Here, we will talk about anything that relates to the risk-return paradox, business, probability, investing, or making money ... Gambler’s fallacy can also occur in some instances where past events are related to future outcomes. An example of this would be a tennis player. If he has to play 24 matches, out of which he has won 12 matches and lost 6, and is now left to play 6 more matches, and now, if one makes the assumption that the losing streak makes him due for a victory in his next match, one would be indulging ... Gambler's fallacy refers to the erroneous thinking that a certain event is more or less likely, given a previous series of events. It is also named Monte Carlo fallacy, after a casino in Las Vegas ... The gambler’s fallacy is a belief that if something happens more frequently (i.e. more often than the average) during a given period, it is less likely to happen in the future (and vice versa). So, if the great Indian batsman, Virat Kohli were to score scores of 100 plus in all matches leading upto the final – the gambler’s fallacy makes one believe that he is more likely to fail in the ... Understanding the gambler’s fallacy, and the problems it can cause, is useful if you plan on being a successful gambler. It will prevent you from making the kind of mistakes that have led to many a gambler going broke. On this page we have explained the fallacy in more detail, with examples. We’ve also covered why it result in gamblers losing money. Understanding the Gambler’s Fallacy ... People who fall prey to the gambler's fallacy think that a streak should end, but people who believe in the hot hand think it should continue. T. Edward Damer: Consider the parents who already have three sons and are quite satisfied with the size of their family. However, they both would really like to have a daughter. They commit the gambler's fallacy when they infer that their chances of ... The gambler's fallacy is the belief that the chances of something happening with a fixed probability, i.e., rolling 10 even dice in a row, become higher or lower as the process is repeated. The ... Gambler's Fallacy. The gambler's fallacy is based on the false belief that separate, independent events can affect the likelihood of another random event, or that if something happens often that it is less likely that the same will take place in the future.. Example of Gambler's Fallacy. Edna had rolled a 6 with the dice the last 9 consecutive times. Surely it would be highly unlikely that she ...

Gamblers Fallacy - Definition & Examples LF