How to Calculate Horse Racing Betting Odds and Payoffs

I bet $5 today for my horse to finish 1st or 2nd at my local track but I had to leave early. Well my horse apparently won her race (figures I didn't get to see!) and the payout chart online for her race says "to place" is 3.60$. Does anybody know about how much I won? Is it as simple as $5 x 3.60 = $18 won?

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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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
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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.
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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.
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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.
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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.

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

For a casino game night, I'm trying to build a horse racing game. The game should be simple to play, but still fun for everyone. My idea was a game board with 6 horses, a '27' round lap (got a big board with that, so that would be easiest to use), a dice for each horse (or 6 decks of playing cards using the Ace to 6 cards) and two extra dice. One of the extra dice determines what horse gets a bonus roll each round, and the 2nd dice is the neutral dice to determine the bonus steps.
Now, I want to make it a little more interesting with different starting positions. I want 1 horse to start at +3, 4 horses at 0 and 1 horse at -6. So basically, the board is actually 33 steps (first on 34 and up wins).
So I made the following Excel spreadsheet: https://docs.google.com/spreadsheets/d/e/2PACX-1vSAfaiaqMIPbsSj4_M6DLexkzwLJ6w1ePCwwog64fGiWY6KcZ4k8A4eW5r6Kobz1sWbeJYBzYdhrNgL/pub?output=xlsx
The problem is that I do not know how to calculate the extra roll. I would assume the extra roll would have bigger impact on the odds of horse number 6 (starting at -6), but that is just my guess.
I did a test run with 133 runs (read; counted) without the extra roll ended up with horse 1 winning 51 times (~38% win), horse 2-5 winning 81 times (~61% chance win, ~15% each), and horse 6 had 1 win in 133 runs, (~1% chance)
Payout would be '3/2' for horse 1, 11/2' horses 2-5, and '99/1' for horse 6. (100 games with 6 players, all betting $2 on a different horse each game, this would result in $17 a profit for the casino)
Some aditonal rules that shouldn't really affect the odds; After two rolls, players have the option to double down. Players who join during a race can still bet, but not after 2 rolls. The payout is always '1/1' for a late bet on any horse. You can only bet on 1 horse .
In case of a draw (for example, horse 1 on 34, horse 2 on 35 and horse 3 on 35, horse 1 would lose, and horses 2 and 3 would keep rolling until one of them rolls higher.
So my question; are my odds correct? Would the odds be influeced by the extra roll? And how do I simulate games (with and without bonus rolls), for example 1 million games, to see a clear view of winning chances?

Look first of all I'd like to be honest with you, I'm not going to claim I "stumbled" upon some "crazy secret system" that nobody knows. In fact, probably more than a few people know what I'm talking about in this article. The truth is that I've been playing the Preakness among many other horse races, for at least 15 years.
The Preakness is the first throroughbred race I ever attended, back in the 1990's. I had played at harness tracks, having been introduced to that at a young age, but had never been to a throroughbred track until 1996.
That year, my good friend and fellow horseplayer convinced me we should go to Pimlico for a big infield party and some big horse races would break out at some point. I didn't know or care much about anything except the infield party and thought it would be fun. We brought a 12 pack and settled in.
Early in the afternoon on the way up, we tuned in to the Baltimore rock station and were hearing all kinds of live music from some of our favorite bands such as Pearl Jam. We were just about pissed off at the fact that we missed some of these bands live, only to show up and find it was just a DJ playing live cuts, and the few local bands on deck hadn't even started playing yet.
I was young and after the party was over and horse races had broke out, I was wondering why Louis Quatorze had won the Preakness and we hadn't bet on him. After that I began some more analysis and started using some figures from Brisnet to help me analyze the races.
A couple years later I liked Charismatic in the Kentucky Derby, among like 10 other horses, but failed to have the right trifecta boxes since I had little clue what I was doing. I liked him in the Preakness as well, still at good odds since people thought his Derby victory was a fluke, but again failed to have the right trifecta when Badge showed up. But at that point I realized that a pattern was emerging.
Eventually I figured this stuff out, although hard-headed about it and unwilling to part from numerical analysis from numbers that I didn't even know how were calculated. I found out it didn't really take a any magic numbers or even much analysis for a basic wagering strategy.
With few exceptions, the Preakness is one of the easiest races to bet. Take the top (4-5) horses from the Kentucky Derby that run at Pimlico two weeks later, and undoubtedly 2 of them will finish in the top 4, in fact, usually the top two horses from the Derby will finish 1-2 in the Preakness. It's really that simple.
After that you do have to put in some analysis to figure out which "outsiders" will infiltrate the trifecta, or possibly even win the Preakness, along with the Kentucky Derby contingent. There are various tools to use to accomplish this but I normally use one I invented.
Unsatisfied with numbers from various other people and organizations with their secret calculations that I did not understand, I decided to make algorithms to create my own numbers and put them into what I call the Grid.
Last year, the Grid gave me Preakness winner Shackleford at 13-1 as the top Speed and Power horse. It was an obvious key horse for me and automatic win bet at those kind of odds. Plus, he was a top four Derby finisher. Apparently people forgot he finished 4th not 14th in the Derby, which was very respectable for a frontrunner.
Combine him with Derby winner and obvious favorite Animal Kingdom at 2nd, and take Astrology as an improving horse with 4th best Early Pace according to the Grid in 3rd place, and you have a very easy trifecta payout. Add Dialed In, the best Late Pace horse coming off a disappointing but respectable 8th place Derby finish, and you have a very easy superfecta.
This is what I call the anatomy of a perfect Preakness exotic bet. You take any of the top 4 Derby finishers that are running at Pimlico, and key them and 1 and 2, get the "outsider" that didn't run in the Derby at good odds, and add another strong contender, usually from the Derby, such as a good late runner for 4th.
You would be surprised how many times the Preakness plays out this way. Often the same horse will win the Preakness that won the Derby, which has happened less in the last few years but they still often finish in the money. And in fact the top two in the Derby often run 1-2 at the Preakness.
So using the top Derby horses is obvious but where will you find the "outsiders" that will undoubtedly take up a spot or two in the superfecta? Well that is tough to come up with by yourself. Normally you will need more of an advanced handicapping tool for that, which is why I use the Grid. I can tell you that the outsider is almost always at odds from 12-1 to 15-1 so that narrows it down.
The year before last the Grid of course gave me the Preakness winner, but only at 2-1 and not much value there, obviously. But also it gave me 11 of 13 winners that day including some nice long shots that provided good exotic payouts.
Of course, since I wrote this, it could just happen that the top Derby horses will finish 1-4 in the Preakness, and it wouldn't surprise me at all if that happens. Especially since of my top 6 Derby winning contenders, out of 20, 4 of them finished 1-4 in the Derby.
So now you know the basic strategy now for betting the Preakness. You just need to find the right long shot or two to add to your obvious Derby contenders for some nice exotic payouts. If I were you, I'd use the Grid to get them, but that's just because it always comes through for me in these situations.

In normal horse racing, the odds of all the horses should add up to over 100% because the house, who decides the odds (how much they'll pay out) gets an edge that way.
In inside track, the odds are decided randomly from a selection of horses with set odds. This can lead to situations where the horses in a given race are all said to have a very low chance of winning, thus all the horses pay out more than usual. But, one horse always has to win, so their odds haven't all gone down proportionally to the increase in payouts.
Therefore, in a given set of 6 horses, the edge increasingly goes to the player the lower the odds are (the higher the numbers) for the horses. The horses with the highest odds of winning have the greatest effect on this, so you pay attention to positions one and two.
The Strategy
In order to not waste time betting on races with a minimal edge, I only bet when the first two horses have odds of 3/1 and 5/1 or worse.
This includes 3/1 - 5/1, 4-1 4-1, 4-1 5-1, and 5-1 5-1.
The other horses also matter, so feel free to glance at 3 and 4 as well, noting that 6/1 odds are very bad for you and 15/1 odds are very good.
Now which horse do you bet on? It doesn't actually matter. No matter which horse you bet on, you will get the same 'edge' over the casino, and win money in the long run. If you want the most consistent winnings with a low risk of having streaks of losses, you should get on the 1 horse as it always has the highest odds of winning.
If you bet on the other horses, your odds of winning will decrease proportionally to how much your payout increases when you win.
Math
When a horse says it has 5/1 odds, it is supposed to have a 1/6 chance of winning because if it wins, you will be paid your original bet + 5 times your original bet = 6 times your money.
In order for the casino to have an edge like the in the rest of the games, a 5/1 horse would have to have a less than 1/6 chance of winning. The only way for this to happen is for the other horses to have a greater chance of winning than 1/6. if all the other horse had a lower chance of winning, then that 5/1 horse must have a greater than 1/6 chance of winning (because there are 6 horses).
In order to calculate the odds of a horse winning, add up the odds of each horse winning, and then divide your target horse's odds by that number. To find the odds of a horse, simply add 1 to the first number listed in their odds and divide it by 1.
Wage of consent has 21/1 odds, and therefore its prescribed odds are 1/22
an example race might contain

1. Evens (1/1)
   
2. 4/1
   
3. 6/1
   
4. 12/1
   
5. 18/1
   
6. 27/1
   

The sum of all these odds is as follows: 1/2+1/5+1/7+1/13+1/19+1/28=1.008
1.008 is above 1 making over 100% of 1
this means the casino has a small edge in each of these bets because if the casino is claiming that the horses all are very likely to win, that means they're paying out less for the bets.
You want that number to be less than 1.
Checking horses 1 and 2 is the fastest way to make sure, but 3 and 4 (which can have as high as 6/1 odds) can also affect your edge significantly.
TL;DR: Bet on any horse you like (but preferably the 1 horse) when the odds of the first two horses are worse than or equal to 3/1 and 5/1. (This includes 3/1 - 5/1, 4/1 - 4/1, 4/1 - 5/1, and 5/1 - 5/1). The worse the odds of all the horses collectively the better you'll do.

Hello i'm a guy who gets into horse racing for 1 week out of the year and likes to do research and think i have it figured it out...that's never the case. Anyway i have a friend that goes to the derby every year and i send him down with $50 to make 4 $2 trifecta box picks with 3 horse each. I just found out through here that it's possible to make 4 horse trifecta boxes and i'm intrigued.
i looked over my bets and realized i could easily make 2 4 horse trifectas and be making the same picks as my 3 horse trifectas. My question is, is it better to place 4 $2 3 horse trifectas or 2 $1 4 horse trifectas? i think the latter has less risk so i'm guessing it's a smaller payout?
also is there any place to calculate your possible payout? like where i can set up my bet put in my horses odds and it would tell me how much money i'll make if i hit? just wondering if i'm dreaming of a 12' aluminum boat or a sweet new bass boat. Thank you!

Someone asked me about how horse races calculate the odds during live betting. I wasn't sure. You can look at how it works and the more someone bets on one horse, the lower the odds. It's such that the odds even out, no matter what the bets are.
Say you have 5 races and each start off with some odds for a payout. If someone bets 100 on #1 and others bet 10 on each of the others, how do you calculate the odds so that it always comes out even?
The odds are posted in real time as the bets are taken, so clearly there is a computer program that figures out how to determine the odds.
I understand that in a real horse race, they start out with odds based on many things. I'm simply looking for the math to calculate the odds based only on the bets and assuming the the results are random.
So you have an array of 5 slots and you simply pick at random, but you alter the odds based on the money that is bet on each one. You alter the odds so that the money comes out even. So if slot 1 has 2X the money of all the rest, it'll change the odds so that the outcome is the same.
I'm thinking that someone has done this before. I just can't seem to find any code to show this. The language doesn't matter, just looking for the math.