Understanding Probability and House Edge
Probability of winning and house edge are two distinct concepts in gambling. The probability of winning refers to the chance that you will win a particular bet, while the house edge is the expected percentage of your bet that you will lose over time. These can vary independently; for example, a high probability of winning doesn't necessarily mean a low house edge [5]. Understanding these concepts is crucial when evaluating different casino games.
Craps: Favorable Odds
Craps is often cited as one of the best games in terms of odds. The "don't pass line" bet is considered to have some of the best odds in the casino [2:1]. Additionally, betting the pass line and following up with maximum odds can reduce the house advantage to around 1-2%
[2:12]. This makes craps a popular choice for those looking to extend their playtime and enjoy the casino experience without losing money too quickly.
Roulette and Slot Machines
Roulette offers various betting options, each with different probabilities and payouts. Strategies can be employed to manage bankroll and extend playtime, but ultimately, roulette remains a game of chance with a significant house edge [4]. Similarly, slot machines, especially penny slots, can offer extended playtime for a small investment, though they generally have a higher house edge compared to table games
[2:5].
Games with High House Edge
Games like French Boule demonstrate how the house edge can be substantial despite seemingly favorable odds. In this game, players have a 1 in 10 chance of winning an 8x payout, resulting in a negative expected return [3:4]. Such games highlight the importance of understanding both the probability of winning and the house edge before placing bets.
Poker: Player vs. Player
Unlike other casino games, poker pits players against each other rather than against the house. This dynamic means that skilled players can potentially have an edge over their opponents, making it a unique option for those who prefer strategy over pure luck [2:10].
Recommendations Beyond the Discussions
When choosing a casino game, consider what you're looking to achieve—whether it's maximizing entertainment or minimizing losses. For those interested in extending playtime, craps and certain video poker games may offer more favorable odds. Always remember that gambling should be approached as a form of entertainment, and setting a budget beforehand can prevent overspending.
Rules of the game:
There are two players.
The first player offers an ante, and the second player must match it. The first player then rolls a 10 sided die. If they get a 9 or 10 they automatically win the pot. (so I know there is automatically a 20% chance to win)
The second player rolls a 4 sided die, a 6 sided die, and an 8 sided die.
If the second player has 0 numbers that match then the first player keeps the pot, if the second player has 1 number that matches the players break even, if there are 2 numbers that match the second player gets double the ante from the first player, with three numbers the second player makes triple the ante from the first player.
Players switch what they roll between every round of play.
WHAT I AM ASKING:
what are the odds of player 1 winning, what are the odds of player 2 winning, what are the odds of a draw, who is favored, is this dumb gambling game mathematically speaking, and how can I make it more interesting/hard to decipher?
WHY I AM ASKING:
One of my players if very savvy with math (I am very much so not), and will get bored with or see the odds of gambling games fairly easily. She loves to gamble in game, but is hard to entice unless it seems mathematically "quirky" or fun. I know that probability is not a hard thing to figure out for most people, and I did try to figure it out on my own. I am just not good at this kind of stuff, so while an answer or giving me the exact formula I need where I can just plug and chug would be appreciated, what I am really looking for is a slightly more thorough explanation.
Let's start with: there are 10x8x6x4 possible outcomes, so 1920.
If player 1 draws a 1, there are 87 outcomes for player 2 to draw the game. D8 is 1, and others are not: 1x5x3=15 D6 is 1, and others are not: 7x1x3=21 D4 is 1, and others are not: 7x5x1=35 D8 and D6 are 1, D4 is not: 1x1x3=3 D8 and D4 are 1, D6 is not: 1x5x1=5 D6 and D4 are 1, D8 is not: 7x1x1=7 All dices are 1: 1x1x1=1
15+21+35+3+5+7+1=87
Repeat for other draws 😂 then sum them all and divide by 1920, you will have the probability of a draw.
Thank you
I was making some mistakes before, I redo my math and make it in excel:
P1win : 896 times out of 1920 : 47%
P2win : 832 times out of 1920 : 43%
Draw : 192 times out of 1920 : 10%
Thank you
I tried to simulate a few strategies used for playing roulette, found that interesting. I have documented what I have done in this article and I think you'll also find that interesting. Please do give it a read and provide feedback!
As someone who realizes casinos are a losing prospect, but views it as “paying to play the game”. Curious the game/strategy for playing the longest/most rounds for a given bankroll.
Eg: if I walk into a casino with $200, what game/strategy has the longest median time to losing it all.
Craps table with a lower limit. It is high energy and fun as heck. There are obviously no guaranteed ways to win, but just playing six and eight keeps you in the fun for a long while. During a vacation, we budget casino time as entertainment. When we run out of our daily budgeted money, we are done with that entertainment.
If you bet the pass line and then follow up with a maximum Odds bet, you can push the house advantage down to 1-2%. Then your task is to get enough free drinks to cancel that out as well, and you are essentially gambling for free!
I played a penny machine in the old part of Los Vegas, out in a dollar and played half an hour before it was all gone. The next day, I played a dollar slot in Caesars Palace and hit on the $20 line. I stopped as I was $18 ahead and could honestly brag I beat Vegas!
I grew up with riverboat gambling always available so there was nothing special to gambling.
Craps! Wife and I took a class in Vegas to learn and then went to Palms resort for their $5 tables. We played for ~2 hours ($160 buy in) playing a simple strategy, enjoyed our free drinks, and left $100 richer. The whole experience was a ton of fun!
What? Best bet would mean expected value (ie, bet vs return percentage on an infinite number of bets), capturing both odds of winning and payout of winning.
The best way to win money in the casino is to be the casino.
Just like how “the movie theater always wins”. Or anyone else selling you entertainment that you may like or not like.
Too many Redditors don’t seem to understand that gambling at a casino can be a fun activity and can be enjoyed in moderation like anything else that costs money.
IIRC the single best odds you can get in a single bet in a casino is the don’t pass line in craps.
Also apparently playing the perfect strategy on some video poker game has a small player edge, like 3% or something.
With continuous shuffle card machines this is no longer true. And the house odds percentage edge in blackjack has always been higher over the player than it is in craps. The only real game a player can have an edge at is poker where its players vs each other instead of the house.
Fun fact: your best single bet odds in a casino is walking up to a stranger and playing rock-paper-scissor for $50
Hi I just need some help with probability (forgot all my highschool math). There is a game in a nearby casino called French Boule and I wanted to know what the probability of winning 5 times in a row is.
Basically, the game consists of a ball you push down a ramp onto a square area that is dimpled with numbers 0-9. There are about 230 or so dimples that each carry a number between that range that is distributed seemingly randomly - and whichever dimple the ball settles into wins a 8x payout.
For example if I bet on 7 and the ball rolls around and settles in a dimple with 7 printed on it then I win.
So theoretically with a 100 dollar start, you could get 3.3 million with just 5 consecutive wins. What would the probability for this look like?
EDIT: Image of the game's platform. . Essentially the ball starts at the bottom indent at the small circle, and is then rolled down into the numbered area. Where the ball settles is the winning number
There is a lot of incorrect and/or misleading information in this thread. First, the expected return for this game, as a percent of initial wager, is -10%, meaning that, on average, the house takes 10 cents from every dollar that you risk. (It's not 20% as /u/FatherBrownstone indicates; when you wager a dollar and win, you win a net of $8, the house doesn't keep the dollar you initially wagered. It's also not 1/3 as /u/idk_lets_try_this indicates, and I can't find a reasonable interpretation that might suggest this value.)
As others have done, we may reasonably assume that the ball is equally likely to land on any given number. (/u/Tarron is incorrect in two different ways here: the distribution of outcomes is not normally distributed, or even approximately normally distributed. And if the distribution were indeed non-uniform, then it would matter; the fact that the player might "guess" just introduces a prior distribution on the wager.)
Finally, re the comment that "So you need to spend 100 USD, 100,000 times to hit 100%," the idea here seems to be that, if you have a one-in-100,000 chance of winning any single wager (each of which is actually five wagers of the game in question), then if you can afford to play 100,000 times, you are guaranteed to win? This is incorrect; the probability of winning is only about 1-1/e, or about 63.2%.
So does that mean the probability of winning one set of 5 games in a row in any given try is 63.2%/100,000 = 0.000632%
No the 63% chance is the chance to win at some point during 100 000 tries.
My math was correct but not entirely clear/ he just didn't understand it.
You are absolutely correct. The chance to win 5 times in a ow when playing 100 000times is indeed not 100%
My 1/3 statement came from the idea that with an infinite amount of money you would get enough 5 time wins to make back 1/3 of that. It is indeed not correct to assume this to be the case when only playing 100K times.
The 10% of every dollar is correct when looking at each wager individually but OP will keep playing until he either loses or gets 5 in a row. That scenario greatly changes the return in favor of the casino.
Alright.
So it’s like one of those coin games where you put a coin in at the top and it rolls down into a hole at the bottom, surpassing dimples that can make it bounce “randomly”. Each hole is numbered with 0-9.
So you have to guess correctly. There is a 1/10 chance that you’ll guess correctly. Since there are 10 numbers it can land on, spread out randomly over 100 holes. I’ve assumed that 0 is still a winning number if you’re guessing correctly. I’ve also made the broad assumption that each hole has the same winning chance, which I’ll explain later why that isn’t really a good thing. But it shouldn’t have anything to do with the real outcome, as the main problem here is not where it’ll land, but you guessing correctly, which isn’t a matter of probability.
Then for you to win 5 times in a row you simply multiply the odds of winning once, with itself five times. Or more mathematically speaking powered to five. Since the odds are individual, and doesn’t affect the next throw. So a^x where a is the odds and x is the number of times you’ll have to win.
So the equation will be: 1/10 * 1/10 * 1/10 * 1/10 * 1/10 = 0.00001 or 0.001%.
Tactics.
The problem lies in distribution. I can’t calculate this now. But mathematically speaking, the chances for the coin to land near the middle is greater than it landing near the edges, because of something called the normal distribution or probability distribution. So the odds ain’t all linear. But!! In your question you have to call out a number, and you could say any number with any probability, so the distribution of the curve hasn’t really got anything to do with the real outcome of the game.
I've added an image of the game's design. Does the distribution of numbers on the board make a difference?
Otherwise a 0.001% chance sounds like a very good payout possibility. So by spending 100,000 (consisting of 100 dollars played 1000 times) I will, probabilistically win 3.3 million. Won't that be against the casino's favor?
Alright, it made it simpler. It doesn’t change the outcome.
0.001% is a very, very small chance.
In your example you hit 1 yes, but that’s 1%. If you’re going for 1 as a decimal, you need to go for the 0.00001.
So you need to spend 100 USD, 100,000 times to hit 100%
I.e. 100,000 * 0.001 = 100
Spending 100 USD, 100,000 times = 10,000,000 which is not a good deal to get 3.3 million.
So it’s still very much I the casinos favor
They payout on this sounds terrible. If it has an equal chance of landing on the numbers 0-9, you have a 1 in 10 chance of winning to make a 8 to 1 payout?
Either way this should be pretty straight forward unless i'm missing something. If you have a 1 in 10 chance of hitting you number you probability of winning 5 times in a row (1/10)^5, which is .00001, or a 1 in 10,000 chance.
Are all numbers just as likely? Without a picture of the setup we will need to make some assumptions resulting in less accuracy.
Assuming that all 100 numbers are as likely you have a 1/100 chance of winning.
Then after you won that you have a 1/100 chance again, then again etc.
To get to the chance of getting 5 right in a row that is 1/(100^5 ) or 1/10.000.000.000 (one in 10 billion)
By comparison the UK national jackpot is about a 1 in 14 million chance and both powerball and mega millions in the US have a chance of about 1 in 175 million.
So yea, do not waste your money hoping you will win 5 times in a row you have a better chance buying lottery tickets but in the end you will be separated from your money in both cases.
Ok OP you just changed the entire question. You could have just replied to me too.
This setup you show means you have a 1/10 chance for the ball to land on the spot you guessed. For this to happen 5 times in a row is 1/10^5 or 1/100.000
That means that you have an average return of 1/3 what is not unusual for games like these.
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I tried to simulate a few strategies used for playing roulette, found that interesting. I have documented what I have done in this article and I think you'll also find that interesting. Please do give it a read and provide feedback!
Good article. My personal strategy is to ask myself 'do I want to enjoy myself, or make money?'
If 'enjoy myself', I take the $200 I would have blown at the casino, get a massage, buy a nice bottle of bourbon, then go to the grocery store and buy a nice cut of meat and all the fixins.
If 'making money' is my goal, I just open my brokerage app and drop $200 into VT and forget about it. Sometimes I take bigger swings. Last year when intel crashed I bought 486 shares 'for the aesthetic' lol
Probability of winning is just that, the chance that you will win, regardless of how much you bet. House edge is the expected percentage of your bet that you will lose, and it depends on how much you will win relative to what you have to wager to get it. The two are related, but can vary independently from each other. High probability of winning does not mean a low house edge, and low probability of winning does not mean a high house edge.
For example, imagine a bet that costs $150 and gives you a 99% chance of winning $1. Then the house edge is 1×0.99 + −150×0.01 = 51%. Even though you have a very high probability of winning, the house edge is huge due to the high cost of the bet relative to how much you win. If the cost of this bet were $100, it would have a house edge of 1%. If the cost were $98, the bet would have a player edge of 1%.
On the other hand, a bet with a 1% chance of winning a million dollars has a low probability of winning. But if the ticket costs $1, you have a massive player edge of 0.01×1,000,000 + −1×0.99 = 999,901%. That's because over enough iterations of the bet, you could expect to make more money than you lose — one win will compensate for a million losses, but it probably won't take you a million losses to get there. This bet has a low probability of winning, but a low house edge.
>For example, imagine a bet that costs $150 and gives you a 99% chance of winning $1. Then the house edge is 1×0.99 + −150×0.01 = 51%.
Not true at all, you're not betting $1, you're betting $150
A house edge of 51% when betting $150 would mean losing just over $75 on average each turn
The house edge would actually be 0.34%, which is about 1/300, this is because it would take about 300 spins for them to expect to win $150 from you
I blame youtube. Absolute morons like Professor Slots, Cowboy Slots, Jackpot Judo, and others have no understanding of even the most basic gamble concepts or math, but they claim to be experts and say things that are absolute bonkers lunacy. Because their audiences are all nomaths4eva folx, the stupidity not only goes unquestioned, but it gets repeated as a fact of truth.
Also, this really maths a failure, I tell you what.
EV of your game:
0.99*1 + (1-0.99)*-150 = -0.51
You will win -0.51 currencies per play.
However, you wager is 150 currencies, so the house edge or hold is 0.51/150, which is 0.0034 or 0.34%. You will lose 0.34% of your money each play.
If the degenerates here could read, they'd be very upset
I'm a surveillance agent and I literally lurk here just for material to laugh at and share with the boys. People that think they have a roulette system are the funniest.
But I can just martingale and chase my losses !! 🙄
That was awesome and I really appreciate that you took the time to map that out. I have always struggled to make sense of things like odds and probability. I have a better understanding now.
Okay so there’s this roulette strategy where you start with a bankroll of $1000 and bet $10 if you win put that $10 into a profit pile if you lose change your bet to $20 to make up for it and if you lose that bet $30 etc.. and the only way to lose money is if you are wrong 7 times in a row which you would end up with a $1000 loss. I’m trying to figure out how much money you are likely to make for every $1000 you lose. (Keep in mind for the times you don’t lose you have a 2/7 chance of making $10 for those first two turns)
so first you would find how many times you would win for every loss of 7 in a row. Then multiply that by the 2/7 chance of making $10. Multiply that number by 10 and if it is greater than 1000 good sir you have figured out how to beat the casino
Please let me know if this is correct when I do the math it works out but I don’t believe it someone double check please.
https://en.m.wikipedia.org/wiki/Gambler%27s_ruin
You're talking about a problem called "Gambler's ruin" using the martingale strategy.
If I understand the strategy right you bet 10 then 20 then 30 then 60 120 240 480, a total of 960, with bets 3-7 trying to compensate if you lose 1 and 2.
The chance of winning bet 1 is 0.49, and the chance of winning on bet 2 is 0.51*0.49.
The expected win is
10 x 0.49 + 10 x 0.51 x 0.49 - 0.51^7 x 960 = -1.216
Not surprisingly, it's negative! (If you change the odds to 0.5 it comes out zero as it should).
Thank you I knew I was doing something wrong
I used this martingale strategy playing red on a roulette game that started at 25 cent minimum and black came up 13 times in a row, lost everything. This is also why casinos have maximum bets too
No, you've got to be doing the math wrong. We don't need to grind it out to know that the strategy must have negative expected value. That follows automatically from the rounds being independent and each having negative expected value.
https://en.wikipedia.org/wiki/Martingale_(betting_system)#Intuitive_analysis
Exactly I get that but I’m getting 1111 for every 1000 lost and the math checks out it seems like it won’t work but somehow it does.
Scratch that I forgot to factor in one thing
Update I still didn’t get the math but I ran a simulator and it’s up about $1500 after 400 spins
Go to unibet and play roulette for fake cash. It looks like you're just using the martingale system.
It’s the same idea but changed up a bit where you have a max loss of $1000 and you don’t add two everytime
Games like Blackjack and craps and baccarat have less than a 1% house edge, while being almost no-skill games. Roulette also has less than a 5% house edge most of the time.
Moreover, when you play in a casino, you get free drinks and stuff which would otherwise cost you $5-10 each at a bar. And most casinos are nicer than bars. If you’re going to buy drinks anyways, you actually come out ahead if you play the odds.
Plus, casinos are heavily regulated which you can’t say about most other forms of gambling besides the state lottery.
Compare this to other forms of gambling such as:
Sports betting - the odds are created by statisticians and the house certainly have more than a 10% edge, especially on parlays which are basically 0% chance of winning
Scratch tickets - the best tickets reportedly have 1 in 3.5 odds of winning your money back, which is horrendous. That would be nearly the equivalent of having a 70% chance of losing in blackjack.
Mega-millions - your chance of winning $20 on a $5 ticket is 1 in 35. You’d have to be winning a 3-4% chance every 4 tickets just to make your money back. The bigger jackpots only have worse odds.
Opening booster packs (pokemon/yu-gi-oh/etc) - your chance of breaking even has to be lower than 50% otherwise the stores would just open the packs themselves. Plus, the store’s have a cost of selling which is passed onto you. Not to mention, it cost you significant time and effort to sell cards and there’s a very high risk of fakes/tampering on packs (resealing, weighing, etc). But at least this is fun unlike other forms of gambling
Conclusion - gambling will always be a loss in the long run. But if you must gamble, many casino games have a nearly 50/50 odds which is pretty amazing relative to most other forms of gambling
Thanks for the GPT garbage.
I agree that sports betting has more house edge, but your view on parlays is actually flawed. Saying that something has near 0% chance of winning isn’t the same as having a lot of house edge. If a parlay is fairly priced with 10% house edge legs, it still has 10% house edge.
It’s impossible to come up with a “fair price” for sports betting. Every house uses different formulas based on different things to come up with odds.
It’s not like blackjack or slots where the odds are guaranteed
You’re still mixing up probability with house edge, which leads me to believe that you’re conjuring up brainless GPT shit.
If you understood probability, you would realize that your comment on parlays made no sense, right?
Did you just say slots were gaurenteed?
Yeah I can see where you're coming from and you're right to a degree however, careful about getting too good or winning too much money at one casino. You'll quickly see how that nice changes into a shadow ban or ban.
They won’t ban you if you’re not counting cards or cheating. If you play enough you will eventually be at a net loss anyways
That's hardly ever the case. I promise you, unless you win other people's money that's one thing, you start winning the casino's money. You'll be out before you can say it's unfair.
Yup. They are amazing, those casinos. That’s why I keep going back.
You only get free drinks in Vegas or on cruise ships. Most casinos everywhere else do not give free drinks
All the casinos I’ve been too gave free drinks to whoever was gambling
Nevada, New Jersey, Mississippi, Louisiana, Pennsylvania, Colorado, Iowa and South Dakota all allow for comp drinks while gambling.
That’s not true lol. I’ve been to casinos in various states and have always had comped drinks. The only places I haven’t are small card rooms.
Never did table games before. I’ve only stuck with machine blackjack and slot machines. Slot machines drained me fast.
I flipped $200 into $550 though doing machine blackjack and machine roulette.
Obviously I want to experience the table, I’m very familiar with blackjack. I feel like if I do a table it would be for that or roulette.
How much should I be putting down on the tables based on what I have?
Craps pass line is best odds I believe, most fun game to play as well because it's a large group against the house.
Close. The Don’t pass “Dark Side” bet has the best odds on the craps table. Basically you’re betting against the shooter and want him to 7 out. When you place this bet and win, don’t celebrate because most of the other players will likely be betting on the pass line bet and have just lost
At the end of the day, the Pass Line is like dating someone way out of your league—it’s fun, it’s exciting, but deep down, you know it’s gonna end with you broke and confused. The Don’t Pass Line is like buying index funds—it makes financial sense, but you also look like the least fun guy at the party.
And the casino? Oh, they don’t give a damn either way. They just wanna keep you in the game, make sure you’re having JUST enough fun to keep losing money, and ensure that the words “Dark Side” keep you too scared to play the smart bet.
So next time you’re at the table, just remember: it’s all rigged, your odds suck, and no matter what you do, the house is always gonna shake you down like a mob boss with alimony payments. But hey, at least you’ll get a couple free drinks out of it.
This so called edge is too small to care and if you’re not a sociopath you’ll have more fun on the pass line. The don’t pass bet is for hermits (no offense). But the craps table is honestly the place to be in the casino. Keep your bets small and only bet on someone if you want to. You don’t have to bet on everybody.
When it comes to casino games with the best odds, generally, blackjack and certain types of bets in roulette tend to have better odds compared to slot machines.
In blackjack, the house edge can be quite low, especially if you learn and use basic strategy. This means you can potentially play for longer with your bankroll. On the other hand, roulette can be more unpredictable, but it can also be exciting to play. The odds in roulette can vary depending on the type of bet you place, with outside bets (such as red/black, odd/even) having higher chances of winning but lower payouts, and inside bets (such as specific numbers) having lower chances of winning but higher payouts.
Considering your budget of $550-$1,000 for 2 1/2 days, it's important to manage your bankroll wisely. Determine a daily gambling budget and consider dividing it into sessions. As a general rule, it's recommended to bet around 1-2% of your overall bankroll per round. For example, if you have $550, placing bets of $5-$11 per hand can help your gaming session last longer. However, it's always a personal decision, and you should feel comfortable with the amount you're betting.
Craps is so underrated. I used to take $100 on a $5 table and play for hours. Few times I played over 12 hours. The whole time I’m drinking for free and having fun.
It's intimidating to new people so they never play but yeah it's the best game. I won't stay at casinos that don't have live craps tables
Katsubet is where I play and made good money.
Best odds are 2 deck blackjack, followed by darkside craps, followed by pass line craps, followed by 6 deck blackjack, followed by baccarat, then Pai Gow, then single zero.
Edited for correction of order.
You probably don't have enough coin to find a 2 deck or single zero.
Where can I find 2 deck BJ?
OP, if you're looking for single zero roulette, MGM Grand has them. Walked through about an hour ago, if you're coming from the pedestrian walk, walk passed the Poker Room, passed the table games and its right before you get to the corner of slots.
For me the best odds are at aviator game actually. I just cash out from 1,2 to 1,5. And play usually 1 bet only. The best odds for me.
Aviator is my favorite. Plinko is good as well, but the odds are much lower.
odds of winning different casino games
Key Considerations for Casino Game Odds
Game Type: Different games have varying odds based on their rules and mechanics. Common categories include table games (like blackjack and roulette), slot machines, and poker.
House Edge: This is the casino's advantage over players, expressed as a percentage. The lower the house edge, the better the odds for players.
Payout Ratios: Understanding the payout ratios for different bets can help you gauge potential returns. For example, a game with a 95% payout means you can expect to win back $95 for every $100 wagered over time.
Skill vs. Luck: Some games, like poker and blackjack, involve skill and strategy, which can improve your odds. Others, like slots and roulette, are purely luck-based.
Odds Overview for Popular Casino Games:
Recommendation: If you're looking to maximize your odds, focus on games like blackjack and baccarat, where strategy can influence outcomes. Avoid high house edge games like certain slot machines and American roulette for better chances of winning. Always remember to gamble responsibly!
Get more comprehensive results summarized by our most cutting edge AI model. Plus deep Youtube search.