Casino math basics come down to one idea: every bet pays a little less than its true odds, and that gap, the house edge, is the casino's built-in profit. Once you know how to turn probabilities into expected value, you can price any game, any bonus and any session in dollars before you play.
The house edge is the gap between what a bet pays and what its true odds would justify.
Expected loss equals total amount wagered times the house edge; RTP is simply 100% minus the edge.
Variance explains short-term wins and losses, but over many bets the edge takes over.
No betting pattern changes the math, because the edge applies to every single bet.
House edge
100% − RTP
Expected loss
Total wagered × house edge
European roulette (RTG)
97.3% RTP reported, 2.7% edge
Jacks or Better (RTG)
99.54% RTP reported
Short-run swings
Grow with the square root of the number of bets
Why casino math basics matter for US players
Casino games are designed so the operator wins over time, and the design is visible in the numbers. You don't need advanced math to see it: fractions, percentages and multiplication are enough. With those you can answer the questions that actually matter, such as what an evening of slots costs on average and whether a bonus is worth taking.
Knowing the math helps you make informed choices. It doesn't create an advantage over the casino: the house edge means losses are the expected result over time.
Probability, odds and payouts
Probability is the chance an outcome happens, written as a fraction or percentage. A single-zero roulette wheel has 37 pockets, so the chance of any one number is 1 in 37, or about 2.7%. Two dice have 36 combinations, and six of them total 7, so the chance of rolling a 7 is 6 in 36, or 1 in 6.
Odds and payouts are not the same thing. True odds compare losing outcomes with winning ones: a single roulette number has true odds of 36 to 1. The payout is what the casino actually pays: 35 to 1. That one-unit gap is where the casino's edge on that bet comes from.
Converting between probability, true odds and a fair payout
The house edge is the average amount the casino keeps from each dollar bet, expressed as a percentage. You calculate it by weighting every result by its probability and adding them up.
List every possible result of the bet.
Write down the probability of each result.
Write down what you win or lose on each result, per $1 bet.
Multiply each win or loss by its probability.
Add the products. A negative total is the house edge per dollar.
Worked example: a $1 straight-up bet on European roulette
You win $35 with probability 1/37 and lose $1 with probability 36/37. Expected value = (1/37 × $35) − (36/37 × $1) = $35/37 − $36/37 = −$1/37, or about −2.7 cents per dollar. That's a 2.7% house edge.
Now try red. You win $1 with probability 18/37 and lose $1 with probability 19/37. Expected value = 18/37 − 19/37 = −1/37. Same 2.7%. On this wheel, the edge is the same whichever standard bet you choose, which is why picking "safer" bets doesn't lower the cost. Our European Roulette page covers the game itself.
A hypothetical paytable
Suppose a game paid 4 to 1 on a dice total of 7, when the true odds are 5 to 1. Expected value per $1 = (6/36 × $4) − (30/36 × $1) = $24/36 − $30/36 = −$6/36, a 16.7% house edge. Check paytables before you play; short payouts on long-odds bets are usually where the steepest edges hide.
RTP and house edge: two sides of one number
Slots and video poker usually advertise return to player (RTP) instead of house edge. RTP is the share of all money wagered that a game is designed to pay back over a very large number of plays. House edge is 100% minus RTP.
Reported RTPs of RealTime Gaming titles and the matching house edge
Expected loss is the single most useful number in casino math. Multiply the total you wager (not the total you deposit) by the house edge.
Expected loss for example sessions (illustrative pace)
Session
Total wagered
House edge
Expected loss
600 hands of Jacks or Better at $5
$3,000
0.46%
$13.80
600 slot spins at $1 on a 96% slot
$600
4%
$24
60 roulette spins at $10, single zero
$600
2.7%
$16.20
300 slot spins at $5 on a 94% slot
$1,500
6%
$90
Notice that the video poker session wagers five times as much as the slot session yet costs less, because the edge is so much lower. Bet size and game choice matter more than any "system". The pace of play is your choice; we've used round numbers so the arithmetic is easy to follow.
Turnover grows quickly because winnings get re-bet. A $100 deposit played at $1 a spin can easily turn over $1,000 before it's gone, and the expected loss tracks that $1,000, not the $100. Our guide to bankroll management turns this into session rules.
Variance: why you can win tonight and still lose over time
If the edge were the whole story, every session would lose a little. In reality results swing widely. That spread is called variance, and it's measured with the standard deviation.
For an even-money bet, the standard deviation of one $10 bet is about $10. Over many bets, the expected loss grows in line with the number of bets, but the typical swing grows only with its square root. That's why luck dominates short sessions and the edge dominates long ones.
Red at European roulette, $10 per bet (rounded)
Number of bets
Total wagered
Expected loss
Typical swing (one standard deviation)
100
$1,000
$27
About $100
1,000
$10,000
$270
About $316
10,000
$100,000
$2,700
About $1,000
After 100 bets, a player could easily be up $70 or down $130; the swing is far bigger than the edge. After 10,000 bets the expected $2,700 loss is larger than a typical swing, so most players in that position are behind. Slots add another layer: high-volatility games pack more of their RTP into rare large wins, which makes swings bigger still. See slot volatility explained.
Streaks and probability: why nothing is ever due
Each spin, hand or roll is independent. The wheel and the random number generator have no memory, so past results don't change the next probability.
The chance of red losing five times in a row on a single-zero wheel is (19/37) to the fifth power, about 3.6%, or roughly 1 in 28.
Ten losses in a row is about 0.13%, roughly 1 in 784.
Over hundreds of bets, several five-loss runs are to be expected, which is why doubling systems eventually hit a run they can't recover from.
The "gambler's fallacy" is the belief that a result is due because it hasn't happened lately. A slot isn't due to pay and a color isn't due to hit. Our pages on roulette strategies and whether online slots are rigged cover the most common myths.
Casino math for bonuses and wagering
The same formulas price a bonus. The cost of clearing it is the wagering requirement (in dollars) times the house edge of the game you play. Compare that cost with the bonus amount.
SlotoCash's welcome terms set 25x (deposit + bonus) on its five-deposit series. A $100 deposit with a $200 bonus means $300 × 25 = $7,500 of required bets. On a 96.25% slot such as Sweet 16, the expected cost is $7,500 × 3.75% = $281.25. The bonus is $200, so on average you'd finish about $81 behind the $100 you deposited, before considering variance.
Use total wagered, which is usually several times the deposit
"Outside bets have a lower edge"
On single-zero roulette every standard bet is −1/37
Lower variance, same edge
"Bigger bets after losses recover money"
The edge applies to each bet
Total wagered rises, so expected loss rises
"A big jackpot means a better game"
Jackpot funding often lowers base-game returns
Check the reported RTP and the paytable
If you want a one-page refresher, the glossary entries for house edge and RTP sum up the key terms.
Putting casino math to work: offers via our links
If you choose to play, run these sums on any offer before you claim it. The casinos below run RealTime Gaming or its Spinlogic brand, according to third-party reviews. All three are offshore and not licensed or regulated by any US state, so there's no state regulator to take a complaint to and no state protection of balances. Only seven states license real-money online casinos (see states with legal online casinos), so check your state's law first.
Slot Madness Casino: $2,500 Welcome Bonus + 50 Free Spins, via our link (new players, 21+ or 18+ where allowed, terms apply). Third-party reviews report 30x (bonus + deposit) wagering on slots, a $30 minimum deposit and no max cashout; they also report the casino runs only RTG games. Read our Slot Madness review.
SlotoCash Casino: $6,000 Welcome Bonus + 60 Free Spins, via our link (new players, 21+ or 18+ where allowed, terms apply). Its terms list 25x (deposit + bonus), a $20 minimum per bonus and no max cashout; the package on its own site differs, and the sign-up terms apply. Read our SlotoCash review.
Decode Casino: $5,000 Welcome Bonus + 50 Free Spins, via our link (new players, 21+ or 18+ where allowed, terms apply). Decode doesn't show its terms publicly; third-party listings report 25x–35x (deposit + bonus) wagering and $25 minimums. Read our Decode review.
Bonus funds and free spins are slot-focused; table games are often excluded or weighted lower. Codes and terms change, so check the current terms before depositing. We earn a commission through these links, and the ranking is commercial. If gambling stops being fun, the National Problem Gambling Helpline (opens in a new tab) is at 1-800-MY-RESET.
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These partners are offshore and not licensed by any US state. Check your state's law first. 21+ (18+ where allowed), terms apply.
Published terms (reported): Third-party reviews report a 275% match up to $2,750 with code MAD275; the casino site could not be checked directly. Eligible games: Slots and keno (reported).
Who runs it: License not shown; third parties report Anjouan, Costa Rica or none. Regulator notes: Named in a Michigan Gaming Control Board cease-and-desist release, August 14, 2025.
21+ (18+ where allowed). New players. Min deposit $30 (reported). Wagering 30x deposit + bonus (reported). Max cashout: None (reported). Withdrawal cap $2,500 / week (reported). Terms source: reported. Terms apply. Offer checked October 28, 2026.
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21+ (18+ where allowed). New players. Min deposit $20 per bonus. Wagering 25x deposit + bonus. Max cashout: None stated. Withdrawal cap $5,000 / week. Terms source: casino terms. Terms apply. Offer checked October 28, 2026.
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Who runs it: License not shown on its site; third parties report Curaçao. Regulator notes: Third parties report it refuses players in MD, NJ, NY and WA.
21+ (18+ where allowed). New players. Min deposit $25 (reported). Wagering Varies by code (25x–35x reported). Max cashout: Varies by code. Withdrawal cap $2,500 / week (reported). Terms source: reported. Terms apply. Offer checked October 28, 2026.
These casinos are offshore operators. They are not licensed or regulated by any US state, and state consumer protections do not apply. Check the law in your state before you play. Terms marked “reported” come from third-party reviews; the terms shown at sign-up apply.
21+ (18+ where allowed). Every casino game has a built-in house edge, so over time you should expect to lose what you stake. Set a budget before you play and stop when it’s gone: responsible gambling tools and free help. Gambling problem? Call or text 1-800-MY-RESET (1-800-697-3738).
Frequently asked questions
What is the basic math behind casino games?
The basic math is that every bet pays slightly less than its true odds, and that gap is the house edge. On single-zero roulette a single number has true odds of 36 to 1 but pays 35 to 1, giving a 2.7% edge. Multiply the edge by the total you wager to get your expected loss. House edge explained goes through more games.
How do you calculate house edge on a roulette bet?
You calculate house edge by multiplying each possible result by its probability and adding the products; a negative total is the edge per dollar. For a $1 bet on red at single-zero roulette: 18/37 × $1 minus 19/37 × $1 equals −$1/37, or 2.7%. For slots and video poker, subtract the published or reported RTP from 100%. See the glossary entry for house edge for a short definition.
What is the difference between RTP and house edge?
RTP and house edge describe the same thing from opposite sides: RTP is the share of wagers a game pays back over the long run, and house edge is the share it keeps. A slot with a reported 96% RTP has a 4% house edge. Both are long-run averages, so a single session can be far from them. For how RTP is measured, see how slot RTP works.
How much will I lose per hour at a casino?
Your expected hourly loss is bets per hour times average bet times house edge. For example, 600 spins at $1 on a slot with a 4% edge works out to $24 an hour on average. Actual results vary widely because of variance, especially on high-volatility slots. Slowing down, betting less or choosing a lower-edge game all reduce the figure. Our bankroll management guide turns this into session limits.
Can math give you an edge over the casino?
No, math explains casino games but doesn't let you overcome the house edge. Basic strategy in blackjack and correct video poker play reduce the edge, but they don't reverse it, and online RNG blackjack reshuffles every hand. Betting systems change how losses are spread, not their expected size. Use the math to choose games and limits instead. Our roulette strategies page shows why systems fail.
What is variance in gambling?
Variance is the spread of results around the average, and it's why you can win in one session even though the expected result is a loss. It grows more slowly than the expected loss: over 100 even-money bets of $10, the typical swing is about $100 against an expected loss of $27. Over 10,000 bets, the expected loss of $2,700 outweighs the typical $1,000 swing. Read slot volatility explained for slot-specific detail.
Is a slot ever due to pay out?
No, a slot is never due to pay out, because each spin is independent and decided by a random number generator. A long losing run doesn't make a win more likely on the next spin. This mistaken belief is known as the gambler's fallacy. Our page on how RNGs work explains the technology, and are online slots rigged covers common concerns about fairness.
How does casino math apply to bonuses?
Casino math prices a bonus by comparing the bonus amount with the expected cost of meeting the wagering requirement. Multiply the required turnover by the game's house edge. A $300 balance with 25x wagering needs $7,500 of bets; at a 3.75% edge, that costs about $281 on average, more than a $200 bonus. The full method is in our expected value of a bonus guide.
Which RTG casino game has the lowest house edge?
Among the RealTime Gaming titles with reported figures, Super 21 and Jacks or Better have the lowest house edge, at about 0.4% and 0.46%. Third-party sources put Super 21’s return at 99.6% and Jacks or Better’s at 99.54% with perfect strategy, so $1,000 wagered costs roughly $4 to $4.60 on average. Mistakes push the real figure higher, and casinos can run different settings, so treat these as reported. Slots sit lower, often at 94% to 97.5%. See what is the best casino game to win and our video poker guide.
What is the house edge on Tri Card Poker?
Third-party game databases report a 95.51% return for RTG’s Tri Card Poker, which works out to a house edge of about 4.49%. That’s higher than blackjack or video poker played well, and higher than many slots in the reported range. In dollars, 60 hands at $10 means $600 wagered and an expected loss of about $26.94. Because the figure is reported rather than published by the partner casinos, check the game’s help screen. Our Tri Card Poker game page and how to play Three Card Poker guide explain the bets.
How do you calculate the expected cost of a Slot Madness bonus?
Multiply the deposit plus bonus by the wagering multiple, then by the game’s house edge. Third-party reviews report Slot Madness’s MAD275 code as a 275% match with 30x (bonus + deposit) wagering on slots. A $100 deposit adds $275, so $375 × 30 = $11,250 of required bets, and on a 96.25% slot with a 3.75% edge the expected cost is about $421.88, more than the bonus. Codes and terms change, so use the figures at sign-up. See the Slot Madness welcome bonus page and our bonus value calculator method.
What are the odds of losing 10 roulette spins in a row?
On a single-zero wheel, the chance of red losing ten spins in a row is about 0.13%, or roughly 1 in 784. Each spin has a 19-in-37 chance of not landing red, and you multiply that probability by itself ten times. That sounds rare, but over thousands of spins such runs are expected, which is why doubling systems like the Martingale eventually hit a streak that exhausts the bankroll or the table limit. See is Martingale a good strategy and our gambler’s fallacy guide.
Why is casino expected loss based on total wagered, not my deposit?
Because winnings get re-bet, the amount you put through a game is usually several times what you deposited, and the house edge applies to every bet. A $100 deposit played at $1 a spin can easily turn over $1,000 before it runs out. On a slot with a 4% edge, the expected loss tracks that $1,000, about $40, not 4% of the $100. That’s why game choice and bet size matter more than deposit size. Our gambling budget guide and low stakes guide put this into practice.
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