Casino odds and maths
Casino maths explains what every bet costs: the house edge, RTP, variance and probability behind each game, with worked examples in pounds. Start here to see why the casino wins over time, how to compare games and why no system changes the numbers.
By the BonusKing editorial team. Last checked .
Casino maths in one line: the house edge
Casino maths comes down to one gap: the difference between the true odds of a bet and what it pays. A straight-up roulette bet on a single-zero wheel wins 1 time in 37, so fair odds would be 36 to 1, but it pays 35 to 1. That missing unit, spread over 37 spins, is the house edge of 2.70%. The general formula, when a bet pays x to 1 and the true odds against it are y to 1, is (y − x) ÷ (y + 1).
RTP is the same figure seen from the player’s side: a 96% RTP slot has a 4% edge. Multiply the edge by the total you stake and you have your expected loss, which casinos call theoretical loss. £10 a spin for 60 spins an hour over three hours at 2.70% comes to £48.60 on average.
Casino odds compared: house edge by game
| Game and bet | House edge | Average cost per £10 |
|---|---|---|
| Video poker, 9/6 Jacks or Better (optimal play) | 0.46% | 5p |
| Blackjack, six decks, European rules (basic strategy) | 0.62% | 6p |
| Baccarat, Banker bet | 1.06% | 11p |
| Roulette, French even-money bet with La Partage | 1.35% | 14p |
| Craps, Pass line | 1.41% | 14p |
| Casino Hold’em, Ante (common pay table) | 2.16% | 22p |
| European roulette, any bet | 2.70% | 27p |
| American roulette, most bets | 5.26% | 53p |
| Baccarat, Tie at 8 to 1 | 14.36% | £1.44 |
| Keno (typical) | 25% to 29% | £2.50 to £2.90 |
Figures come from standard game maths and Wizard of Odds’ house edge tables (opens in a new tab). Blackjack and video poker figures assume correct strategy and the stated rules; check each game’s rules screen. Our full house edge table covers more bets.
Sections
All pages in this section
Variance, probability and why streaks mean nothing
The house edge tells you the average; volatility tells you how far one session can stray from it. Expected loss grows in step with the number of bets, but the spread of results grows only with its square root, so short sessions swing widely and long ones drift towards the edge. That is why a winning night says nothing about whether a game is beatable.
Every spin, roll and online deal is independent. Red is 18 in 37 on a single-zero wheel whatever came before, and believing otherwise is the gambler’s fallacy. UK rules back this up: RTS 7 (opens in a new tab) requires online results to be acceptably random and bans compensated games that adjust to past outcomes, and approved test houses check games before release.
Where to start with casino maths
- New to the numbers? Read probability basics, then house edge, then expected value.
- Choosing a game? Compare cost per hour on our cost per hour page or with the house edge calculator.
- Wondering about systems? Our gambler’s ruin page shows why a limited bankroll against a house edge runs out eventually.
18+. 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: safer gambling tools and support. Free, confidential help: National Gambling Helpline 0808 8020 133.
Frequently asked questions
What is the house edge in simple terms?
It is the share of each bet the casino keeps on average over a very long run. A 2.70% edge means that, across thousands of £10 bets, you lose about 27p per bet on average, though any single session can be far above or below that. It comes from paying less than the true odds. Our house edge guide shows the calculation for roulette, blackjack and slots.
Which casino game has the best odds?
Among common games, full-pay video poker and blackjack with good rules have the lowest house edges, at 0.46% for 9/6 Jacks or Better and around 0.62% for six-deck European-rules blackjack, both with correct strategy. Baccarat’s Banker bet at 1.06% needs no strategy at all. Our page on games with the best odds ranks them and explains the rules that change each figure.
Is RTP the same as the house edge?
They are two views of one number. RTP is the share of stakes a game returns on average, and the house edge is the rest: 96% RTP means a 4% edge. Slots usually quote RTP, while table games usually quote house edge. Both are long-run averages and say nothing about one session. Our RTP vs house edge page converts between them for common games.
Can a betting system beat the house edge?
No. Every bet in a system carries the same edge, so changing stake sizes changes how results are spread, not the average cost. Martingale-style doubling wins small amounts often but risks large losses and table limits. Wizard of Odds’ simulations show the loss-to-bet ratio heading to the edge whatever the system. Our gambler’s ruin page explains why.
Are online casino games random in the UK?
Yes, they must be. Gambling Commission technical standards require online outcomes to be acceptably random and unpredictable, and ban games that adjust results to make up for past wins or losses. New games and random number generators are tested by approved test houses before release. Our guide to how casino games are tested explains what the checks cover.