How we calculate the odds: exact maths first, simulation where needed

The principle behind every figure

A bet's value depends on two things: the probability of each result, and what the bet pays when that result happens. Multiply one by the other for every result, add them up, and you have the expected return per pound staked. The house edge is that return with its sign turned round. We use this definition everywhere, so a figure on one page can always be compared with a figure on another. The house edge explained page works it through with examples.

Wherever a game can be counted exactly, we count it. Only where counting every case would take too long do we simulate, and a simulated figure is always labelled as one, with the size of the sample.

Casino games, one method each

Roulette: counting pockets

A roulette wheel is the simplest case. A European or French wheel has 37 pockets and an American wheel 38, each equally likely. For every bet we count the pockets it covers, set that against the payout, and read off the edge. Red on a European wheel covers 18 of 37 pockets and pays even money, so the expected return is 18/37 − 19/37 = −1/37 and the edge is 2.70%. La Partage, which returns half an even-money stake on zero, is added as a separate result, which halves that edge to 1.35%.

Blackjack: exact expected values

Our blackjack engine calculates the expected value of every possible decision for every starting hand against every dealer up card. It assumes an infinite deck, in which each card from ace to nine keeps a chance of 1 in 13 and ten-value cards 4 in 13 on every draw. The rules modelled are a common set: the dealer checks for blackjack under an ace or ten, a pair may be split once, split aces receive one card each, and doubling after a split is allowed unless a rule says otherwise. The best play on each hand then gives the house edge: 0.57% for a table paying 3 to 2 where the dealer stands on soft 17.

An infinite deck is a close model but not a perfect one. Published figures for the same rules with six decks come out a little lower, because each card dealt changes the make-up of a real shoe. The win, lose and push shares shown on the blackjack odds page come from 2,000,000 rounds played by the same engine's best decisions, and are rounded to one decimal place.

Baccarat: the whole eight-deck shoe

Baccarat has no decisions, so every hand follows fixed drawing rules. That makes an exact count possible: every way the first four, five or six cards can come out of an eight-deck shoe, weighted by how many ways each can happen. The count gives banker 45.86%, player 44.62% and tie 9.52%, and from those the banker edge of 1.06% after commission.

Craps: 36 combinations

Two fair dice give 36 equally likely combinations, and every craps bet is a question about them. One-roll bets are read straight off the combinations. Bets that last several rolls, such as the pass line, use the chance that a number appears before a 7, which is its number of combinations divided by that number plus six. The pass line comes out at exactly 244/495 to win, an edge of 1.41%. The craps odds page shows the working for every bet.

Slots: the published return

A slot's return to player is decided by its maker, who sets the reel strips and the paytable. We do not guess or estimate those settings for individual games. UK slots publish their RTP in the game rules, and that is the figure to use; most sit between 94% and 97%. To show how an RTP arises, the slot machine odds page uses one example slot whose return we calculate exactly by counting every combination of reel positions against its paytable: 96.04%.

Poker: enumeration and sampling

The chance of being dealt each five-card hand comes from counting all 2,598,960 possible hands. For match-ups between known hands, the poker odds calculator counts every remaining board exactly once at least three board cards are known. Before the flop there are too many boards to count in a browser, so it deals 100,000 random boards for two or three hands, or 60,000 for four to six, and reports the result as a sample. With that many boards the standard error on a share near 50% is about 0.2 percentage points, so the answer is usually within 0.3 points of the exact one. The hand evaluator itself is checked against exact results, such as A♠A♥ v K♦K♣ winning 81.06% of the time over all 1,712,304 possible boards.

Lotteries: counting combinations

A lottery draw is pure counting. The number of ways to choose the winning numbers gives the jackpot odds, and the tiers below come from counting the ways to match some numbers and miss the rest. EuroMillions draws 5 from 50 and 2 Lucky Stars from 12, so there are 139,838,160 possible lines, one of which wins the jackpot. Lotto has drawn two rounds from the same 6 from 59 since June 2026: one round has 45,057,474 combinations, and either of two rounds gives a chance of 1 in 22,528,737.25 per draw.

The operators publish rounded figures, nearly always rounded up, so the Lotto jackpot above is published as 1 in 22,528,738. Our pages show the operator's figure next to each prize and use the exact value in the calculators. The game rules, prices and prize amounts come from the operators' published game procedures for each draw and from the Gambling Commission's breakdown of where National Lottery money goes. All of these were checked on 24 September 2026, and the few points we could not confirm are recorded with our sources.

How we round

Figures are calculated at full precision and rounded only once, at the moment they are displayed. A house edge is shown to two decimal places, with trailing zeros dropped from figures of 1% and above: a European wheel shows 2.70%, a 96% slot shows 4%, and an edge below 1% always keeps two decimals, as with 0.57%. Chances to win are shown to one decimal place, and lottery odds as "1 in" a whole number once they pass 100. Because every page reads the same stored value, the same bet shows the same figure everywhere.

Independent checks

Each calculator and table is recomputed by a separate program, using a different method from the one the page uses: where the site uses a formula, the check counts every case by brute force, and the other way round. The two must agree before a figure is published. Each tool also has a short list of test inputs with the answers it should give, which we run by hand.

Edition

This edition of the site was calculated and published on 2 October 2026. The maths of a casino game does not change unless its rules do, but lottery formats and prizes can, and if a game changes, its page is recalculated. If a number here looks wrong to you, please tell us. Knowing the odds tells you what gambling costs; it never turns it into income, and the responsible gambling page has free help if the cost is becoming a worry.

Where to go next

Our method: questions people ask