Roulette odds calculator: the numbers behind every bet
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Every roulette odds question comes down to three numbers: how many pockets the wheel has, how many your bet covers, and what the bet pays if it wins. From those you can work out the probability, the fair payout, the house edge and what a session will cost on average. This page does the arithmetic for every standard bet on the three common wheels and shows the working, so you can check any table you sit at.
The formula, once
Probability of winning = numbers covered ÷ pockets on the wheel. Fair payout = (pockets − numbers covered) ÷ numbers covered, to 1. House edge = (fair payout − actual payout) × probability of winning.
For a straight-up on a European wheel: 1 ÷ 37 = 2.70% to win; fair payout (37 − 1) ÷ 1 = 36:1; actual payout 35:1; edge (36 − 35) × 1/37 = 2.70%. The same working gives 2.70% for every bet on that wheel, because every payout is set as if the wheel had 36 pockets.
European wheel: 37 pockets
| Bet | Covers | Wins | Pays | Edge |
|---|---|---|---|---|
| Straight-up | 1 | 2.70% | 35:1 | 2.70% |
| Split | 2 | 5.41% | 17:1 | 2.70% |
| Street | 3 | 8.11% | 11:1 | 2.70% |
| Corner | 4 | 10.81% | 8:1 | 2.70% |
| Six line | 6 | 16.22% | 5:1 | 2.70% |
| Dozen / column | 12 | 32.43% | 2:1 | 2.70% |
| Even-money | 18 | 48.65% | 1:1 | 2.70% |
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American wheel: 38 pockets
Same payouts, one more pocket. Every probability drops and every edge rises to 5.26%: a straight-up wins 2.63% of the time, red 47.37%. The five-number basket (0, 00, 1, 2, 3) pays 6:1 against a fair 6.6:1 and carries a 7.89% edge, the worst standard bet on any roulette layout.
French wheel: 37 pockets with La Partage
Inside bets, dozens and columns: identical to European, 2.70%. Even-money bets: when zero comes up, half the stake is returned. That halves the edge on red, black, odd, even, high and low to 1.35%. If a table offers En Prison instead, the stake is held for the next spin with a near-identical effect.
From edge to cost
Expected loss = stake × spins × edge. The table below is per 100 spins.
| Stake | European 2.70% | French even-money 1.35% | American 5.26% |
|---|---|---|---|
| £1 | £2.70 | £1.35 | £5.26 |
| £5 | £13.50 | £6.75 | £26.30 |
| £10 | £27.00 | £13.50 | £52.60 |
These are long-run averages. One session of 100 spins at £5 on red will land anywhere from about £60 down to £50 up most of the time; the £13.50 is what it costs on average across many such sessions.
Multiplier tables
Live tables with random multipliers usually pay 29:1 on an unstruck straight-up instead of 35:1. Run that through the formula: (36 − 30) × 1/37, allowing for the multiplier rounds that pay out on average, comes to roughly 2.90% on straight-ups against 2.70% on a plain table. Outside bets on the same table are unchanged. The exact figure depends on the multiplier frequencies, which the game publishes as an overall return.
Using the numbers
Pick the wheel with the lowest edge available, which is French for outside bets and European otherwise. Pick a bet by the variance you want, since the edge is the same across the layout. Multiply stake by spins by edge before you start and decide whether that figure is a price you are happy to pay for the session. If it is not, change the stake or the spin count, because nothing else on the table will change it.
Put it into practice
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Short answers
How do you calculate roulette odds?
Divide the numbers your bet covers by the pockets on the wheel. Red covers 18 of 37 on a European wheel, so 18 ÷ 37 = 48.65%. A straight-up covers 1 of 37, so 2.70%. On an American wheel divide by 38 instead.
What is the house edge formula?
Edge equals the gap between what a bet should pay for a fair game and what it does pay, as a share of the stake. On a European wheel every standard bet comes out at 1/37, which is 2.70%.
Which wheel gives the best odds?
French, for even-money bets, at 1.35% with La Partage. European at 2.70% for everything else. American at 5.26% is the worst of the three for every bet.