Roulette Odds, Explained
After reading this you can compute the exact win probability, payout and house edge of any roulette bet, and see why the wheel you choose matters far more than the bet you pick.
What roulette odds actually measure
A roulette wheel is a fixed lottery. Each spin lands on one of a known set of pockets, every pocket is equally likely, and the payout for winning is set in advance. Because all the numbers are known, you can calculate your exact chance of winning and your exact expected loss before you place a single chip.
Here is the hook. On a European wheel a straight bet on a single number pays 35 to 1. There are 37 pockets, so you win once in 37 spins on average. If the game were fair it would pay 36 to 1. That missing unit is the entire house edge, and it works out to 2.70% of every bet. Change to an American wheel with 38 pockets and the same bet, still paying 35 to 1, and the edge nearly doubles to 5.26%.
The payout never changes with the wheel. The number of pockets does. That single fact drives everything below.
When this calculator helps, and when it does not
Use it to compare bets and wheels before you play, to check that a casino is paying the standard odds, and to estimate what a night at the table costs on average. It answers three questions for one bet: how often you win, how much you win when you do, and how much the house keeps in the long run.
It does not predict the next spin. Roulette has no memory. If red has come up ten times running, the chance of red on the next spin is still 18/37 \approx 0.4865 on a European wheel. It also does not model betting systems like Martingale. Those change the shape of your wins and losses but never the expected value, because the edge applies to every chip independently.
No sequence of past results shifts the odds of a future spin. The wheel does not owe you a red. Any system that claims to beat a negative-edge game by changing bet sizes is rearranging variance, not removing the edge.
The formula and the intuition behind it
Every roulette bet covers some set of winning pockets. Let n be the number of winning pockets and N the total pockets on the wheel (37 European, 38 American, 39 triple-zero). The win probability is simply the fraction of pockets you cover.
Here p is your chance of winning a single spin, n is how many pockets pay you, and N is the count of all pockets. A corner bet covers 4 numbers, so on a European wheel p = 4/37 \approx 0.1081.
Each bet has a fixed payout b stated as "b to 1". A straight bet has b = 35, a corner has b = 8. The expected value of a one-unit bet combines the two outcomes: win b with probability p, lose 1 with probability 1-p.
The house edge is the negative of this expected value, expressed as a percentage of the stake. A positive edge means the house profits on average.
The term (b+1) \cdot p is the fraction of your stake returned on average, including the stake itself. For every standard bet on a European wheel this equals 36/37, so the edge is always 1 - 36/37 = 1/37 \approx 2.70\%. That is why the footnote on the calculator holds: every bet on the same wheel shares the same edge.
Worked example: a straight bet on the European wheel
Reproducing the demo
Set the wheel to European, the bet to straight, and the stake to 10, then read the results.
- Winning pockets: a straight bet covers n = 1 number, and the European wheel has N = 37 pockets.
- Win probability: p = 1/37 \approx 0.02703, or about 2.70%.
- Payout: 35 to 1, so a winning 10 unit stake returns your 10 plus 35 \times 10 = 350, for 360 back.
- Expected value per unit: 35 \times (1/37) - (36/37) = 35/37 - 36/37 = -1/37.
- House edge: 1/37 \approx 0.02703, so
2.70%. - Expected loss on 10 staked: 10 \times 0.02703 \approx 0.27, so you lose about 27 cents per spin on average.
The lump of 27 cents is small per spin. Over 100 spins at 10 each you stake 1000 in total and expect to lose about 27, but the swings around that are large: most of the time you finish a session down, occasionally you hit a 350 payout and finish well ahead.
Reading and interpreting the results
The three numbers work together. Win probability tells you how often, payout tells you how much, and house edge tells you the long-run cost. On a single wheel the edge is constant, so the choice between bets is a choice about variance, not about value.
| Bet | Pockets | Win prob. | Payout (to 1) | Edge |
|---|---|---|---|---|
| Straight | 1 | 0.02703 | 35 | 2.70% |
| Split | 2 | 0.05405 | 17 | 2.70% |
| Street | 3 | 0.08108 | 11 | 2.70% |
| Corner | 4 | 0.1081 | 8 | 2.70% |
| Six line | 6 | 0.1622 | 5 | 2.70% |
| Dozen | 12 | 0.3243 | 2 | 2.70% |
| Even money | 18 | 0.4865 | 1 | 2.70% |
Every row shows the same 2.70% edge. What differs is the ride. An even-money bet wins nearly half the time and returns a small amount. A straight bet wins once in 37 spins and returns a large amount. Same expected cost, wildly different experience.
Common mistakes
The most frequent error is believing that spreading chips across many bets lowers the edge. Covering 35 of 37 numbers on a European wheel does not help. Each chip loses 2.70% on average, so the total loss is still 2.70% of the total staked. You have only reduced the chance of a large swing.
A second mistake is treating the American and European wheels as interchangeable. They pay the same, but the extra double-zero pocket raises the edge from 2.70% to 5.26%. Over 1000 spins at 10 each, that is an expected loss of 270 versus 526. Always check the wheel first.
A third mistake concerns the "en prison" or "la partage" rule found on some European even-money bets, where you recover half your stake if zero hits. That halves the edge on those specific bets to about 1.35%. This calculator uses the standard rules without that concession, so treat its even-money edge as the worst case if your table offers la partage.
If you only care about lasting the longest on a fixed bankroll, bet even money on a European wheel. If you want the chance of a big win and accept losing most sessions, bet straight. The average cost is identical; only the shape of the outcome differs.
Related tools
Roulette has one of the cleanest edges to compute because every outcome is equally likely. Other games need more work. For blackjack, the edge depends on the exact table rules, so use the Blackjack House Edge calculator. For the dice bets and their very different edges, see Craps Odds. To turn any edge into a session cost across many spins, use the Expected Loss Calculator. And for reels rather than tables, the Slot Session Calculator shows both the expected loss and the spread.
Frequently asked questions
Why does every roulette bet have the same house edge?
Because the payouts are all set relative to a 36-pocket fair game while the wheel actually has more pockets. On a European wheel each bet returns 36/37 \approx 97.30\% of your stake on average, leaving a 2.70% edge no matter how many numbers you cover.
Which roulette wheel gives the best odds?
The European single-zero wheel, at a 2.70% edge. The American double-zero wheel is 5.26%, and the triple-zero wheel is 7.69%. Choosing European over triple zero cuts your expected loss by almost two thirds.
Does betting red every time improve my chances?
No. Red wins with probability 18/37 \approx 48.65\% on a European wheel on every spin, regardless of past results. The edge on red is the same 2.70% as on any other bet.
How much do I lose per hour at roulette?
Multiply your bet size by the edge by the number of spins per hour. At 10 per spin, 40 spins an hour, and a 2.70% edge, expect to lose about 10 \times 40 \times 0.027 = 10.8 per hour on a European wheel, and about 21 on an American wheel.
Can any betting system beat roulette?
No system changes the expected value, because the edge applies independently to every chip. Systems like Martingale can raise your chance of a small win in a session while adding a small chance of a very large loss. The average result stays negative.
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