The Probability Behind Roulette
Roulette is the most honest game on the casino floor about how it makes money — if you know where to look. The whole edge lives in a tiny gap between the odds of winning and the amount you get paid for winning. Find that gap and the wheel stops being mysterious. It's the same trick on every bet, dressed up in green felt.
The wheel: 37 or 38 pockets
A roulette wheel has numbers 1 through 36, colored red and black, plus one or two green zeros. That zero count is everything.
- European wheel: 37 pockets — 1 to 36 plus a single 0.
- American wheel: 38 pockets — 1 to 36 plus 0 and 00.
The numbers 1–36 are split evenly: 18 red, 18 black, 18 odd, 18 even. If the wheel stopped there, even-money bets like red/black would be a true coin flip. The zeros are what break the symmetry — and that broken symmetry is the house's entire business model.
True odds vs payout odds
Here's the heart of it. When you bet a single number on a European wheel, your chance of winning is 1 in 37. Fair odds — odds that would make the bet break even — would pay you 36 to 1 (your stake back plus 36 times it, so the 36 losing spins are covered by the one win). On an American wheel with 38 pockets, fair odds would be 37 to 1.
But the table pays a single number only 35 to 1, on both wheels. That shortfall — getting paid as if there were 36 pockets when there are really 37 or 38 — is the house edge, quietly skimmed off the top of the winners.
Key idea: roulette doesn't take a fee when you lose. It takes it by underpaying when you win — paying true-but-shrunken odds that pretend the zeros aren't there.
Every bet, same edge
Newcomers assume "outside" bets like red/black are safer than betting a single number. They're less volatile — you win far more often — but the house edge is identical. On a single-zero wheel, almost every bet carries the same 2.70% edge; on a double-zero wheel, almost every bet carries 5.26%. The math is engineered so it doesn't matter where you place your chips.
| Bet type | Numbers covered | Payout odds | True odds (European) |
|---|---|---|---|
| Single number | 1 | 35 to 1 | 36 to 1 |
| Split (two numbers) | 2 | 17 to 1 | 17.5 to 1 |
| Corner (four numbers) | 4 | 8 to 1 | 8.25 to 1 |
| Dozen / column | 12 | 2 to 1 | 2.083 to 1 |
| Red / black, odd / even | 18 | 1 to 1 | 1.056 to 1 |
Look down the table: in every row, the payout odds are slightly stingier than the true odds, and the gap always works out to the same 2.70%. Spreading chips across the felt doesn't dodge the edge — it just averages it.
The handful of exceptions
There are a couple of footnotes. Some European tables offer "la partage" or "en prison" rules, which return half your even-money bet (or hold it for one more spin) when the ball lands on zero. That cuts the edge on those specific bets roughly in half, to about 1.35%. Going the other way, one American bet — the five-number row of 0, 00, 1, 2, 3 — is the sucker's special, carrying a worse-than-usual 7.89% edge. Outside of those, the edge is flat across the table.
On Riskr, the Roulette table runs on these exact odds — single number pays 35 to 1, the zero does its quiet work — only the chips are fake. It's the cleanest way to watch true odds and payout odds drift apart, with nothing real at stake.