How this instrument works
A roulette payout is quoted as a ratio, like 35:1 for a straight-up bet on a single number — win, and you receive 35 units of profit for every 1 unit staked, plus your original stake back. If that payout matched the true odds of winning exactly, the game would be fair with no advantage to either side. On a European wheel, a single number has a 1-in-37 chance of hitting, so a truly fair payout would be 36:1 — but the casino pays only 35:1, one unit short of fair. That one-unit shortfall, spread across every possible outcome, is exactly what generates the house edge.
The house edge itself comes out to (wheel pockets - 36) / wheel pockets x 100%. A European wheel has 37 pockets (numbers 1-36 plus a single zero), giving an edge of 1/37 ≈ 2.70%. An American wheel adds a second zero (00), for 38 pockets total, nearly doubling the edge to 2/38 ≈ 5.26%. That extra pocket is the entire reason American roulette is mathematically worse for players than the European version — same betting rules, same payout ratios, just one additional way to lose.
A subtle but important fact: on a given wheel, every standard bet type carries the same house edge, regardless of its payout ratio. A straight-up bet (35:1, on 1 number) and a corner bet (8:1, on 4 numbers) both have exactly a 2.70% house edge on a European wheel, because the higher payout on the rarer, single-number bet is offset exactly by its lower chance of winning — the expected-value arithmetic works out identically either way. The one well-known exception is the American-only five-number bet (0, 00, 1, 2, 3, paying 6:1), which carries a noticeably worse house edge of about 7.89% and isn't modeled by this instrument's standard formula.
- Choose your wager from Bet type — straight-up, split, street, corner, six line, dozen/column, or an even-money bet, each with its standard payout ratio.
- Choose European (37 pockets, single zero) or American (38 pockets, double zero) from Wheel type.
- Read Payout ratio (X : 1) for how much profit you'd win per unit staked on a winning bet.
- Read House edge (%) for the long-run percentage of every bet the casino expects to keep, on average, for standard bets on that wheel.
- The American five-number bet (0, 00, 1, 2, 3, paying 6:1) has its own, noticeably worse house edge of about 7.89% and isn't one of the standard bet types this instrument computes.
Worked example — a straight-up bet on a European wheel
Select 'Straight-up (single number) — pays 35:1' from Bet type, and 'European (single zero, 37 pockets)' from Wheel type. Payout ratio (X : 1) reads 35, and House edge (%) reads 2.702703%.
The true odds of a single number hitting on a 37-pocket wheel are 1 in 37, so a perfectly fair payout would be 36:1 — the casino instead pays 35:1, one unit short. That single-unit gap divided across the 37 possible outcomes is exactly (37-36)/37 x 100 = 1/37 x 100 ≈ 2.7027%, the same edge you'd get checking a corner bet (8:1) on the same European wheel, since standard bets balance their higher payout against their lower win chance to land on identical expected-value math.
Questions
Why is the house edge the same whether I bet on one number or four?
Because the higher payout on a rarer bet exactly offsets its lower chance of winning. A straight-up bet on 1 number wins 1/37 of the time and pays 35:1; a corner bet on 4 numbers wins 4/37 of the time and pays 8:1. Working out the expected value for each — (win probability x payout) minus (loss probability) — gives -1/37 either way, so both land on the same 2.70% edge on a European wheel. This holds for every standard bet type on this instrument, not just these two.
Why is American roulette worse for players than European roulette?
The American wheel adds a second zero pocket (00) alongside the single zero, for 38 total pockets instead of 37 — one extra way for the ball to land somewhere that loses every standard bet. That single extra pocket nearly doubles the house edge, from about 2.70% on a European wheel to about 5.26% on an American wheel, even though the payout ratios for each bet type stay exactly the same on both wheels.
What's the difference between the payout ratio and my actual odds of winning?
The payout ratio (like 35:1) is what the casino pays you if you win. Your actual probability of winning is a separate number entirely, determined by how many pockets the wheel has and how many numbers your bet covers. The gap between a truly fair payout (based on the real odds) and the actual, lower payout the casino offers is exactly what produces the house edge.
What is the American five-number bet, and why isn't it included here?
It's a bet unique to American wheels, covering 0, 00, 1, 2 and 3 together, paying 6:1. Its house edge works out to roughly 7.89% — clearly worse than every other standard bet's 5.26% on the same wheel — because those five numbers don't divide evenly into the wheel's structure the way other standard groupings do. This instrument's formula is built for the standard bets that share a uniform edge, so the five-number bet is deliberately excluded, as noted in its own field label.
Does bigger bet size change the house edge?
No — the house edge is a percentage of each unit wagered, not a fixed dollar figure, so it applies the same way whether you bet $1 or $1,000 on a standard bet. What changes with bet size is the expected dollar amount lost over time, not the underlying percentage: a larger bet has a proportionally larger expected loss, but the edge percentage itself stays fixed for a given bet type and wheel.