European and American roulette: where the extra pocket goes

The difference between the two common roulette wheels is a single extra pocket, and the whole edge lives in it. The payouts printed on the layout are identical between the two wheels. Only the number of pockets changes, which means only the denominator changes.

The single-zero wheel

A single-zero wheel has thirty-seven pockets: numbers one to thirty-six plus a zero. A straight-up number pays thirty-five to one. If the payout were fair it would pay thirty-six to one, because one pocket in thirty-seven wins. The gap between the fair price and the paid price, spread across all thirty-seven pockets, is the edge, and it works out at one part in thirty-seven, or about 2.7 per cent.

The double-zero wheel

Add a second zero and the wheel has thirty-eight pockets while the straight-up payout stays at thirty-five to one. Now two pockets sit outside the payout schedule instead of one, and the edge roughly doubles to about 5.26 per cent. Nothing about the felt or the chips signals this; the only visible difference is one extra green pocket.

Why the even-money bets are not safer

Red, black, odd and even feel different because they win about half the time, but they are priced from the same pocket count. Eighteen winning pockets out of thirty-seven, paid at even money, carries the same 2.7 per cent as the straight-up bet on the same wheel. Bet size and variance change across the layout; the edge, on almost every bet, does not.

The practical consequence

Checking the pocket count before checking anything else tells you more than any betting pattern will. No sequence of bets on a thirty-eight pocket wheel produces the pricing of a thirty-seven pocket wheel, because the pricing is a property of the wheel rather than of the wager.