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Roulette

Field: Game mechanics. This page was last modified on 17 August 2026.

Roulette is the clearest illustration in the whole subject of how a payout schedule creates an edge. The mechanism is a symmetric wheel with numbered pockets. The bets cover different sized groups of those pockets at correspondingly different prices. Because one price rule was applied throughout, almost every bet on the table carries an identical expected value.

A single-zero wheel divided into thirty-seven equal sectors 37 sectors Every pocket is one sector wide, so each carries probability 1/37 = 0.0270 The marked sector is a single straight-up number.
A single-zero wheel divided into thirty-seven equal sectors. One sector is marked; every sector has the same width.

The wheel

The single-zero wheel carries thirty-seven pockets numbered zero to thirty-six. Eighteen are red, eighteen are black, and the zero is green. The double-zero wheel adds a second green pocket, giving thirty-eight. The numbers are not arranged in sequence around the rim; they are distributed so that high and low, red and black, and odd and even alternate as evenly as the arithmetic allows, which spreads any small mechanical bias across the betting categories rather than concentrating it in one of them.

The layout of the betting cloth is separate from the layout of the wheel. The cloth arranges the numbers in three columns of twelve, which is what makes the column and dozen bets convenient to place; the wheel arranges them for physical balance. Confusing the two is the source of most mistaken claims about roulette patterns.

The bet catalogue

Inside bets cover one to six numbers, outside bets cover twelve or eighteen. The payout for each is set by one rule: a bet covering k numbers on a single-zero wheel pays (36 / k) - 1 to one.

Bets on a single-zero wheel, with payout, true odds and resulting edge
BetNumbers coveredPays True odds againstEdge
Straight up135 to 1 36 to 12.70%
Split217 to 1 35 to 22.70%
Street311 to 1 34 to 32.70%
Corner48 to 1 33 to 42.70%
Line65 to 1 31 to 62.70%
Column or dozen122 to 1 25 to 122.70%
Red, black, odd, even, high, low18 1 to 119 to 182.70%

Every row carries the same edge because every row applies the same rule. The one classic exception belongs to the double-zero wheel: the five-number bet covering zero, double zero, one, two and three pays 6 to 1 where the schedule implies 6.6 to 1, giving an edge of 7.89%, noticeably worse than every other bet on the same table.

Rules that reduce the edge

Some single-zero tables apply a rule under which an even-money bet is not lost outright when zero comes up. Depending on the variant the stake is either returned in part or held for the next spin. Either way the loss on that class of bet is halved, and the edge on those bets alone falls from 2.70% to 1.35%. The rule does not touch the inside bets, which is a useful reminder that a published edge always belongs to a specific wager under a specific rule set.

Systems and bias

Staking systems rearrange the sequence of bet sizes. They do not change the expected value of any individual bet, and because expected value adds across bets, they cannot change the expected value of the sequence. A progression that doubles after each loss converts a large number of small wins into a rare very large loss; the average is unmoved, only the shape of the distribution changes, and it changes in the direction of higher variance.

Physical bias is a different matter and is genuinely possible in principle: a wheel with a worn frame or an uneven rotor can favour a region of the rim. Detecting it requires enough recorded spins to distinguish a real deviation from ordinary scatter, which is a large number, and modern maintenance and wheel monitoring exist largely to close that possibility. It is a mechanical question, not a mathematical one.