sacstat mark: a grid of pockets with a single one filledsacstat pockets = 37 | 38

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roulette

pockets = 37 | 38

Roulette is the clearest example in the subject of a game whose entire margin is visible in its physical construction. The wheel has thirty-seven or thirty-eight pockets. The payout table is written as though it had thirty-six. Everything else follows.

The pocket census

A single-zero wheel carries the numbers one to thirty-six, half red and half black, plus a single green zero: thirty-seven pockets. A double-zero wheel adds a second green pocket, making thirty-eight. The numbers are arranged around the rim so that neighbours differ in colour and in high-low, which spreads any local bias but has no effect whatever on the arithmetic.

A single-zero roulette wheel drawn as thirty-seven segments: eighteen red, eighteen black and one green zero, with a census listing one green, eighteen red, eighteen black, total thirty-seven pockets.
The pocket census is the whole game: eighteen red, eighteen black, one green, thirty-seven in total.

Why one edge covers nearly every bet

A straight-up number pays 35 to 1. There are thirty-seven pockets, so the true price of a single number is 36 to 1. Expected value per unit is (35 × 1 − 1 × 36) / 37 = −1/37. A split pays 17 to 1 across two numbers; the same computation gives −1/37 again. An even-money bet covers eighteen and returns −1/37 a third time.

This uniformity is deliberate. Every payout on the table is computed as though the wheel had thirty-six pockets, so every bet gives up exactly the value of the missing pocket. The bettor can choose the shape of the distribution — rare and large, or frequent and small — but not the price.

Single-zero wheel: several bets, one edge
betpockets coveredpayoutexpected value per unit
straight up135 to 1(35 − 36)/37 = −2.70%
split217 to 1(34 − 35)/37 = −2.70%
corner48 to 1(32 − 33)/37 = −2.70%
dozen122 to 1(24 − 25)/37 = −2.70%
red / black181 to 1(18 − 19)/37 = −2.70%

The double-zero exception

On a double-zero wheel the same construction gives −2/38, or 5.26%, on almost every bet — and one bet is worse. The five-number bet covering zero, double zero, one, two and three pays 6 to 1. Five pockets out of thirty-eight paying six is expected value (5 × 6 − 33) / 38 = −3/38, which is 7.89%.

It is the only line on the standard layout whose payout was rounded rather than derived, and it is a useful reminder that the uniformity of the table is a design decision rather than a law.

The five-number bet
pockets covered      5   (0, 00, 1, 2, 3)
pockets not covered 33
payout               6 to 1

E[unit] = (5 x 6 - 33 x 1) / 38
        = (30 - 33) / 38
        = -3/38 = -7.8947%

every other bet on the same wheel: -2/38 = -5.2632%

Sequences and the wheel's memory

Commonly misread. A wheel has no memory. Recording previous results and betting against a run assumes that the wheel is compensating for its history, and it is not: each spin draws from the same thirty-seven pockets regardless of what preceded it. Long runs of one colour are ordinary features of independent trials and are treated in the variance entry.

Physical bias — a genuinely uneven wheel favouring some pockets — is the one mechanism that could in principle break the arithmetic, which is precisely why modern wheels are manufactured, balanced and rotated to eliminate it, and why pocket-frequency monitoring is a standard part of table operations.

Return to the Wheel and dice games index on the reference landing.

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Last modified 17 August 2026.