Games of chance, counted and priced

Featured record — wheel games

Single-zero roulette

Wheel games / 37 pockets / straight-up pays 35 to 1

The wheel has thirty-seven pockets and a bet on one number wins when that pocket comes up. There is one way to win and thirty-six ways to lose, so the true odds against are thirty-six to one, and the table pays thirty-five to one.

The arithmetic. Stake one unit on a single number.

Win: probability 1/37, return +35 units. Lose: probability 36/37, return −1 unit.

Expected result = (1/37 × 35) − (36/37 × 1) = (35 − 36)/37 = −1/37 = −2.70%.

Every other bet on a single-zero wheel gives the same figure, because every one of them is priced the same way against the same thirty-seven pockets.

The full wheel-games record

Notes on the index

Why the payout is always short of the oddsA single number on a thirty-seven pocket wheel comes up once in thirty-seven spins, so the honest price for that risk is thirty-six to one. The table pays thirty-five. That missing unit is the whole business: not a fee, not a charge, but a payout deliberately set one step below the true odds, applied automatically to every bet whether it wins or loses.

The bet that costs nothingInside a craps game there is a wager that pays exactly true odds and therefore has no edge at all. It is not generosity. It can only be made as a supplement to a bet that does carry an edge, so the operator's average take per stake falls while the number of units on the table rises. A game can contain a fair bet and still be an unfair game.

A lottery is not a bad roulette wheelA wheel takes a small slice from a bet that is settled in seconds and repeated all evening. A draw takes a very large slice from a ticket bought once a week. The percentages are not comparable because the number of trials is not comparable, and a figure per bet says nothing until you know how many bets an hour the game invites.