A quick caution
Roulette is a game of chance with a built-in house edge. No bet type, system or timing changes the odds in the player’s favor over time, most players lose money in the long run, and nobody should gamble money they cannot afford to lose. The point of this article is to show how bets are priced, not to suggest that any of them is a better way to play.
Two families of bets
Every roulette bet is a wager that the ball will land in a particular set of pockets. The table sorts them into two groups, based on where the chips are placed.
- Inside bets are placed on the number grid itself and cover between one and six numbers (or, with the zeros, a few more combinations).
- Outside bets are placed in the boxes around the grid and cover larger groups of 12 or 18 numbers.
The names describe position on the felt, not value or risk. Both kinds follow the same pricing logic.
The pricing rule
On a wheel with 37 pockets, a bet that covers n numbers wins with probability n/37. The casino pays winners at a ratio of (36 ÷ n) − 1 to 1. In other words, it pays as if the wheel had 36 pockets instead of 37. The extra pocket, the zero, belongs to nobody who bets on ordinary numbers, and that is where the house edge comes from.
Different payout ratios are the same idea in a different form: shorter chances get longer payouts.
| Bet | Numbers covered | Win probability (37 pockets) | Pays |
|---|---|---|---|
| Straight | 1 | 1/37 | 35 to 1 |
| Split | 2 | 2/37 | 17 to 1 |
| Street | 3 | 3/37 | 11 to 1 |
| Corner | 4 | 4/37 | 8 to 1 |
| Six line | 6 | 6/37 | 5 to 1 |
| Dozen or column | 12 | 12/37 | 2 to 1 |
| Red, black, odd, even, low, high | 18 | 18/37 | 1 to 1 |
Check the pattern: 36 ÷ 2 − 1 = 17, 36 ÷ 3 − 1 = 11, 36 ÷ 4 − 1 = 8, 36 ÷ 6 − 1 = 5, 36 ÷ 12 − 1 = 2 and 36 ÷ 18 − 1 = 1. The same payout ratios appear at every single-zero table.
Inside bets in detail
A straight bet puts a chip on one number. It wins rarely but pays the most.
A split puts a chip on the line between two adjacent numbers on the grid, such as 8 and 11 or 14 and 15. Either number wins it.
A street covers a row of three numbers, such as 4, 5 and 6, by placing a chip at the edge of that row.
A corner, sometimes called a square or four-number bet, sits where four numbers meet, such as 8, 9, 11 and 12.
A six line spans two adjacent rows, covering six numbers, such as 4 through 9.
Near the zero, the grid offers a few extra combinations, such as a bet on 0, 1 and 2, or on the first four numbers, 0 through 3. These are priced by the same rule: three numbers pay 11 to 1 and four pay 8 to 1.
Outside bets in detail
Dozens cover 1 to 12, 13 to 24 or 25 to 36. Columns cover each vertical line of 12 numbers. Both pay 2 to 1.
The six even-money bets are red, black, odd, even, low (1 to 18) and high (19 to 36). They pay 1 to 1 and win a little under half the time, because the zero belongs to none of them. This is why even-money bets are not as even as the name suggests.
Why the cost is the same, and the experience is not
Take a $1 split on a single-zero wheel. It wins with probability 2/37 and gains $17, and it loses with probability 35/37 and costs $1. The expected result is (2 × 17 − 35) / 37 = (34 − 35) / 37 = −1/37, about −$0.027. A $1 corner works out to (4 × 8 − 33) / 37 = −1/37 as well. You can verify the same figure for the other bets in the table. Each bet carries the same expected cost per unit staked, which is the idea of a uniform edge across bets.
What differs is the pattern of results. Straight bets lose most spins but occasionally pay a lot. Outside bets win nearly half the time but pay little. Because the swings differ, the same total amount wagered can feel very different, though the expected cost per dollar is the same. Standard deviation is the usual measure of this difference.
Combinations and chip placement
Players often place several chips at once, and some “called” combinations are really just several of the bets above sold as a bundle. A pattern of splits and corners placed together is still just those separate bets, each with its own win chance and payout.
Chips can be spread over several places at once, but spreading does not remove the house edge. The expected loss on the whole layout equals the edge times the total amount staked. With many chips in play, a roulette round can also use up a bankroll faster.
On a double-zero wheel
On a 38-pocket wheel the payout ratios are the same as above, but the win probabilities are n/38, so the edge rises to 2/38, about 5.26%. The same formula says a straight bet there should pay 37 to 1 to be fair, and it pays 35 to 1.
Table limits
Tables set separate minimum and maximum bets for inside and outside areas, and the allowed maximums for single-number bets are usually much lower than for even-money bets, reflecting the large payouts. These table limits affect how much a given bet can win, and they can only change the size of swings, never the expected cost.