The payout (except for the special case of Top line bets), for American and European roulette, can be calculated by:
where n is the number of squares the player is betting on. The initial bet is returned in addition to the mentioned payout. It can be easily demonstrated that this payout formula would lead to a zero expected value of profit if there were only 36 numbers. Having 37 or 38 numbers gives the casino its edge.
| Bet name | Winning spaces | Payout | Odds against winning (French) | Expected value (on a $1 bet) (French) | Odds against winning (American) | Expected value (on a $1 bet) (American) |
|---|---|---|---|---|---|---|
| 0 | 0 | 35 to 1 | 36 to 1 | −$0.027 | 37 to 1 | −$0.053 |
| 00 | 00 | 35 to 1 | 37 to 1 | −$0.053 | ||
| Straight up | Any single number | 35 to 1 | 36 to 1 | −$0.027 | 37 to 1 | −$0.053 |
| Row | 0, 00 | 17 to 1 | 18 to 1 | −$0.053 | ||
| Split | any two adjoining numbers vertical or horizontal | 17 to 1 | 35 to 2 | −$0.027 | 18 to 1 | −$0.053 |
| Street | any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.) | 11 to 1 | 34 to 3 | −$0.027 | 11.667 to 1 | −$0.053 |
| Corner | any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21, etc.) | 8 to 1 | 33 to 4 | −$0.027 | 8.5 to 1 | −$0.053 |
| Top line or Basket | 0, 00, 1, 2, 3 | 6 to 1 | 6.6 to 1 | −$0.079 | ||
| Six line | any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.) | 5 to 1 | 31 to 6 | −$0.027 | 5.33 to 1 | −$0.053 |
| 1st column | 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| 2nd column | 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| 3rd column | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| 1st dozen | 1 through 12 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| 2nd dozen | 13 through 24 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| 3rd dozen | 25 through 36 | 2 to 1 | 25 to 12 | −$0.027 | 21⁄6 to 1 | −$0.053 |
| Odd | 1, 3, 5, ..., 35 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
| Even | 2, 4, 6, ..., 36 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
| Red | 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
| Black | 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
| 1 to 18 | 1, 2, 3, ..., 18 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
| 19 to 36 | 19, 20, 21, ..., 36 | 1 to 1 | 19 to 18 | −$0.027 | 11⁄9 to 1 | −$0.053 |
Note that Top line (0, 00, 1, 2, 3) has a different expected value because of approximation of the correct 6.2 payout obtained by the formula to 6. Note also that 0 and 00 are not odd or even, or high or low.
En prison rules, when used, reduce the house advantage.
No comments:
Post a Comment