Another type of bet in craps is a ‘don’t pass bet’. Here, the winning opportunities are the opposite of what we have seen before. Well, not really; had that been the case, the player would have got an exactly opposite, +1.41% advantage, which is absurd. A player never holds winning odds in gambling! The rules are almost the opposite, but getting 12 in the first throw makes a pass (no win. no loss). Let’s list down all the possible outcomes and the payoff table.
- The player throws the dice and wins at once if the total for the first throw is 2 or 3.
- The player loses if the outcome is 7 or 11.
- It’s a pass if the outcome is 12.
- The throws 4, 5, 6, 8, 9 or 10 are called points.
- If the first throw is a point, it is repeated until the same number (the point) comes back (player loses) or 7 (player wins).
The probability of winning a point 4 is the joint probability of winning 4 in the first roll and the probability of getting 7 (and not 4) in the second.
| Dice Roll | Payoff | Probability | Return |
| 7 or 11 (come-out loss) | -1 | 16.67 + 5.56 = 22.23 | -22.23 |
| 2, 3 (come-out win) | 1 | 2.78 + 5.56 = 8.34 | 8.34 |
| 12 (come-out push) | 0 | 2.78 | 0 |
| Point 4 loss | -1 | 8.33*8.33/(8.33+16.67) = 2.78 | -2.78 |
| Point 5 loss | -1 | 11.11*11.11/(11.11+16.67) = 4.44 | -4.44 |
| Point 6 loss | -1 | 13.89*13.89/(13.89+16.67) = 6.31 | -6.31 |
| Point 8 loss | -1 | 13.89*13.89/(13.89+16.67) = 6.31 | -6.31 |
| Point 9 loss | -1 | 11.11*11.11/(11.11+16.67) = 4.44 | -4.44 |
| Point 10 loss | -1 | 8.33*8.33/(8.33+16.67) = 2.78 | -2.78 |
| Point 4 win | 1 | 8.33*16.67/(8.33+16.67) = 5.55 | 5.55 |
| Point 5 win | 1 | 11.11*16.67/(11.11+16.67) = 6.67 | 6.67 |
| Point 6 win | 1 | 13.89*16.67/(13.89+16.67) = 7.58 | 7.58 |
| Point 8 win | 1 | 13.89*16.67/(13.89+16.67) = 7.58 | 7.58 |
| Point 9 win | 1 | 11.11*16.67/(11.11+16.67) = 6.67 | 6.67 |
| Point 10 win | 1 | 8.33*16.67/(8.33+16.67) = 5.55 | 5.55 |
| Overall | 100 | -1.35 |
So, as usual, the house wins.
