Dice mathematics
Two dice create 36 ordered outcomes—but totals are not equally likely.
Seven has six combinations. Two and twelve have one each. That asymmetry drives much of craps.
| Total | Combinations | Probability |
|---|---|---|
| 2 / 12 | 1 each | 2.78% each |
| 3 / 11 | 2 each | 5.56% each |
| 4 / 10 | 3 each | 8.33% each |
| 5 / 9 | 4 each | 11.11% each |
| 6 / 8 | 5 each | 13.89% each |
| 7 | 6 | 16.67% |
Point races
Once a point is established, only that point and 7 matter to the Pass/Don’t Pass resolution. For point 4, for example, there are three ways to roll 4 and six ways to roll 7, so fair odds pay 2:1 on the point occurring first.