Craps odds: the 36 ways to roll two dice
Why 7 rules craps. The 36 ways two dice can land, the odds of rolling each number, the odds of making each point, and how true odds compare to what the bets pay.
Every price in craps comes from one small fact: two dice can land 36 ways, and more of those ways add up to 7 than to anything else. Learn that, and every payout on the table starts to make sense.
The 36 combinations
Each die has six faces, so two dice have 6 × 6 = 36 ways to land. Count how many of those make each total:
| Total | Ways out of 36 | How often | Odds against |
|---|---|---|---|
| 2 | 1 | 2.8% | 35 to 1 |
| 3 | 2 | 5.6% | 17 to 1 |
| 4 | 3 | 8.3% | 11 to 1 |
| 5 | 4 | 11.1% | 8 to 1 |
| 6 | 5 | 13.9% | 31 to 5 |
| 7 | 6 | 16.7% | 5 to 1 |
| 8 | 5 | 13.9% | 31 to 5 |
| 9 | 4 | 11.1% | 8 to 1 |
| 10 | 3 | 8.3% | 11 to 1 |
| 11 | 2 | 5.6% | 17 to 1 |
| 12 | 1 | 2.8% | 35 to 1 |
The 7 comes up six ways: 1 and 6, 2 and 5, 3 and 4, and each of those the other way round. The 2 and 12 come up only one way each. The numbers on either side of the 7 mirror each other: 6 and 8 have five ways each, 5 and 9 have four, 4 and 10 have three.
The odds of making a point
Once a point is on, only two numbers matter: the point and the 7. Everything else is a roll again. So the odds of making the point come down to its ways against the 7’s six ways.
| Point | Ways to roll it | Ways to roll 7 | Odds against making it |
|---|---|---|---|
| 4 or 10 | 3 | 6 | 2 to 1 |
| 5 or 9 | 4 | 6 | 3 to 2 |
| 6 or 8 | 5 | 6 | 6 to 5 |
That’s exactly what the Odds bet pays: 2 to 1 on 4 or 10, 3 to 2 on 5 or 9, and 6 to 5 on 6 or 8. Paying true odds is why the Odds have no house edge.
True odds vs what the table pays
Most bets pay a little less than their true odds. The gap is the house edge.
| Bet | True odds | Pays | House edge |
|---|---|---|---|
| Odds on the 6 | 6 to 5 | 6 to 5 | None |
| Place 6 | 6 to 5 | 7 to 6 | 1.52% |
| Place 4 | 2 to 1 | 9 to 5 | 6.67% |
| Hard 6 | 10 to 1 | 9 to 1 | 9.09% |
| Any Seven | 5 to 1 | 4 to 1 | 16.67% |
| Aces (2) | 35 to 1 | 30 to 1 | 13.89% |
Questions
What are the odds of rolling a 7?
Six ways out of 36, or one roll in six. Against it: 5 to 1.
What are the odds of winning on the Pass Line?
A little under half. Add up the come-out wins on 7 and 11 and the chance of making each point, and the Pass Line comes out just short of a coin flip. That shortfall is its 1.41% house edge.
Are the dice “due”?
No. Every roll is independent. If the shooter has rolled four 6s in a row, the next roll is still a 6 five times in 36. Streaks feel meaningful at the table, and that’s half the fun, but the dice don’t remember.
What are the house odds on craps?
It depends on the bet. The Odds have no house edge at all, and the line bets keep it under 1.5%. The props in the middle cost far more. Good bets, bad bets ranks every bet, and the craps payout chart puts them all on one page.
Play money only: nothing is wagered or paid out.
Next: Craps payout chart →