Craps dice probability: the odds of rolling every total
With two dice there are 36 equally likely combinations. The most likely total is 7: 6 of the 36 combinations, a probability of 1/6 (16.67%), or odds of 5 to 1 against. The least likely totals are 2 and 12, with 1 combination each (1/36, 2.78%, 35 to 1 against).
Nearly every craps bet is a race between some number and the 7, so these few tables explain the whole game. Every figure on this page is computed from the 36 combinations by the same math module the crappy app uses.
What are the odds of rolling each total with two dice?
| Total | Combinations | Ways (of 36) | Probability | Percent | Odds against |
|---|---|---|---|---|---|
| 2 | 1-1 | 1 | 1/36 | 2.78% | 35 to 1 |
| 3 | 1-2, 2-1 | 2 | 1/18 | 5.56% | 17 to 1 |
| 4 | 1-3, 2-2, 3-1 | 3 | 1/12 | 8.33% | 11 to 1 |
| 5 | 1-4, 2-3, 3-2, 4-1 | 4 | 1/9 | 11.11% | 8 to 1 |
| 6 | 1-5, 2-4, 3-3, 4-2, 5-1 | 5 | 5/36 | 13.89% | 31 to 5 |
| 7 | 1-6, 2-5, 3-4, 4-3, 5-2, 6-1 | 6 | 1/6 | 16.67% | 5 to 1 |
| 8 | 2-6, 3-5, 4-4, 5-3, 6-2 | 5 | 5/36 | 13.89% | 31 to 5 |
| 9 | 3-6, 4-5, 5-4, 6-3 | 4 | 1/9 | 11.11% | 8 to 1 |
| 10 | 4-6, 5-5, 6-4 | 3 | 1/12 | 8.33% | 11 to 1 |
| 11 | 5-6, 6-5 | 2 | 1/18 | 5.56% | 17 to 1 |
| 12 | 6-6 | 1 | 1/36 | 2.78% | 35 to 1 |
What are all 36 dice combinations?
Each cell is the total of one combination. Count a total's cells to get its ways.
| First die | Second die 1 | Second die 2 | Second die 3 | Second die 4 | Second die 5 | Second die 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
What are the odds of rolling a 7?
A 7 has 6 ways in 36, so it comes up 1/6 of the time (16.67%), or 5 to 1 against on any one roll. A shooter's hand, from the first come-out to the seven-out, lasts 8.53 rolls on average.
| Rolls | Chance of at least one 7 |
|---|---|
| 1 | 16.7% |
| 2 | 30.6% |
| 3 | 42.1% |
| 4 | 51.8% |
| 5 | 59.8% |
| 6 | 66.5% |
| 10 | 83.8% |
| 20 | 97.4% |
What are the odds of making the point before a 7?
Once a point is set, only the point and the 7 matter. The Odds bet pays exactly these true odds, which is why it has no house edge (see the odds bet at 1x to 100x).
| Point | Ways vs 7 | Chance to roll it before a 7 | True odds | Odds bet pays |
|---|---|---|---|---|
| 4 | 3 vs 6 | 1/3 (33.33%) | 2 to 1 | 2 to 1 |
| 5 | 4 vs 6 | 2/5 (40.00%) | 3 to 2 | 3 to 2 |
| 6 | 5 vs 6 | 5/11 (45.45%) | 6 to 5 | 6 to 5 |
| 8 | 5 vs 6 | 5/11 (45.45%) | 6 to 5 | 6 to 5 |
| 9 | 4 vs 6 | 2/5 (40.00%) | 3 to 2 | 3 to 2 |
| 10 | 3 vs 6 | 1/3 (33.33%) | 2 to 1 | 2 to 1 |
What are the odds of rolling a hard way?
A hardway wins on the pair and loses on the easy way or a 7. It pays less than its true odds, and the difference is the house edge.
| Bet | Chance to win | True odds | Pays | House edge |
|---|---|---|---|---|
| Hard 4 | 1/9 (11.11%) | 8 to 1 | 7 to 1 | 11.11% |
| Hard 6 | 1/11 (9.09%) | 10 to 1 | 9 to 1 | 9.09% |
| Hard 8 | 1/11 (9.09%) | 10 to 1 | 9 to 1 | 9.09% |
| Hard 10 | 1/9 (11.11%) | 8 to 1 | 7 to 1 | 11.11% |
Roll hundreds of times in the app and watch the totals settle into this shape.
Roll the dice in crappy: free, play money