Craps Odds Calculator
After the Come-Out Roll, the Math Changes Completely
Once a shooter establishes a point (4, 5, 6, 8, 9, or 10), the pass line bet's outcome depends on a straightforward race: will that point number reappear before a 7 does. Because a 7 can be formed by six different two-dice combinations — more than any other total — the probability of any given point beating a 7 is never better than even, but it varies noticeably by which point was set.
The Formula
Both counts come from the 36 equally likely combinations of two six-sided dice — a 7 is formed by exactly 6 of those 36 combinations, regardless of which point is in play.
Point Probability by Number
| Point | Ways to roll (of 36) | P(point before 7) |
|---|---|---|
| 4 | 3 | 33.33% |
| 5 | 4 | 40.00% |
| 6 | 5 | 45.45% |
| 8 | 5 | 45.45% |
| 9 | 4 | 40.00% |
| 10 | 3 | 33.33% |
Points 6 and 8 are the easiest to make (5 ways each out of 36), while 4 and 10 are the hardest (3 ways each) — this is the same combinatorial pattern behind the classic 2d6 probability distribution. The overall Pass Line bet, factoring in the come-out roll as well, carries a standard published house edge of approximately 1.41%.
Where This Gets Used
- Understanding odds bets — the "true odds" bet craps allows behind the pass line pays out at exactly this probability's fair rate, which is why it's one of the few zero-house-edge wagers in a casino.
- Comparing point difficulty — explaining why players react differently to a point of 6 versus a point of 4 being established.
- Teaching dice combinatorics — craps point probabilities are a concrete, widely recognized example of counting favorable outcomes among 36 equally likely dice combinations.
How to Use This Calculator
- Select the Point — 4, 5, 6, 8, 9, or 10.
- Select Calculate to see the probability that point rolls before a 7.
Related Calculations
Work out any dice-sum probability directly with the Dice Probability Calculator, or compute a wager's house edge with the House Edge Calculator.