Craps Odds and Probability: The 36 Dice Combinations
Two fair independent six-sided dice have 36 equally likely ordered outcomes. Totals are not equally likely: 7 has six combinations, while 2 and 12 have one each. This guide distinguishes a one-roll probability from a multi-roll settlement and a profit payout.
One-Roll Combination Table
The last column expresses a probability as “1 in X,” not odds against. For example, 1 in 36 corresponds to 35:1 odds against, not 36:1. Percentages are rounded.
| Total | Combinations | Probability (%) | Probability expressed as 1 in X |
| 2 | 1-1 | 2.78% | 1 in 36 |
| 3 | 1-2, 2-1 | 5.56% | 1 in 18 |
| 4 | 1-3, 2-2, 3-1 | 8.33% | 1 in 12 |
| 5 | 1-4, 2-3, 3-2, 4-1 | 11.11% | 1 in 9 |
| 6 | 1-5, 2-4, 3-3, 4-2, 5-1 | 13.89% | 1 in 7.2 |
| 7 | 1-6, 2-5, 3-4, 4-3, 5-2, 6-1 | 16.67% | 1 in 6 |
| 8 | 2-6, 3-5, 4-4, 5-3, 6-2 | 13.89% | 1 in 7.2 |
| 9 | 3-6, 4-5, 5-4, 6-3 | 11.11% | 1 in 9 |
| 10 | 4-6, 5-5, 6-4 | 8.33% | 1 in 12 |
| 11 | 5-6, 6-5 | 5.56% | 1 in 18 |
| 12 | 6-6 | 2.78% | 1 in 36 |
The Distribution Is Triangular
Combination counts rise from one at total 2 to six at total 7, then fall symmetrically to one at 12. This is a discrete triangular distribution, not a bell-shaped normal distribution.
A Point Before Seven Is a Different Event
For a point of 4, three combinations produce 4 and six produce 7. Other totals leave the wager unresolved. The probability that 4 appears before 7 is therefore 3/(3+6) = 1/3. That is different from the one-roll probability of 4, which is 3/36.
The corresponding before-seven probabilities are 4/10 = 40% for 5 or 9, and 5/11 ≈ 45.45% for 6 or 8. These describe a race until one of the two relevant totals occurs, not the chance of winning on the immediately next roll.
True Odds and Paid Odds
A one-unit wager with probability 1/3 needs a 2:1 profit payout to have zero expected gain or loss: a win returns three units including the stake. If the payout is instead 9:5 profit, expected loss is 1/15, approximately 6.67%, per resolved stake.
The taking and laying odds guide explains true-odds components. Those components can still lose and require underlying wagers with their own negative expectation.
House Edge Requires a Defined Bet
Conventional Pass/Come has approximately 1.41% house edge per initial stake. Don’t Pass/Don’t Come with bar 12 is approximately 1.36% including initial pushes. Place-bet percentages are usually quoted per resolved wager, while one-roll bets settle immediately. Mixing denominators can make a comparison misleading.
At 4:1 profit, Any Seven returns five stakes on six of the 36 outcomes: expected return is 30/36 and house edge is 16.67%. A Field payout change on 2 or 12 changes that wager’s calculation; no single percentage covers every Field paytable.
Independent Rolls and Session Results
A previous 7, a long point sequence or a “cold” table does not change the next roll’s probabilities under the independent-dice model. Expected return is not a maximum loss or a guarantee that a balance survives a chosen number of rolls.
See bets and payout assumptions, Field calculations and proposition payout notation. WinnerOnline provides information and does not host games.
Related reading: Sic Bo Odds and Payouts: Probabilities Explained.
