Two Dice Probability Chart: Odds of Rolling Every Total
By Matty Dice ·
Two six-sided dice are the most common combination in board games, from Monopoly to Settlers of Catan to craps. Knowing which totals come up most often gives you a real edge. Here is the full picture.
36 possible outcomes
Each die has 6 faces, so two dice can land 6 × 6 = 36 different ways. Totals that can be made in more ways come up more often. Only one combination makes 2 (1+1), but six make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
| Total | Combinations | Ways | Probability |
|---|---|---|---|
| 2 | 1-1 | 1 | 2.8% |
| 3 | 1-2, 2-1 | 2 | 5.6% |
| 4 | 1-3, 2-2, 3-1 | 3 | 8.3% |
| 5 | 1-4, 2-3, 3-2, 4-1 | 4 | 11.1% |
| 6 | 1-5, 2-4, 3-3, 4-2, 5-1 | 5 | 13.9% |
| 7 | 1-6, 2-5, 3-4, 4-3, 5-2, 6-1 | 6 | 16.7% |
| 8 | 2-6, 3-5, 4-4, 5-3, 6-2 | 5 | 13.9% |
| 9 | 3-6, 4-5, 5-4, 6-3 | 4 | 11.1% |
| 10 | 4-6, 5-5, 6-4 | 3 | 8.3% |
| 11 | 5-6, 6-5 | 2 | 5.6% |
| 12 | 6-6 | 1 | 2.8% |
Using the odds in real games
Settlers of Catan. The number tokens have dots showing how many ways each number can be rolled. A settlement touching a 6 and an 8 will produce far more resources than one on a 2 and a 12. Settle on the five-dot numbers when you can.
Monopoly. Because 7 is the most common roll, the squares about seven spaces past Jail (the orange properties) are landed on more than most others. That makes them a favorite among experienced players.
Craps. The 7 dominates the game: it wins on the come-out roll and ends the round after a point is set. Points of 6 and 8 are the easiest to hit again, which is why place bets on 6 and 8 are so popular.
Doubles
There are six doubles (1-1 through 6-6), so the chance of rolling doubles on any turn is 6 in 36, or 1 in 6. In Monopoly, the chance of rolling doubles three times in a row and going to jail is 1 in 216.
Want to see the distribution for yourself? Roll two dice a few dozen times on the online dice roller and watch the history: you'll see 6s, 7s and 8s far more than 2s and 12s.