Dice Probability

Master dice probability step by step

Sum Probabilities for Two Dice

When rolling two dice, the sum can range from 2 (1+1) to 12 (6+6). The number of ways to achieve each sum varies, affecting the probability.

Sum = 7 is the most probable because it has the most combinations (6 ways). Sums near the extremes (2 and 12) are least probable.

Sum = 21/36 = 2.78%

(1,1)

Sum = 32/36 = 5.56%

(1,2), (2,1)

Sum = 43/36 = 8.33%

(1,3), (2,2), (3,1)

Sum = 54/36 = 11.11%

(1,4), (2,3), (3,2), (4,1)

Sum = 65/36 = 13.89%

(1,5), (2,4), (3,3), (4,2), (5,1)

Sum = 76/36 = 16.67%

(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

Sum = 85/36 = 13.89%

(2,6), (3,5), (4,4), (5,3), (6,2)

Sum = 94/36 = 11.11%

(3,6), (4,5), (5,4), (6,3)

Sum = 103/36 = 8.33%

(4,6), (5,5), (6,4)

Sum = 112/36 = 5.56%

(5,6), (6,5)

Sum = 121/36 = 2.78%

(6,6)

The number of ways to get sum follows this pattern:

This creates a symmetric "pyramid" distribution peaking at 7.

Sums of 10, 11, or 12:

Sums of 2, 4, 6, 8, 10, 12:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6):