One die
A fair six-sided die gives each number with a probability of 1 in 6, about 16.7%.
Two dice
Two dice have 6 × 6 = 36 equally likely combinations, but the totals are not equally likely, because some totals can be made in more ways:
- 2 or 12: 1 way (2.8%)
- 3 or 11: 2 ways (5.6%)
- 4 or 10: 3 ways (8.3%)
- 5 or 9: 4 ways (11.1%)
- 6 or 8: 5 ways (13.9%)
- 7: 6 ways (16.7%)
That is why 7 is the most common total, and why games such as Catan put their best numbers on 6 and 8.
Doubles
6 of the 36 combinations are doubles, so the chance is 1 in 6. Double sixes are 1 in 36.
At least one six
Work out the chance of no six and subtract it from 1. With four dice, the chance of no six is (5/6)⁴ = 48.2%, so the chance of at least one six is 51.8%. With one die you need about four rolls to have a better-than-even chance.
Dice have no memory
After five rolls without a six, the next roll is still 1 in 6. Believing a number is "due" is the gambler's fallacy.
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