Dice Probability Explained: Odds for One, Two and Three Dice
By RithyVerse Studio · Updated October 12, 2026 · 3 min read
Dice are the classic randomness tool, and the maths behind them is a perfect first lesson in probability. Whether you are playing a board game, planning a tabletop adventure or helping a student with homework, these are the numbers worth knowing.
One six-sided die
A fair six-sided die has six equally likely faces, so each number from 1 to 6 comes up with a probability of 1 in 6, or about 16.7 percent. Rolling a particular number does not make it more or less likely next time. Every roll is independent.
The chance of an even number is 3 in 6, which is 50 percent. The chance of rolling 5 or more is 2 in 6, or about 33 percent.
Two dice: why 7 is special
With two dice the total ranges from 2 to 12, but the totals are not equally likely. There are 36 equally likely combinations of the two dice (6 times 6), and different totals can be made in different numbers of ways. A total of 7 can be made six ways, while a total of 2 can only be made one way (1 and 1).
- 2 and 12: 1 way each, 1 in 36 (about 2.8 percent)
- 3 and 11: 2 ways each, 2 in 36 (about 5.6 percent)
- 4 and 10: 3 ways each, 3 in 36 (about 8.3 percent)
- 5 and 9: 4 ways each, 4 in 36 (about 11.1 percent)
- 6 and 8: 5 ways each, 5 in 36 (about 13.9 percent)
- 7: 6 ways, 6 in 36 (about 16.7 percent)
This is why a 7 is the most common total in games that use two dice, and why board games such as Settlers of Catan give the most common totals (6 and 8) the best production odds.
Rolling doubles
A double means both dice show the same number. There are six doubles among the 36 combinations, so the chance is 1 in 6. Many games give a bonus for doubles, and it feels rarer than it is because people notice the streaks more than the misses.
Three dice
With three dice there are 216 combinations (6 times 6 times 6) and totals from 3 to 18. The most common totals are 10 and 11, each with 27 combinations, or 12.5 percent. The least common are 3 and 18, each with just one combination, about 0.46 percent. The shape of the distribution forms a bell curve: the more dice you add, the more the totals cluster around the middle.
The chance of at least one six
People often think that rolling six dice guarantees a six. It does not. The chance of getting no sixes on six dice is (5/6) to the power of six, about 33.5 percent, so the chance of at least one six is roughly 66.5 percent. It is a useful reminder that probabilities multiply rather than add.
Other dice sizes
Tabletop games use dice with 4, 8, 10, 12 and 20 sides. For any fair die with N sides, each face has a 1 in N chance. A twenty-sided die gives a 5 percent chance for each number, which is why rolling a natural 20 feels so special.
Are real dice fair?
Cheap or worn dice can have slight imperfections, such as rounded edges or off-centre pips, that nudge the odds. A digital roller does not have that problem, because the result is chosen by a random process and the animation simply shows it. Try the 3D dice roller and compare your results with the tables above after a few dozen rolls.
Key takeaways
- Each face of a fair die is equally likely, and rolls are independent.
- With two dice, totals near 7 are far more common than 2 or 12.
- The more dice you add, the more results bunch around the average.
Next, read about the other classic randomiser in Coin Flip Odds and Myths.