Guide · The 2d6 bell curve
Roll Two Dice
Updated: June 2026
Rolling two dice is the heartbeat of board games from Monopoly to backgammon, and it hides a lovely piece of maths: the totals are not equally likely. Seven turns up far more than two or twelve, and once you see why, the whole bell-shaped pattern of 2d6 falls into place. Roll a pair here and watch it happen.
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36 combinations, 11 totals
Each die has 6 faces, so two dice produce 6 × 6 = 36 equally likely combinations. But those 36 combinations only add up to 11 different totals, from 2 to 12 — and the totals in the middle can be reached more ways than the ones at the edges. That mismatch is the whole story: every combination is equally likely, but the totals are not, because some totals collect more combinations than others.
Why seven wins
Seven is the most common total because it has the most ways to be made: 1-6, 2-5, 3-4, and the same three reversed — six combinations in all. As you move away from seven toward the extremes, the number of combinations falls off symmetrically, until you reach 2 (only 1-1) and 12 (only 6-6), each with a single combination. Plot the counts and you get the familiar triangular bell that peaks at seven.
| Total | Ways | Probability |
|---|---|---|
| 2 | 1 | 1/36 ≈ 2.8% |
| 3 | 2 | 2/36 ≈ 5.6% |
| 4 | 3 | 3/36 ≈ 8.3% |
| 5 | 4 | 4/36 ≈ 11.1% |
| 6 | 5 | 5/36 ≈ 13.9% |
| 7 | 6 | 6/36 ≈ 16.7% |
| 8 | 5 | 5/36 ≈ 13.9% |
| 9 | 4 | 4/36 ≈ 11.1% |
| 10 | 3 | 3/36 ≈ 8.3% |
| 11 | 2 | 2/36 ≈ 5.6% |
| 12 | 1 | 1/36 ≈ 2.8% |
Doubles and snake eyes
Doubles are a category of their own. There are six of them — 1-1 up to 6-6 — among the 36 combinations, so the chance of rolling some double is 6 in 36, or 1 in 6. A specific double, though, such as double ones ("snake eyes") or double sixes ("boxcars"), is just one combination in 36. That gap explains why "any double" feels routine in a game while "snake eyes exactly" feels like a rare event — both are true.
- Any double: 1 in 6 (≈16.7%).
- A specific double like snake eyes: 1 in 36 (≈2.8%).
- Average total of 2d6: exactly 7.
See it for yourself
Set the count to 2 and the sides to 6, then roll repeatedly and watch the totals in the history. Over a handful of rolls the results look random and lumpy, but as the rolls add up the middle totals clearly pull ahead, and seven leads the pack. It is the clearest hands-on way to feel the difference between "every combination equally likely" and "totals shaped like a bell."
Frequently asked questions
What's the most common total on two dice?
Seven, made six ways out of 36 combinations — about 16.7%.
What are the odds of doubles?
Any double is 1 in 6; a specific double like snake eyes is 1 in 36.
What's the average total of two dice?
Seven — each die averages 3.5, and 7 is also the peak of the distribution.
Why isn't every total equally likely?
Combinations are equally likely, but middle totals can be made more ways, so they come up more often.