Dice notation
Roll 2d6
The first curve most people ever see, and the backbone of nearly every board game with dice in the box.
The shape of 2d6
Your last roll is marked in white. The tall bars are where this notation actually lives.
- Lowest
- 2
- Highest
- 12
- Average
- 7.00
- Most likely
- 7
- Chance of 7
- 16.7%
- Possible totals
- 11
Peak at 7 (16.7%). Average 7.00. Range 2–12.
There is exactly one way to roll 2 and one way to roll 12, so each sits at 2.78%, or 1 in 36. There are 6 ways to make 7, which is why the middle of the range dominates. Rolling 2 dice instead of one trades range for reliability.
The most rolled pair in gaming
Two six sided dice added together is the oldest randomiser in mass use, and the reason is the shape you can see above. Thirty six equally likely combinations collapse into eleven possible totals, and they do not collapse evenly: six of those combinations make 7 and exactly one makes 12. That single fact is the engine of craps, of Monopoly's board spacing, and of the numbered tiles in Catan, where the pips printed under each number are just a redrawing of this histogram.
It shows up in tabletop RPGs too, most obviously as greatsword and maul damage, where the designers wanted a weapon that reliably deals around 7 rather than one that swings wildly. Compare it with a d12 greataxe: nearly the same average, completely different feel. The axe deals 1 through 12 flat, so it whiffs for 1 or 2 about 17% of the time. The greatsword's 2d6 lands under 4 only 8% of the time. Buying the sword is buying the middle of the curve.
The practical rule of thumb: on 2d6, anything from 6 to 8 is ordinary, it happens 44% of the time. Anything at 10 or above is genuinely notable at 17%, and boxcars are a one in thirty six event you will see roughly once an hour of steady play.
Every total on 2d6, with odds
Exact figures, enumerated rather than simulated.
| Total | Chance | Odds | This or higher | This or lower |
|---|---|---|---|---|
| 2 | 2.78% | 1 in 36 | 100.0% | 2.78% |
| 3 | 5.56% | 1 in 18 | 97.2% | 8.33% |
| 4 | 8.33% | 1 in 12 | 91.7% | 16.7% |
| 5 | 11.1% | 1 in 9 | 83.3% | 27.8% |
| 6 | 13.9% | 1 in 7 | 72.2% | 41.7% |
| 7 | 16.7% | 1 in 6 | 58.3% | 58.3% |
| 8 | 13.9% | 1 in 7 | 41.7% | 72.2% |
| 9 | 11.1% | 1 in 9 | 27.8% | 83.3% |
| 10 | 8.33% | 1 in 12 | 16.7% | 91.7% |
| 11 | 5.56% | 1 in 18 | 8.33% | 97.2% |
| 12 | 2.78% | 1 in 36 | 2.78% | 100.0% |
Common questions about 2d6
Why is 7 the most common roll on two dice?
Seven is the most common roll on 2d6 because it has six different combinations behind it and no other total has more: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. Twelve has only one, 6+6. Seven is also the only total that every face on the first die can reach, whatever it shows, because there is always a matching face on the second.
What are the odds of rolling doubles on 2d6?
The odds of rolling doubles on 2d6 are 6 in 36, or 16.7%, since there are six doubles among the thirty six combinations. That is the same figure as rolling a 7, which surprises people, but 7 and doubles are different things: 7 can never be a double, and the six doubles are spread across six different totals.
What are the odds of rolling 12 on 2d6?
The odds of rolling 12 on 2d6 are 2.78%, or 1 in 36. The minimum of 2 is equally rare at 2.78%. Both extremes need every die to cooperate.
What is the most likely result of 2d6?
The most likely result of 2d6 is 7, at 16.7%. There are 6 different combinations that add up to 7, against 1 for 12. That gap is what makes the curve.