Home·Dice odds

Dice sum odds — all 111 outcomes

Every sum you can roll with one to six ordinary dice, with the number of ways it happens and how likely it is. Handy when you want to know what a board game roll will really give you.

One die6

6 equally likely rolls, with sums from 1 to 6.

123456
116.67%Ways to roll it 1 · Most likely sum216.67%Ways to roll it 1 · Most likely sum316.67%Ways to roll it 1 · Most likely sum416.67%Ways to roll it 1 · Most likely sum516.67%Ways to roll it 1 · Most likely sum616.67%Ways to roll it 1 · Most likely sum

2 dice11

36 equally likely rolls, with sums from 2 to 12.

23456789101112
22.78%Ways to roll it 135.56%Ways to roll it 248.33%Ways to roll it 3511.11%Ways to roll it 4613.89%Ways to roll it 5716.67%Ways to roll it 6 · Most likely sum813.89%Ways to roll it 5911.11%Ways to roll it 4108.33%Ways to roll it 3115.56%Ways to roll it 2122.78%Ways to roll it 1

3 dice16

216 equally likely rolls, with sums from 3 to 18.

357911131517
30.46%Ways to roll it 141.39%Ways to roll it 352.78%Ways to roll it 664.63%Ways to roll it 1076.94%Ways to roll it 1589.72%Ways to roll it 21911.57%Ways to roll it 251012.5%Ways to roll it 27 · Most likely sum1112.5%Ways to roll it 27 · Most likely sum1211.57%Ways to roll it 25139.72%Ways to roll it 21146.94%Ways to roll it 15154.63%Ways to roll it 10162.78%Ways to roll it 6171.39%Ways to roll it 3180.46%Ways to roll it 1

4 dice21

1,296 equally likely rolls, with sums from 4 to 24.

49141924
40.08%Ways to roll it 150.31%Ways to roll it 460.77%Ways to roll it 1071.54%Ways to roll it 2082.7%Ways to roll it 3594.32%Ways to roll it 56106.17%Ways to roll it 80118.02%Ways to roll it 104129.65%Ways to roll it 1251310.8%Ways to roll it 1401411.27%Ways to roll it 146 · Most likely sum1510.8%Ways to roll it 140169.65%Ways to roll it 125178.02%Ways to roll it 104186.17%Ways to roll it 80194.32%Ways to roll it 56202.7%Ways to roll it 35211.54%Ways to roll it 20220.77%Ways to roll it 10230.31%Ways to roll it 4240.08%Ways to roll it 1

5 dice26

7,776 equally likely rolls, with sums from 5 to 30.

51015202530
50.01%Ways to roll it 160.06%Ways to roll it 570.19%Ways to roll it 1580.45%Ways to roll it 3590.9%Ways to roll it 70101.62%Ways to roll it 126112.64%Ways to roll it 205123.92%Ways to roll it 305135.4%Ways to roll it 420146.94%Ways to roll it 540158.37%Ways to roll it 651169.45%Ways to roll it 7351710.03%Ways to roll it 780 · Most likely sum1810.03%Ways to roll it 780 · Most likely sum199.45%Ways to roll it 735208.37%Ways to roll it 651216.94%Ways to roll it 540225.4%Ways to roll it 420233.92%Ways to roll it 305242.64%Ways to roll it 205251.62%Ways to roll it 126260.9%Ways to roll it 70270.45%Ways to roll it 35280.19%Ways to roll it 15290.06%Ways to roll it 5300.01%Ways to roll it 1

6 dice31

46,656 equally likely rolls, with sums from 6 to 36.

6111621263136
60.0021%Ways to roll it 170.01%Ways to roll it 680.05%Ways to roll it 2190.12%Ways to roll it 56100.27%Ways to roll it 126110.54%Ways to roll it 252120.98%Ways to roll it 456131.62%Ways to roll it 756142.49%Ways to roll it 1,161153.57%Ways to roll it 1,666164.82%Ways to roll it 2,247176.12%Ways to roll it 2,856187.35%Ways to roll it 3,431198.37%Ways to roll it 3,906209.05%Ways to roll it 4,221219.28%Ways to roll it 4,332 · Most likely sum229.05%Ways to roll it 4,221238.37%Ways to roll it 3,906247.35%Ways to roll it 3,431256.12%Ways to roll it 2,856264.82%Ways to roll it 2,247273.57%Ways to roll it 1,666282.49%Ways to roll it 1,161291.62%Ways to roll it 756300.98%Ways to roll it 456310.54%Ways to roll it 252320.27%Ways to roll it 126330.12%Ways to roll it 56340.05%Ways to roll it 21350.01%Ways to roll it 6360.0021%Ways to roll it 1

How to read this

  • Two dice do not land evenly. There are six ways to make 7 and only one way to make 2.
  • The more dice, the tighter the middle. With six dice almost everything lands near 21, while 6 or 36 turns up about once in 47,000 rolls.
  • The average sum is 3.5 per die, because one die averages 3.5.
  • Rare is not never — but nor is it due. Roll two dice thirty-six times and there is still roughly a 36% chance you never see a 2.

Frequently asked questions

Q. What are the odds of rolling a 7 with two dice?

Six of the thirty-six outcomes make 7, so 16.67% — one roll in six. It is built from 1+6, 2+5 and 3+4 each way round, which is why it is the most common total on two dice.

Q. Why is one sum more likely than another?

Each die is fair, but the sums are not built from the same number of paths. There is one way to make 2 and six ways to make 7, and the sum with more paths comes up more often.

Q. Is a number that has not come up “due”?

No. Dice keep no memory of earlier rolls. After six 1s in a row, the chance of another 1 is still one in six.

Q. Why do more dice bunch up in the middle?

High and low faces cancel each other out. Getting six 1s means six things going the same way at once, while thousands of different combinations add up to 21.

Q. How were these numbers worked out?

Only the die count and the sum are stored. The distribution for one die is convolved with another die at a time to count the ways, and dividing by six to the power of the die count gives the probability.