Average Roll of a D6
The average roll of a fair six-sided die is 3.5. That is a long-run average, not a possible result on a single roll.
Expected value
3.5
(1 + 2 + 3 + 4 + 5 + 6) ÷ 6
How the average is calculated
Add the six possible results: 1 + 2 + 3 + 4 + 5 + 6 = 21. Each has probability 1/6, so the expected value is 21 ÷ 6 = 3.5.
That is the whole answer to “what is the average roll on a D6?” The table shows how each face contributes its share.
| Result | Probability | Result × probability |
|---|---|---|
| 1 | 1/6 | 1/6 |
| 2 | 1/6 | 2/6 |
| 3 | 1/6 | 3/6 |
| 4 | 1/6 | 4/6 |
| 5 | 1/6 | 5/6 |
| 6 | 1/6 | 6/6 |
| Total | 6/6 = 1 | 21/6 = 3.5 |
Why you cannot roll 3.5
Each individual roll is a whole number from 1 to 6. The average of many results can be a decimal. A short sequence does not have to average exactly 3.5.
Three rolls have an expected sum of 10.5
Add the expected values: 3.5 + 3.5 + 3.5 = 10.5. The actual sum is always an integer between 3 and 18. Each roll remains independent.
You can try it with the Three rolls mode when you roll a D6 here.
Common questions
No. Each roll is independent, so a streak does not make low results more likely. Over a very large number of rolls, the running average tends to settle near 3.5.
It is 7, because 3.5 + 3.5 = 7. The actual sum of two dice is always a whole number from 2 to 12.