Table of Contents
Dice Averages
The average (expected value) of a die roll is the long-run mean over many rolls. For a single die with s sides, the average is (s+1)/2. For multiple dice, averages add together. This is fundamental to game balance, damage calculations in RPGs, and probability theory.
Knowing the expected average helps game designers balance encounters, players make tactical decisions, and statisticians model discrete uniform distributions.
Formula
Common Dice Averages
| Dice | Average | Min | Max |
|---|---|---|---|
| 1d4 | 2.5 | 1 | 4 |
| 1d6 | 3.5 | 1 | 6 |
| 1d8 | 4.5 | 1 | 8 |
| 1d10 | 5.5 | 1 | 10 |
| 1d12 | 6.5 | 1 | 12 |
| 1d20 | 10.5 | 1 | 20 |
| 2d6 | 7.0 | 2 | 12 |
Game Design Uses
Average damage per round (DPR) calculations use dice averages to compare weapons and abilities. 2d6 averages 7 while 1d12 averages 6.5, making 2d6 slightly higher on average with less variance. This distinction matters for game balance.
Frequently Asked Questions
Is 2d6 better than 1d12?
2d6 averages 7 vs 1d12's 6.5 and has lower variance (range 2-12 with a peak at 7 vs flat 1-12). 2d6 is more consistent; 1d12 has higher highs and lower lows.
How does adding dice affect variance?
More dice means lower relative variance. The coefficient of variation decreases as you add more dice, producing more consistent results centered around the average.
Does the average change with advantage?
Yes. Rolling with advantage (take higher of 2d20) raises the average from 10.5 to about 13.8. Disadvantage lowers it to about 7.2.