Quick Answer: The probability of any specific outcome on a fair N-sided die is 1/N. For a d6: each number has 16.67% probability. For two d6: the probability of each sum varies (7 is the most likely at 16.67%). Higher numbers of dice create a bell curve of outcomes.
Single Die Probability
A fair N-sided die gives each face an equal probability of 1/N. So for a standard 6-sided die (d6), each face (1 through 6) has P = 1/6 ≈ 16.67% probability. For a d20, each face has P = 1/20 = 5%. This is called a uniform distribution — all outcomes are equally likely.
| Die Type | Sides | Probability per Face | Common Uses |
|---|---|---|---|
| d4 | 4 | 25% | Small weapons in D&D |
| d6 | 6 | 16.67% | Board games, Monopoly, Yahtzee |
| d8 | 8 | 12.5% | Medium weapons in D&D |
| d10 | 10 | 10% | Percentile rolls, heavy weapons |
| d12 | 12 | 8.33% | Greataxe, barbarian hit die |
| d20 | 20 | 5% | Attack rolls and ability checks in D&D |
Two Dice: The Bell Curve
When you roll two d6 dice and add them, the probability is no longer uniform. There are 36 possible combinations (6×6), and some sums appear more often than others. The sum of 7 is the most likely result:
| Sum | Combinations | Probability |
|---|---|---|
| 2 | 1 way (1+1) | 2.78% |
| 3 | 2 ways | 5.56% |
| 4 | 3 ways | 8.33% |
| 5 | 4 ways | 11.11% |
| 6 | 5 ways | 13.89% |
| 7 | 6 ways | 16.67% |
| 8 | 5 ways | 13.89% |
| 9 | 4 ways | 11.11% |
| 10 | 3 ways | 8.33% |
| 11 | 2 ways | 5.56% |
| 12 | 1 way (6+6) | 2.78% |
More Dice = Stronger Bell Curve
Adding more dice pushes the distribution toward a classic bell curve. Rolling 3d6 (like ability score generation in D&D) produces a nearly normal distribution centered on 10-11, making extreme results (3 or 18) rare. This is the Central Limit Theorem — the sum of many independent random variables approaches a normal distribution.
Probability Notation
In tabletop gaming, dice are denoted as [number]d[sides]. So 2d6 means roll two 6-sided dice and sum them. 3d6 means roll three 6-sided dice and sum them. 1d20 means roll one 20-sided die.