Dice Probability Guide: The Math Behind Every Roll
What are the odds of rolling a natural 20? Or snake eyes? Here's the complete probability guide for every common dice scenario — with charts and calculators.
The Problem: Gut Feelings Are Wrong About Dice
Humans are terrible at estimating probability. A study found that people overestimate the chance of rolling a 7 on 2d6 by 40%. Understanding real odds improves game strategy.Common Dice Probabilities
Step-by-Step: Calculate Any Dice Probability
Common Mistakes
| Roll | Dice | Probability | Odds |
|---|---|---|---|
| Natural 20 | 1d20 | 5% | 1 in 20 |
| Snake eyes | 2d6 | 2.78% | 1 in 36 |
| Rolling 7 | 2d6 | 16.67% | 1 in 6 |
| Rolling 10+ | 2d6 | 83.33% | 5 in 6 |
| Triples | 3d6 | 4.63% | 1 in ~22 |
| All same | 3d6 | 0.46% | 1 in ~216 |
Try it now: Open the Dice Tool →
Frequently Asked Questions
What are the odds of rolling a natural 20?
5% or 1 in 20. Each face of a d20 has an equal probability. The 'gambler's fallacy' is thinking that after not rolling a 20 for a while, you're 'due' for one — each roll is independent.
What is the most likely sum when rolling 2d6?
7, with a probability of 16.67% (6 out of 36 combinations). The distribution follows a bell curve: 2 and 12 are least likely (2.78% each), 7 is most likely.
How do I calculate dice probability?
For a single die: 1/number of faces. For multiple dice: count favorable combinations / total combinations. For 2d6, there are 36 total combinations. 6 of them sum to 7, so P(7) = 6/36 = 16.67%.