How to calculate dice probability
Every face of a fair die is equally likely, and dice don’t affect each other. So the chance of a total is the number of rolls that make it, divided by all possible rolls. Here it is for the total you just rolled:
Here it is with your numbers:
- All possible rolls = 6 × 6
- All possible rolls = 36
- Ways to roll 7 = 6
- Chance = 6 ÷ 36
- Chance = 16.6667%
It means a total of 7 comes up 6 times in every 36 rolls of 2 × d6, on average.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
Two dice probability chart
With two six-sided dice, totals in the middle are the most likely, because more pairs add up to them. Your total is highlighted when you roll 2 × d6.
| Total | Ways out of 36 | Chance |
|---|---|---|
| 2 | 1 | 2.7778% |
| 3 | 2 | 5.5556% |
| 4 | 3 | 8.3333% |
| 5 | 4 | 11.1111% |
| 6 | 5 | 13.8889% |
| 7 | 6 | 16.6667% |
| 8 | 5 | 13.8889% |
| 9 | 4 | 11.1111% |
| 10 | 3 | 8.3333% |
| 11 | 2 | 5.5556% |
| 12 | 1 | 2.7778% |
Average dice roll
One die averages (sides + 1) ÷ 2: 3.5 for a d6, 10.5 for a d20, 50.5 for a d100. Several dice average that times the number of dice. That is the long-run average, shown as “Expected average” above; the running average of your own rolls drifts toward it the more you roll.
Source OpenStax · Introductory Statistics 2e, 4.2 Mean or Expected Value ↗
How this dice roller works
Each die uses your browser’s built-in cryptographically strong random number generator. To keep every face exactly equally likely, it takes just enough random bits to cover the faces and simply tries again when they land past the last face (a d6 uses 3 bits, 0 to 7, and redraws a 6 or 7). Nothing is sent anywhere.
Source W3C · Web Cryptography Level 2, the Crypto interface ↗
FAQs
What’s the probability of getting a 7 when rolling 2 dice?
6 in 36, which is 1 in 6, or 16.6667%. Six of the 36 equally likely rolls add up to 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1). No other total has as many.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗
What are the 36 possible outcomes of rolling two dice?
Each die has 6 faces, so there are 6 × 6 = 36 ordered pairs, from 1 and 1 up to 6 and 6. A 2 and a 5 is a different outcome from a 5 and a 2, which is why a total of 7 has six ways and a total of 2 has only one.
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
What is the average roll of two dice?
7. One die averages 3.5 (1 to 6 added up is 21, divided by 6), so two average 7. That is the long-run average: the running average above gets close to it after many rolls.
Source OpenStax · Introductory Statistics 2e, 4.2 Mean or Expected Value ↗
What is the hardest number to roll with two dice?
2 and 12 are the hardest, with one way each out of 36 (2.7778%): double 1 and double 6.
Source OpenStax · Introductory Statistics 2e, 3.1 Terminology ↗
Is 11 or 12 more likely on two dice?
11 is twice as likely: it can be 5 + 6 or 6 + 5 (2 ways, 5.5556%), while 12 needs double 6 (1 way, 2.7778%).
What are the chances of rolling 1, 2, 3, 4, 5, 6 with 6 dice?
720 in 46,656, which is 1.5432% (about 1 in 65). The first die can be any of 6 numbers, the next any of the 5 left, and so on: 6 × 5 × 4 × 3 × 2 × 1 = 720 winning rolls out of 6⁶ = 46,656.
Source OpenStax · Introductory Statistics 2e, 3.3 Two Basic Rules of Probability ↗
Sources
- OpenStax: Introductory Statistics 2e, 3.1 Terminology
- OpenStax: Introductory Statistics 2e, 3.3 Two Basic Rules of Probability
- OpenStax: Introductory Statistics 2e, 4.2 Mean or Expected Value
- W3C: Web Cryptography Level 2, the Crypto interface