Dice Probability Calculator
Calculate the probability of rolling specific outcomes with any number and type of dice. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
P(sum=k) = count of combinations that sum to k / total outcomes (sides^dice)
Total outcomes = sides^numDice. The number of ways to achieve a specific sum follows a bell curve centered on the average roll.
Worked Examples
Example 1: 2d6 rolling 7
Problem:2 six-sided dice, target sum 7
Solution:6 ways out of 36 = 16.67%
Result:16.67% (1 in 6)
Frequently Asked Questions
What is the difference between odds and probability?
Probability is expressed as a number between 0 and 1 (or a percentage), representing the likelihood of an event. Odds compare favorable outcomes to unfavorable ones — odds of 3:1 means 3 wins for every 1 loss, which is a probability of 3/(3+1) = 75%. Casinos often express odds differently from true probability to build in their house edge.
What is the probability of rolling a specific number on a standard die?
A fair six-sided die has 1/6 ≈ 16.67% probability for each face. Rolling at least one specific number in two rolls = 1 − (5/6)² ≈ 30.6%. Rolling two specific numbers on two dice = 1/36 ≈ 2.78%. These calculations multiply individual probabilities for independent events.
What is a fair game in probability theory?
A fair game is one where the expected value for all players is zero — no participant has a mathematical advantage. In practice, most casino games are unfair (negative EV for players) due to the house edge. Flipping a coin for even money is a fair game; flipping for $0.90 per win and $1 per loss is unfair.
What is the birthday problem in probability?
The birthday problem asks: how many people are needed for a 50% chance two share a birthday? The answer is just 23 people — surprising because there are 365 days. The probability no two people share a birthday with n people = (365/365)(364/365)(363/365)...(365−n+1)/365. With 23 people this equals ≈50.7%, meaning a shared birthday is more likely than not.
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy