Dice probability calculator
Find the exact chance of a roll: how likely 10 dice are to give five 4s or better, or how often 2d6+3 makes 10. Worked out exactly, not guessed from practice rolls.
Worked out exactly with general probability maths, not by rolling lots of times. Percentages are rounded.
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Chance to hit a target
Use this when you roll a handful of dice and count the ones that reach a number. Set how many dice, how many sides and the number each one needs, for example 10 dice needing 4 or more on a d6. Choose a reroll if your game lets you roll 1s, or any misses, a second time. The tool shows the chance of at least the number of successes you ask for, the average, and the chance of every count from none to all.
Some games roll in two steps: dice that pass the first number are picked up and rolled again against a second one. Tick "Add a second step" and set that number too.
Chance of a total
Type a roll the same way as in the dice roller: 2d6+3, 4d6 drop lowest, 2d20kh1 to roll two and keep the higher, 3d6r1 to reroll 1s once, or d6! for exploding dice. Pick this or more, this or less, or exactly, and a total. You get the chance, the average and the most likely result, with a chart and a table of every total.
How to read the chart and table
Each bar is one result, and the taller it is, the more likely it is to come up. The blue bars are the results that count for the question you asked. In the table, "Exactly" is the chance of that result on the nose, and "This or more" adds up everything from it upwards, which is usually the number you want before a big roll. Very rare results, under 1 in 20,000, are left off so the table stays readable.
How it works
It's general probability maths, done exactly rather than by rolling thousands of times. On one die every face has the same chance, and a reroll moves some of that chance onto the other faces: on a d6 needing 4 or more, a straight roll works half the time, and rerolling 1s adds a sixth of a half, so 7 in 12. For counting successes the tool uses the binomial formula, which gives the chance that exactly so many dice out of a handful succeed. For totals it adds the dice in one at a time, counting every way the faces can fall (mathematicians call this convolution), and for keep and drop it counts how many dice land on each number. Exploding dice could in theory go on for ever, so the tool stops once what is left is too small to change any answer.
When you have the numbers, the game clock keeps a long game moving, and the games room guide has ideas for the table itself.
Questions and answers
What are the odds of rolling 7 on two dice?
6 in 36, which is 1 in 6 or about 16.7%. Six of the 36 ways two dice can land add up to 7: 1 and 6, 2 and 5, 3 and 4, and each of those the other way round. No other total has as many.
How much does rerolling 1s help?
On a d6 needing 4 or more it lifts your chance from 1 in 2 to 7 in 12, about 58.3%. Rerolling every miss once does more: 3 in 4, or 75%.
What is the chance of 15 or more on a d20 with advantage?
51%. Rolling two and keeping the higher only misses when both dice show 14 or less, which happens 14/20 × 14/20 = 49% of the time.
What is the average of 4d6 drop lowest?
About 12.24 (exactly 15,869 divided by 1,296), against 10.5 for a plain 3d6. The calculator shows the full spread from 3 to 18.
Is this a simulation?
No. Every chance is worked out exactly from the faces of the dice, so it gives the same answer every time. The percentages are rounded to show them.