Dice Probability Calculator
Calculate the exact probability of rolling a specific sum (or at least / at most a value) with multiple dice, with the complete distribution of all possible sums. Handy for board games or role-playing games. Fully local computation, no server.
How it works
The calculation enumerates all possible outcome combinations for the chosen number of dice (using dynamic programming, no random dice rolls), then counts, for each possible sum, how many combinations lead to it. The exact probability is that count divided by the total number of combinations.
Why is the sum of 7 the most likely with two 6-sided dice?
Because there are 6 different ways to get a 7 with two dice (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) versus only one way to get a 2 (1+1) or a 12 (6+6): the more 'central' a sum is in the possible range, the more combinations lead to it.
What do the 'at least' and 'at most' options mean?
'At least X' calculates the cumulative probability of getting X or more (useful for a saving throw you need to succeed), while 'at most X' calculates the cumulative probability of getting X or less.
The calculation is purely mathematical and local: no data is sent to a server.