Probabilities for the Sum of 1 to 25 Dice

Introduction

This section endeavors to answer the frequently asked question on the probability for any given total over the throw of multiple dice. I shall show the number of combinations (up to 15 significant digits) and probability (to 15 decimal places) of totals for 1 to 10, 15, 20, and 25 dice. I also keep just the number of combinations for all numbers of dice from 1 to 26, without the 15 significant digit constraint, in a section for the unedited data.

Combinations for One to Six Dice.

The first table shows just the number of combinations for one to six dice.

Notice how for two or more dice the number of combinations equals the sum of combinations one column to the left, starting from one row higher to seven rows higher. For example, comb(12 with 3 dice)=comb(11 with 2 dice)+comb(10 with 2 dice)+comb(9 with 2 dice)+comb(8 with 2 dice)+comb(7 with 2 dice)+comb(6 with 2 dice), or 25=2+3+4+5+6+5. Assume the number of combinations for any total less than 1 is 0. This method will work for any number of dice.

1 Die

2 Dice

3 Dice

4 Dice

5 Dice

6 Dice

7 Dice

8 Dice

9 Dice

10 Dice

15 Dice

20 Dice

25 Dice