Introduction

First calculations

For 2d6 you could easily draw a table with the results of the roll to gain insight:

first dice→
second dice↓
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

This then would show you the odds of each result:

2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 5 4 3 2 1

If you add more dice, or additional rules, or both (e.g. 4d6, drop lowest for creating characters in DnD5e) this model quickly becomes unwieldy. An additional detriment was that my calculator, a TI-36x Pro, could not calculate such tables, so I had to find another solution.

One could naively try to calculate all the possibilities the dice could roll, but even with 3 dice you can’t use a table directly, and with nested loops in a program you can see the runtime rising exponentially

Dice(d6) Size of event space
1 6
2 36
3 216
+1 *6

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