About Mini-Cactpot Odds

[Jambalaya]

Someone with more time could explain this better than I, but certain totals have lower or higher probability of happening, it's not a matter of odds of sequence such as 1,2,3 or 7,8,9. For sequence, all combinations have equal odds of appearing (1,2,4 has the same odds as 1,2,5 and 1,3,7, etc.)

However sums don't have the same odds. There are 84 sum possibilities.

I made a quick excel on the odds of each, hopefully this pastes well:

Outcome | Number of times | Odds of Outcome
6 1 1.1905%
7 1 1.1905%
8 2 2.3810%
9 3 3.5714%
10 4 4.7619%
11 5 5.9524%
12 7 8.3333%
13 7 8.3333%
14 8 9.5238%
15 8 9.5238%
16 8 9.5238%
17 7 8.3333%
18 7 8.3333%
19 5 5.9524%
20 4 4.7619%
21 3 3.5714%
22 2 2.3810%
23 1 1.1905%
24 1 1.1905%


Also note that in a 3x3 grid, you get 7 of these rolls, some of them exclude the others as each value can only appear once. That would also affect these possibilities, but I'm too lazy to factor them in. This gives a good overview though.