A brief nod to the fantastically useful Troll, a dice roller and probability calculator. I used it to estimate the probabilities of rolling matches in Hollowpoint or a similar D6 mechanic. Brief summary in a not-very-pretty table:
2d | 3d | 4d | 5d | 6d | 7d | 8d | 9d | 10d | |
Nothing | 83 | 56 | 28 | 9 | 2 | 0 | 0 | 0 | 0 |
Anything | 17 | 44 | 72 | 91 | 98 | 100 | 100 | 100 | 100 |
One Set | 17 | 44 | 65 | 64 | 43 | 20 | 7 | 2 | 1 |
Two Sets | 0 | 0 | 7 | 27 | 52 | 62 | 51 | 33 | 18 |
Three Sets | 0 | 0 | 0 | 0 | 4 | 18 | 40 | 54 | 54 |
Four Sets | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 11 | 26 |
Five Sets | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
At least triple | 0 | 3 | 10 | 21 | 37 | 54 | 71 | 84 | 93 |
At least two sets | 0 | 0 | 7 | 27 | 56 | 80 | 93 | 98 | 99 |
At least double+triple | 0 | 0 | 0 | 4 | 17 | 40 | 64 | 82 | 93 |
At least three sets | 0 | 0 | 0 | 0 | 4 | 18 | 42 | 65 | 81 |
At least quad | 0 | 0 | 0 | 2 | 5 | 11 | 18 | 28 | 40 |
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p>Interesting outcomes there. If you want to have a system where PCs get more than 1 set per round the sweet spot is a pool of around 6 dice. If triples are significant then they start to appear around the same time; and if quads are significant, you get one about 1 time in 20 for a 6d pool, but they stay relatively unlikely up to 10d.
The thing about Hollowpoint is that burning a trait automatically bumps up the threshold by 2 dice, but the probabilities just shift 2 columns to the right. Also for info, Hollowpoint base dice pools are 1 to 6. To be continued.