Math Behind 4d6 Drop Lowest

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While it's best known for its association with D&D, there are several games that have used the mechanic of "roll 4d6 and drop the lowest" to produce a favorably weighted 3d6 roll. But the math geeks and RPG designers among us need to know exactly what results this produces — and the options are either (A) code VBA For/Next loops in Excel followed by pivot tables, or (B) wait for someone else to do that work and just read the results. Like, here. You're welcome.

Result Occurrences Likeliness
3 1 0.08%
4 4 0.31%
5 10 0.77%
6 21 1.62%
7 38 2.93%
8 62 4.78%
9 91 7.02%
10 122 9.41%
11 148 11.42%
12 167 12.89%
13 172 13.27%
14 160 12.35%
15 131 10.11%
16 94 7.25%
17 54 4.17%
18 21 1.62%
  • Mean: 12.24
  • Median: 12
  • Mode: 13

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