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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