I was curious what comparative odds where. So, I wrote a litte test program using my Die Python dice library.
2d20(worst) 2d20(best) d20+2 d20+4 d24 d30 1 -> 9.75% 9.75% 0.24% 0.24% 0.00% 0.00% 0.00% 0.00% 4.19% 4.19% 3.36% 3.36% 2 -> 9.28% 19.03% 0.76% 1.00% 0.00% 0.00% 0.00% 0.00% 4.20% 8.38% 3.34% 6.69% 3 -> 8.69% 27.72% 1.25% 2.26% 4.98% 4.98% 0.00% 0.00% 4.16% 12.54% 3.38% 10.07% 4 -> 8.25% 35.97% 1.75% 4.01% 4.97% 9.96% 0.00% 0.00% 4.17% 16.71% 3.33% 13.40% 5 -> 7.77% 43.74% 2.25% 6.25% 5.03% 14.98% 5.02% 5.02% 4.15% 20.86% 3.29% 16.69% 6 -> 7.22% 50.95% 2.76% 9.02% 5.00% 19.99% 5.01% 10.03% 4.14% 25.00% 3.32% 20.01% 7 -> 6.76% 57.71%a 3.25% 12.27% 5.01% 25.00% 5.00% 15.03% 4.17% 29.17% 3.34% 23.35% 8 -> 6.27% 63.98% 3.77% 16.03% 5.03% 30.03% 4.98% 20.01% 4.19% 33.36% 3.34% 26.70% 9 -> 5.74% 69.72% 4.25% 20.28% 5.02% 35.05% 4.97% 24.97% 4.18% 37.54% 3.35% 30.04% 10 -> 5.25% 74.97% 4.73% 25.01% 4.98% 40.03% 4.99% 29.96% 4.18% 41.71% 3.34% 33.39% 11 -> 4.74% 79.71% 5.26% 30.27% 4.96% 44.99% 5.00% 34.96% 4.14% 45.85% 3.33% 36.71% 12 -> 4.26% 83.97% 5.74% 36.00% 4.99% 49.99%a 4.97% 39.93% 4.15% 50.00%a 3.33% 40.04% 13 -> 3.76% 87.73% 6.23% 42.23%a 4.96% 54.95% 4.98% 44.91% 4.17% 54.18% 3.34% 43.39% 14 -> 3.27% 91.00% 6.76% 48.99% 5.03% 59.99% 5.05% 49.96%a 4.16% 58.34% 3.34% 46.73% 15 -> 2.75% 93.76% 7.31% 56.30% 4.97% 64.96% 4.99% 54.94% 4.17% 62.51% 3.30% 50.03%a 16 -> 2.25% 96.00% 7.71% 64.01% 5.00% 69.95% 5.02% 59.96% 4.18% 66.70% 3.34% 53.37% 17 -> 1.77% 97.77% 8.27% 72.27% 5.03% 74.98% 5.02% 64.98% 4.18% 70.88% 3.36% 56.74% 18 -> 1.24% 99.01% 8.72% 80.99% 5.04% 80.02% 5.02% 70.00% 4.16% 75.04% 3.34% 60.07% 19 -> 0.74% 99.75% 9.21% 90.20% 5.00% 85.02% 5.00% 75.00% 4.15% 79.19% 3.34% 63.41% 20 -> 0.25% 100.00% 9.80% 100.00% 14.98% 100.00% 25.00% 100.00% 20.81% 100.00% 36.59% 100.00%
Percentages are off a few 100ths cause results were rolled (1,000,000 times each) rather than calculated. It ends at 20 cause any natural roll >= 20 is a critical. The d20+2 and d20+4 only crit on 20, 5%, but was interesting to compare the 20 or above's. If not obvious d20 has 5% chance for any roll. Assuming GameScience ;)
I'm no longer so sure I like 2d20(best/worst) as general mechanic. Kind of extreme, less than 7 (or more than 14) 50% of the time. All the other rolls are strictly linear and 50% is in the middle of range. Linear curve (except stats) is one of the things that make D&D, D&D.
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