Quote:
Originally Posted by zot
Quote:
Originally Posted by David Bofinger
That was in fact my first plan. But my intuition underestimated how fast the benefits drop off. - D6: mean 3.5
- D8: mean 2.88, i.e. 0.63 better than D6
- D10: mean 2.5, i.e. 1.0 better than D6, 0.37 better than D8
- D12: mean 2.25, i.e. 1.25 less than D6, 0.63 better than D8
- D20: mean 1.75, i.e. 1.75 better than D6, 0.5 less than D12
The gap between D12 and D20 is actually smaller than the gap between D6 and D8. I also considered a system where it cost 2 to buy a D8, 3 to buy a D10, 4 to buy a D12 and 6 to buy a D20. |
Have you analyzed the effects on criticals? If you roll 3d20 and anything over a 6 on each die counts as a 1, that's a much larger chance for a critical than 3d6. |
So off the top of my computer, these seem to be the chances for rolling all 1s or all 6s (i.e. ((sides-5) / sides)^3 * 100%):
d6: 0.46%
d8: 5.27%
d10: 12.5%
d12: 19.85%
d14: 26.57%
d16: 32.5%
d18: 37.67%
d20: 42.19%
It is a much smoother progression of you don't omit d10 and d14-d18.