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<blockquote data-quote="NotAYakk" data-source="post: 7849871" data-attributes="member: 72555">Blue that isn't right; if your highest roll is 15, the other die doesn't have a uniform distribution from 1 to 20 (it cannot be &gt; 15 for example).The actual math looks annoyingly complex; every simplification I've tried runs into issues like that.For example, if you are rolling 2d20 and using the high roll and get a crit on doubles, the distribution of the high roll not uniform, but the distribution of doubles ends up being a uniform distribution.&nbsp; So you get 0.05 times the 1d20 hit chance (P) crits, and 1-(1-P)^2 hit chance.On the plus side, there are only 20^3 or 8000 cases.&nbsp; So counting is plausible, you could even do it in a spreadsheet.Doing so we get:<table style='width: 100%'><tr><td>0.07375</td></tr><tr><td>0.073625</td></tr><tr><td>0.073125</td></tr><tr><td>0.07225</td></tr><tr><td>0.071</td></tr><tr><td>0.069375</td></tr><tr><td>0.067375</td></tr><tr><td>0.065</td></tr><tr><td>0.06225</td></tr><tr><td>0.059125</td></tr><tr><td>0.055625</td></tr><tr><td>0.05175</td></tr><tr><td>0.0475</td></tr><tr><td>0.042875</td></tr><tr><td>0.037875</td></tr><tr><td>0.0325</td></tr><tr><td>0.02675</td></tr><tr><td>0.020625</td></tr><tr><td>0.014125</td></tr><tr><td>0.00725</td></tr></table>so a 7.4% crit chance if you hit on a 1, and a 0.7% crit chance if you hit on a 20.The number of ways that the two highest rolls land on N is equal to 3N-2 based on the spreadsheet.</blockquote>

[QUOTE="NotAYakk, post: 7849871, member: 72555"] Blue that isn't right; if your highest roll is 15, the other die doesn't have a uniform distribution from 1 to 20 (it cannot be > 15 for example). The actual math looks annoyingly complex; every simplification I've tried runs into issues like that. For example, if you are rolling 2d20 and using the high roll and get a crit on doubles, the distribution of the high roll not uniform, but the distribution of [B]doubles[/B] ends up being a uniform distribution. So you get 0.05 times the 1d20 hit chance (P) crits, and 1-(1-P)^2 hit chance. On the plus side, there are only 20^3 or 8000 cases. So counting is plausible, you could even do it in a spreadsheet. Doing so we get: [TABLE] [TR] [TD]0.07375[/TD] [/TR] [TR] [TD]0.073625[/TD] [/TR] [TR] [TD]0.073125[/TD] [/TR] [TR] [TD]0.07225[/TD] [/TR] [TR] [TD]0.071[/TD] [/TR] [TR] [TD]0.069375[/TD] [/TR] [TR] [TD]0.067375[/TD] [/TR] [TR] [TD]0.065[/TD] [/TR] [TR] [TD]0.06225[/TD] [/TR] [TR] [TD]0.059125[/TD] [/TR] [TR] [TD]0.055625[/TD] [/TR] [TR] [TD]0.05175[/TD] [/TR] [TR] [TD]0.0475[/TD] [/TR] [TR] [TD]0.042875[/TD] [/TR] [TR] [TD]0.037875[/TD] [/TR] [TR] [TD]0.0325[/TD] [/TR] [TR] [TD]0.02675[/TD] [/TR] [TR] [TD]0.020625[/TD] [/TR] [TR] [TD]0.014125[/TD] [/TR] [TR] [TD]0.00725[/TD] [/TR] [/TABLE] so a 7.4% crit chance if you hit on a 1, and a 0.7% crit chance if you hit on a 20. The number of ways that the two highest rolls land on N is equal to 3N-2 based on the spreadsheet. [/QUOTE]

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