Post/Author/DateTime	Post
Fallenangel359 01-06-07, 08:25 PM	my group has the houserule for hit dice being that you roll it 3 times, and take the best... I'm curious on how to mathematically calculate what, on average, will be the best roll of the 3, for each hit dice. Any help here?
Solaris 01-06-07, 08:48 PM	Here are the average results for the best of three dice, for each type of die: d4: 55/16 = 3.4375 d6: 119/24 = 4.9583333333... d8: 207/32 = 6.46875 d10: 319/40 = 7.975 d12: 455/48 = 9.4791666666... d20: 1239/80 = 15.4875 As for how it's done, here's an example. For the best of 3d4, there are 37 ways to get a 4, 19 ways to get a 3, 7 ways to get a 2, 1 way to get a 1, and a total of 64 possible rolls. The mean is therefore (37*4 + 19*3 + 7*2 + 1*1) / 64 = (148 + 57 + 14 + 1) / 64 = 220/64 = 55/16 In general, the easiest way to do it is to write a computer program which finds the frequencies of all the outcomes and works out the mean for you.
Fallenangel359 01-07-07, 12:52 AM	Thats overly complicated to figure out... Wow... thanks. It definitely means that the d4 gets the best deal, and the d12 gets the worst
Solaris 01-07-07, 01:12 AM	The benefit increases with the number of sides -- your method gives the d4 character 138% of normal hit points, and the d12 character 146% of normal hit points.