Posted 05 January 2009 - 10:22 PM
"Hmm, interested myself actually, so let's see if i can work it out. The roller works by having base stats (set by race), then a random number from 1 to 12 added on.
This is based on the binomial distribution, with the probability of getting a max stat being 1/12, and therefore the probability of a stat not being max is 11/12.
To get a 1-stat crit, whereby 1 of the 6 stats is 12 and the rest are not 12. We have (1/12) * (11/12)^5, but we have 6 stats, so we multiply this number by 6 to get .32, which is about 1 in 3.
To get a 2-stat crit, whereby 2 of the 6 stats are 12 and the rest are not 12. We have (1/12)^2 * (11/12)^4, but we have 6 stats and it could be any 2 of them that are max which means we have to work out all ways of getting 2 of the stats max out the 6 available (ie, str-int, str-dex, str-con etc). Or using nCr or the formula n!/r!(n-r)! we get 6!/2!4! which is 6*5/2 = 15 combinations. So 15*(1/12)^2*(11/12)^4 = .0735, which is about 1 in 14.
To get a 3-stat crit, (6!/3!3!)*(1/12)^3*(11/12)^3 = about 1 in 112.
4-stat crit, (6!/4!2!)*(1/12)^4*(11/12)^2 = about 1 in 1645.
5-stat crit, (6!/5!1!)*(1/12)^5*(11/12)^1 = about 1 in 45,242.
6-stat crit, (6!/6!0!)*(1/12)^6*(11/12)^0 = 1*(1/12)^6*1 = 1 in 2,985,984.
For interest, a 0-stat crit is (6!/0!6!)*(1/12)^0*(11/12)^6 = 1*1*(11/12)^6 = 0.59, which is about 1 in 1.7" -JLH
had to search old forum.. wasnt on this one lol....
