Posted: Dec 21, 2012 8:02 am
lpetrich wrote:As to coins and dice, coins can be interpreted as d2 dice.
A sequence of all distinct for d(n)? The probability that any one sequence will have all distinct will be 1*(1-1/n)*(1-2/n)*...*(1/n) = n!/(nn) ~ e-n*sqrt(2*pi*n).
Number of faces, probability of an all-faces sequence:
2 0.5
3 0.222222
4 0.09375
5 0.0384
6 0.0154321
7 0.0061199
8 0.00240326
9 0.000936657
10 0.00036288
11 0.000139906
12 0.0000537232
So this method quickly becomes impractical.
It quickly becomes impractical even with heavily unfair coins as well, as the likelihood of HT or TH popping up becomes very low.