Dice probabilities

[Albert Chan]

Dice = (x^2 + x^1 + x^0) / 3 = 100%      // see Probability-generating function
Dice^5 = 100% probability too.

From this distribution, just pick what we needed.

>10101^5                     // (x^2+x+1)^5, for x=100
 1.05153045515E20
>(1+5+15+30+45+51+45+30+15+5+1)/3^5
 1
>(1+5+15+30)/3^5      // P(sum >= 7)
 .20987654321