A standard six-sided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the n-th n appears.
Let P(n)=the probability the game terminates with the n-th n.
Find the distribution of n.
Feel free to generalize for m sides.
Warning: I have not managed this past m=4.
(In reply to re: more results (11 and 12)
I didn't really expect those ratios to be quite √10, but I did expect them to have a more regular behavior. That down and up is a bit of a shock.
Posted by Jer
on 2015-07-05 16:07:34