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(3): computer aided solution
After more than 5 1/2 hours the 7-sided calculation is only up to where the first three throws are 2, 3, 6. Seeing no hope of getting to 7,7,7, I'm shutting it down, especially as its window had taken to setting itself for some reason to be always on top, and then when minimizing it, not being able to bring it back from minimization.
Makes me wonder what the Big O time is for this calculation, going from milliseconds for the first few, then 2 minutes and now it looks like days or weeks for the next.
Edited on July 2, 2015, 3:45 pm
Posted by Charlie
on 2015-07-02 15:41:55