A standard sixsided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the nth n appears.
Let P(n)=the probability the game terminates with the nth 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(2): computer aided solution by Charlie)
I'm trying the 7sided version.
Of course I've removed the rational exactvalue calculation.
After evaluating a firstthrow value of 1, the next thing it needs to evaluate is all the possibilities for 2,3,3,4,4. Evaluating just those possibilities takes 45 seconds. I'll see how far we get after an hour.

Posted by Charlie
on 20150702 09:39:18 