I'm having some trouble with a maths problem I thought up. I wondered if any smart people on here could tell me if this problem has a proper name and has already solve it, or perhaps give it a try themselves.
The Problem:
Me and you have 5 counters each, mine are numbered from 1 to 5 and yours are numbered from 6 to 10. A random number generator picks a number between 1 and 10. Whoever owns that counter takes a random counter from the other player. This continues until 1 player has all the counters. Given you win the first counter, what's the probability you win outright? What if we had n counters each?