At some point, you're going to have two guys with points, the counter and some other guy. In order to transfer them, the one will have to go directly before the other. On any two days, each has a 1 in 100 chance of being selected. The consecutive chance is 1 in 10,000, even if you are trying every single day (which you can't, because the day holds a variable). So, even to do just that last exchange, I can't see how it is mathematically possible to average 3,000 days?
Daniel, have you found a solution to this, or am I just too pessimistic about the probability? Does the math work out like the "two people in the room with the same birthday" problem? No...it can't. Hmmm...