IBM Ponder This #054 · October 2002

This month's problem was sent in by Sudipta Das from Calcutta:

In a certain tournament, N players have been numbered 1 through N.
But, only M players can play the game together (1<M<N).
So, Players 1 through M start the game.
One of them goes out, and Player (M+1) joins the game.
This continues until there is no one left to join the game.

As a function of N and M, what is the probability that the game ended with an even-numbered player going out?

Closed-form solution is preferred (expressed without sums or recursion).

Solution

Best opened after a real attempt

To be added.