Ping Paja Pong

Chef and Paja are bored, so they are playing an infinite game of ping pong. The rules of the game are as follows: - The players play an infinite number of games. At the end of each game, the player who won it scores a point. - In each game, one of the players *serves*. Chef serves in the first game. - After every $K$ points are scored (regardless of which players scored them), i.e. whenever $K$ ga