Consider Marienbad, a variation of the game described in the Guided Exercise of this chapter. As before, players take turns removing balls from the baskets, except that players are allowed to remove as many balls as they wish, provided that each player removes balls from only one of the baskets in each round.

For example, player 1 might remove three red balls in one round and four blue balls in another round. Each player must remove at least one ball when it is his turn to move. The player who is forced to remove the last ball (whichever basket it is in) is declared the loser. As the result of this chapter establishes, one of the players has a winning strategy in this game.

Explain which player has the winning strategy and how the identity of the winning player depends on m and n. If you can, also describe the winning strategy.