Alice and Bob are going to play a game, with the following rules:

1st Alice picks a probability p, 0 <= p < 0.5

2nd Bob takes any finite number of counters B.

3rd Alice takes any finite number of counters A.

These happen in sequence, so Bob chooses B knowing p, and Alice chooses A knowing p and B.

A series of rounds are then played. Each round, either Bob gives Alice a counter (probability p) or Alice gives Bob a counter (probability 1-p). The game terminates when one player is out of counters, and that player is the loser.

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