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# A deterministic probability game

Best Answer k-man, 25 March 2014 - 03:18 PM

Spoiler for Assuming the number of available counters is not limited...

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Posted 25 March 2014 - 02:11 PM

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.

Whom does this game favor?

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### #2 k-man

k-man

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Posted 25 March 2014 - 03:18 PM   Best Answer

Spoiler for Assuming the number of available counters is not limited...

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### #3 m00li

m00li

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Posted 02 May 2014 - 11:00 PM

Spoiler for biased

Edited by m00li, 02 May 2014 - 11:01 PM.

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