seanieg89
Well-Known Member
- Joined
- Aug 8, 2006
- Messages
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- HSC
- 2007
People seem to like game theory on here. Here is a nice and simple game that shows some of the mathematics present in poker (beyond mere probability calculations).
Suppose there are three cards in a deck, A > K > Q. Players 1 and 2 are each dealt a card out of this three card deck. Each player inputs an ante of $P before each hand.
In this game player 1 is forced to check and then player 2 has the option of checking or betting $1. In the former case the player with the higher card wins the pot of size $2P, in the latter case player 1 must decide whether or not to 'call' player 2's bet.
A mixed strategy is defined as a predetermined ratio governing your actions. Eg a mixed strategy for player 2 could be betting half of the time and checking half of the time when you have a king, betting 100% of the time when you have an ace and checking 100% of the time when you have a queen. A mixed strategy for player 1 just entails three percentages, the percentage of the time you will call a bet with the cards A,K,Q respectively.
Discuss what it means for one mixed strategy to be "better" than another. Do there exist strategies that are "optimal" in some sense?
Which player (if any) will profit from this game being played a large number of times, assuming both players play optimally.
(This is meant to be a question for discussion rather than just posting complete solutions, a lot can be learned from discussion when it comes to game theory.)
Suppose there are three cards in a deck, A > K > Q. Players 1 and 2 are each dealt a card out of this three card deck. Each player inputs an ante of $P before each hand.
In this game player 1 is forced to check and then player 2 has the option of checking or betting $1. In the former case the player with the higher card wins the pot of size $2P, in the latter case player 1 must decide whether or not to 'call' player 2's bet.
A mixed strategy is defined as a predetermined ratio governing your actions. Eg a mixed strategy for player 2 could be betting half of the time and checking half of the time when you have a king, betting 100% of the time when you have an ace and checking 100% of the time when you have a queen. A mixed strategy for player 1 just entails three percentages, the percentage of the time you will call a bet with the cards A,K,Q respectively.
Discuss what it means for one mixed strategy to be "better" than another. Do there exist strategies that are "optimal" in some sense?
Which player (if any) will profit from this game being played a large number of times, assuming both players play optimally.
(This is meant to be a question for discussion rather than just posting complete solutions, a lot can be learned from discussion when it comes to game theory.)