Game thoery question

[MrTeddyKGB]

My question is about using game theory to call on the end when I can only beat a bluff. Ex. say on the end I find myself Heads Up with a hand that can only beat a bluff it is a 10-20 game and there is $80 in the pot and a $20 bet. Say my opp. bluffs opptimal in this spot or close to it, not out of line in either spot. Would it be a resonable statagy to call 1 out of 5 here by using some random device to keep him off balance. Would I be making a mistake in this spot, is my understanding of game theory off? I understand that i could call or fold and get the same value if he is really bluffing optimaly. I just want to know if calling in a mixed random way loses any value. I want to keep an expert off balance and keep me from being a folder or calling station against him. Any comments would be appreciated.

[jdl22]

As you say if you always call or always fold then you will get the same payoff if he is bluffing properly. That means that if you mix between always folding and calling you will also get that payoff. To see this notice that your expectation will be the weighted average of the two payoffs and since they are the same the average must be the same.

So in GT terms it doesn't matter. In poker terms though you are correct. It would change your image greatly if you always folded or always called in these spots. One option is to do so and then exploit this image. This works well because your image doesn't match how you play - remember you are playing perfect poker on the end by calling always so you can't be calling/folding too much in these situations. In other words if you always call your opponents will probably adjust their bluffing frequency toward not enough while if you always fold they will try to bluff too much.

[Jerrod Ankenman]

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My question is about using game theory to call on the end when I can only beat a bluff. Ex. say on the end I find myself Heads Up with a hand that can only beat a bluff it is a 10-20 game and there is $80 in the pot and a $20 bet. Say my opp. bluffs opptimal in this spot or close to it, not out of line in either spot. Would it be a resonable statagy to call 1 out of 5 here by using some random device to keep him off balance. Would I be making a mistake in this spot, is my understanding of game theory off?

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The game theory reason you would call with a mixed strategy is to prevent him from changing his strategy to exploit you. To do that, you would call 4/5 of the time, not 1/5.

Jerrod Ankenman