blitzing on third and long and the problem with poker forum advice

[Jerrod Ankenman]

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TSo this bluffing into a dry side pot thing isn't really a very good example, because it's not an example of an "optimal" or "equilibrium" solution - it's an example of perturbing the (three-player Nash) equilibrium solution by threatening to transfer equity from one guy to the other in order to make the threatened guy pay you.

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So basically this "isn't really a very good example" because it doesn't fit into the narrowly contrived parameters that make the math work out all pretty.

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Right, even though poker is usually a zero-sum game, Pete has managed to create a non-zero sum situation for the only two players with choices to make, shouldn't we explore it?

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We specifically discussed two dry side pot bluffing situations in our book and of course the possibility of forming alliances is present because these games are (at your convenience) either three-player zero-sum games or two-player non-zero-sum games.

The bluffer can unilaterally form an alliance with the all-in guy by bluffing sometimes. This is a deviation from his "equilibrium" strategy -- we don't use "optimal" to describe strategies other than for ZSTPGs. He can sometimes increase his equity by doing so, if his opponent responds in his preferred way. However, if his opponent responds by playing his equilibrium strategy, he usually loses expectation by doing this. The big winner in this case, of course, is the all-in guy.

Nevertheless, Pete is wrong to disbelieve the following statement:

If a strategy X that comprises one player's strategy in a Nash equilibrium contains mixed strategies where two or more options have non-zero weight, then the expectation of those strategic options against the equilibrium strategies of the other players must be equal.