Balancing Flop Caps

[James.]

ah, i see. thanks again eric.

[PokrLikeItsProse]

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The right answer is, I think, to think of each street a bit more in isolation.

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Chen/Ankenmen seem to think differently. See page 264 of The Mathematics of Poker: "....multi-street games are not single-street games chained together; the solution to the full game is often quite different from the solutions to individual streets." Using the methods in their book, it feels like the full solution involves starting out by determining your optimal bluffing strategy on the river when you miss your draws (or is that what you mean by thinking of each street in isolation) and working backwards to ensure a proper balance between your multi-street bluffing lines and your value bets. It is my understanding that the solution is beyond (computer-aided) human capacity.

Part of the complication is because you may pick up additional semibluffing opportunities on the turn, such as when you hold two black aces and a third spade comes.

I can only make educated guesses based on simplified cases that are hopefully analogous. Based on what I have studied, I tossed hands like AK and 77 out of an optimal opponent's likely three-betting range because a) those hands have more value as bluff-catchers and b) I suspect that range doesn't include very much three-betting with pure air or with a weak draw such as an overcard pair draw or an underpair set draw.

[elindauer]

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Chen/Ankenmen seem to think differently. See page 264 of The Mathematics of Poker: "....multi-street games are not single-street games chained together; the solution to the full game is often quite different from the solutions to individual streets."

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Indeed, you are totally correct. I've read this book and it's exactly this argument that leads me to describe the proper strategy as just "a bit more" in isolation.

It's true that the complete strategy is different from single street games chained together. However, the complete strategy will probably not allow any individual street where your opponent is going to be able to bluff his entire range profitably. Assuming that your opponent will only call with made hands that can call the river as well will lead to that kind of exploitation I think, as you are not obligated to bluff all the way.

I really need to run one of these single hand simulations and give out a complete strategy for two ranges on one flop heads up. Just seeing one solution would be really instructive. Anybody already done this and care to share?

thanks,
Eric