Balancing Flop Caps

[elindauer]

Good stuff James.

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Now maybe elindauer can come in and blow it up showing me where I’m completely wrong.

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I think your range is a significant improvement on my initial attempt. The biggest thing you are doing is to consider how your capping range effects your calling range. My first shot left the calling range far too weak. That's a HUGE improvement. I think your handling of overpairs is great. Saving some draws / made hands for turn raises / semibluffs is very strong. I really like your logic for choosing which hands go in which range... you mix concepts like waiting with cards whose value changes a lot on the turn with game theory concepts like avoiding being exploited very nicely. This is exactly the kind of thinking that leads players from good to great, I think.


You are making a few small mistakes though. Here are the ones I notice.

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QQ(1 combo b/c 2/3 the time I wait for the turn)

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QQ has 6 combinations. 1/3 of 6 = 2.

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I often use the average pot size as the primary function in determining what combinations of drawing hands I will wait and raise on the turn(feel free to jump in if you don’t think this is correct).

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This is totally correct. Pot size is critical in determining how you play your range.

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When I raise it makes the pot 9bb and it indicates to my opponent that he will need to put in 2 more bb to call me down. This gives him effectively 4.5-1.

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This isn't quite right. As stated in other posts, your turn raise doesn't obligate you to bet the river. In fact, if you know he's thinking about calling the turn only if he can call the river, you'd be a fool to follow through with a river bet with your entire range. You'd have to bet less. But then his turn calling range would be wrong. But then you'd bluff more. Back and forth.

The right answer is, I think, to think of each street a bit more in isolation. So focus on him getting 9:1 to call the turn, and semi-bluff accordingly. Note though that your bluffing hands have excellent equity, and take that into account. For example, if your bluffing range has 20% equity, then:

made + .2*draw : .8*draw should offer him 9:1 (where made = # of made combos you raise, and draw = # of draw combos you semibluff raise).

Rearranging...

draw = made / 7

in a pot this size. So your raising range actually encourages him to call a bit more than the optimal strategy would suggest, not a bit less (I think).

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I apologize it’s taken me so long to respond to this post. I also apologize my response was so longwinded.

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There's no other way it could be. We're in the very early stages of understanding this logic, so we have to discuss both the process and the results at the same time. It'll get faster with practice.

good luck.
Eric

[One Outer]

I keep thinking if I read this enough times I'll understand it. I'm silly.

[elindauer]

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I keep thinking if I read this enough times I'll understand it. I'm silly.

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I'm sorry I'm not a good enough teacher to make it clear. I'll keep trying. Stick with it.

-eric

[James.]

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You are making a few small mistakes though. Here are the ones I notice.

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QQ(1 combo b/c 2/3 the time I wait for the turn)

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QQ has 6 combinations. 1/3 of 6 = 2.

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doh. sorry. i'm at work and get distracted multiple times in making a post that long. i apologize for the oversight.

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When I raise it makes the pot 9bb and it indicates to my opponent that he will need to put in 2 more bb to call me down. This gives him effectively 4.5-1.

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This isn't quite right. As stated in other posts, your turn raise doesn't obligate you to bet the river.

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thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

[One Outer]

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thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

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I agree with this. If aren't we exploiting our opponents by taking the free showdown sometimes?

[elindauer]

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I agree with this. If aren't we exploiting our opponents by taking the free showdown sometimes?

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I don't understand your question. Rephrase?

I think the answer though, is that if your opponent only calls with made hands that can stand to call the river also, then he is folding too much. You exploit this mistake by bluffing more on the turn and then giving up if called. He counters that by calling more and bluffing the river. You counter by giving up less. Back and forth. This back and forth is the defition of an imperfect solution.

-eric

[elindauer]

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thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

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Totally understand this, and it's a very important concept for play in practice. You're opponent may very well think like this.

However, when considering what the game theory perfect play of your range is, you begin with the assumption that your oppnonent knows what you are doing and will play his hand perfectly against you. In this context, it's incorrect to say that the calldown ratio is important. So I'm trying to show what odds you really should be using to mix in bluffs, and that is, I think, the true odds your opponent is receiving immediately.

It might seem like hair-splitting, but I don't think so. It's a common flaw in limit holdem players to make calldown-all-the-way-or-not decisions, which can be exploited by bluffing early and giving up later in the hand. I think this is a hole that prevents lots of TAGs from moving up. So elliminating this hole in our understanding of game theory and seeing the effect it has on the default range can be important in helping us understand how we should deal with tough players in spots like these.

-eric

[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