Exploitive play question

[SeanC]

Hi,

Quick question on exploitive play. When exploiting an OPP's strategy, is it right that you determine the indifference threshold for certain actions and then play pure strategies according to the OPP's actual play falling under or over the ITs?

For example, if you determine that OPP bluffs too much in certain situations, you should play the pure strat of always calling with bluff-catchers. If he doesn't bluff enough, you should always fold bluff-catchers, etc.

If an opponent is playing pretty optimally, all you can do is respond as optimally as possible to, hopefully, create an EV of 0, right?

[holdem2000]

Seems like your theoretical understanding is right, but if you start doing something like always calling with bluff catchers most OPPs will adapt pretty quickly... usually if you're going to keep playing this OPP it's better to just call with bluff catchers a lot (but not all) of the time so you continue to understand how they think in these situations. Our knowledge of our opponent might be something more like:

OPP bluffs too much in situation X while I employ a strategy of calling with bluff catchers 75% of the time, but OPP never bluffs while I call with bluff catchers 100% of the time.

[SeanC]

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Seems like your theoretical understanding is right, but if you start doing something like always calling with bluff catchers most OPPs will adapt pretty quickly... usually if you're going to keep playing this OPP it's better to just call with bluff catchers a lot (but not all) of the time so you continue to understand how they think in these situations. Our knowledge of our opponent might be something more like:

OPP bluffs too much in situation X while I employ a strategy of calling with bluff catchers 75% of the time, but OPP never bluffs while I call with bluff catchers 100% of the time.

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Yeah, I wasn't worrying about an adapting opponent--I was just curious about the theory.

Correct me if I'm wrong, but while it's tough to exactly quantify how much of the OPP's range hs is bluffing with, you can exactly quantify the indifference threshold of calling or folding for any given bet and then see if, given the current circumstances, the OPP is bluffing more or less of his range than that IT and play accordingly (call or fold), right?

You'd take the OPP's adaption into account when determining his bluffing range.

[TyFuji]

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Seems like your theoretical understanding is right, but if you start doing something like always calling with bluff catchers most OPPs will adapt pretty quickly... usually if you're going to keep playing this OPP it's better to just call with bluff catchers a lot (but not all) of the time so you continue to understand how they think in these situations. Our knowledge of our opponent might be something more like:

OPP bluffs too much in situation X while I employ a strategy of calling with bluff catchers 75% of the time, but OPP never bluffs while I call with bluff catchers 100% of the time.

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Yeah, I wasn't worrying about an adapting opponent--I was just curious about the theory.

Correct me if I'm wrong, but while it's tough to exactly quantify how much of the OPP's range hs is bluffing with, you can exactly quantify the indifference threshold of calling or folding for any given bet and then see if, given the current circumstances, the OPP is bluffing more or less of his range than that IT and play accordingly (call or fold), right?

You'd take the OPP's adaption into account when determining his bluffing range.

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You could make very good estimations, yes. But such analysis would only be useful as an avenue for more complicated and less discrete strategies which would actually be employable against a human opponent.

[SeanC]

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Seems like your theoretical understanding is right, but if you start doing something like always calling with bluff catchers most OPPs will adapt pretty quickly... usually if you're going to keep playing this OPP it's better to just call with bluff catchers a lot (but not all) of the time so you continue to understand how they think in these situations. Our knowledge of our opponent might be something more like:

OPP bluffs too much in situation X while I employ a strategy of calling with bluff catchers 75% of the time, but OPP never bluffs while I call with bluff catchers 100% of the time.

[/ QUOTE ]

Yeah, I wasn't worrying about an adapting opponent--I was just curious about the theory.

Correct me if I'm wrong, but while it's tough to exactly quantify how much of the OPP's range hs is bluffing with, you can exactly quantify the indifference threshold of calling or folding for any given bet and then see if, given the current circumstances, the OPP is bluffing more or less of his range than that IT and play accordingly (call or fold), right?

You'd take the OPP's adaption into account when determining his bluffing range.

[/ QUOTE ]

You could make very good estimations, yes. But such analysis would only be useful as an avenue for more complicated and less discrete strategies which would actually be employable against a human opponent.

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I understand the words but not the overall concept, hehe. Can you explain?

[holdem2000]

If we're in some situation where the villain's hand is concretely defined to be either a hand he should value bet or a hand he can either bluff with or check with (and I guess some hands in between that he just checks with), and if we also assume that there's a set of our holdings rigidly defined as bluff-catchers (hands better than all his bluffing hands and worse than all his value betting hands), then there will be some optimal amount of the time he should bluff when he has a bluffing hand. If he bluffs precisely this optimal amount, we will be indifferent to calling and folding with our bluff-catchers.

If the opponent bluffs more often than this than our correct strategy is to call with 100% of our bluff-catchers, while if he bluffs less often than this our correct strategy is to fold all of our bluff-catchers.

OP asked if we could easily calculate this indifference threshold, and I agree that we could in this artificial situation where hands may be rigidly defined as hands you bet for value or hands you bet as a bluff, and also where hands can be rigidly defined for bluff-catchers (the A, K, Q game is the most iconic game of this type, where aces are bet for value, kings are always checked, and queens are only bet as bluffs, while kings become bluff-catchers).

[punter11235]

For bluff/bluff catching situations if he plays optimally it doesnt matter at all what you do with your bluff catchers. The only dangerous situation is when he guesses what strategy you are using but then again it gives you chance to outguess him. It follows that you should not worry about following optimal strategy unless your opponent is much better than you and you are afraid that he will guess correctly what you are doing.

[SeanC]

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If we're in some situation where the villain's hand is concretely defined to be either a hand he should value bet or a hand he can either bluff with or check with (and I guess some hands in between that he just checks with), and if we also assume that there's a set of our holdings rigidly defined as bluff-catchers (hands better than all his bluffing hands and worse than all his value betting hands), then there will be some optimal amount of the time he should bluff when he has a bluffing hand. If he bluffs precisely this optimal amount, we will be indifferent to calling and folding with our bluff-catchers.

If the opponent bluffs more often than this than our correct strategy is to call with 100% of our bluff-catchers, while if he bluffs less often than this our correct strategy is to fold all of our bluff-catchers.

OP asked if we could easily calculate this indifference threshold, and I agree that we could in this artificial situation where hands may be rigidly defined as hands you bet for value or hands you bet as a bluff, and also where hands can be rigidly defined for bluff-catchers (the A, K, Q game is the most iconic game of this type, where aces are bet for value, kings are always checked, and queens are only bet as bluffs, while kings become bluff-catchers).

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That makes sense, thanks.

Practically speaking then, how do we determine when someone is bluffing too much or too little? I assume there's some mathematical method applied, right? Or is it just an "obvious" kind of thing that strikes you ("wow, he's bluffing a lot")? As the correct exploitive response to an over-bluffer is to call with all bluff-catchers (until he wisens up and stops bluffing so much), I'd think there is some kind of math to determine what is "too much," even if it's pretty simple...

[holdem2000]

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If we're in some situation where the villain's hand is concretely defined to be either a hand he should value bet or a hand he can either bluff with or check with (and I guess some hands in between that he just checks with), and if we also assume that there's a set of our holdings rigidly defined as bluff-catchers (hands better than all his bluffing hands and worse than all his value betting hands), then there will be some optimal amount of the time he should bluff when he has a bluffing hand. If he bluffs precisely this optimal amount, we will be indifferent to calling and folding with our bluff-catchers.

If the opponent bluffs more often than this than our correct strategy is to call with 100% of our bluff-catchers, while if he bluffs less often than this our correct strategy is to fold all of our bluff-catchers.

OP asked if we could easily calculate this indifference threshold, and I agree that we could in this artificial situation where hands may be rigidly defined as hands you bet for value or hands you bet as a bluff, and also where hands can be rigidly defined for bluff-catchers (the A, K, Q game is the most iconic game of this type, where aces are bet for value, kings are always checked, and queens are only bet as bluffs, while kings become bluff-catchers).

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That makes sense, thanks.

Practically speaking then, how do we determine when someone is bluffing too much or too little? I assume there's some mathematical method applied, right? Or is it just an "obvious" kind of thing that strikes you ("wow, he's bluffing a lot")? As the correct exploitive response to an over-bluffer is to call with all bluff-catchers (until he wisens up and stops bluffing so much), I'd think there is some kind of math to determine what is "too much," even if it's pretty simple...

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If you restrict yourself to limit (or some single bet size the opponent will always make) then the math is pretty simple, but it depends on the size of the pot, how often the opponent holds a value betting hand, how often the opponent holds a bluffable hand, how often we hold bluff catchers / hands we always call with for value / hands we always fold. If you're really interested this is the sort of stuff Mathematics of Poker is about and I highly recommend it.

[SeanC]

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For bluff/bluff catching situations if he plays optimally it doesnt matter at all what you do with your bluff catchers. The only dangerous situation is when he guesses what strategy you are using but then again it gives you chance to outguess him. It follows that you should not worry about following optimal strategy unless your opponent is much better than you and you are afraid that he will guess correctly what you are doing.

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Yeah, I understand that. I'm not too worried about optimal play for my stakes--exploitive play can reap plenty of profits. Using the indifference threshold to determine correct exploitive plays (bluff-catching or bluffing myself) is what I'm interested in. Is the following example realistic/applicable for exploitive play?

OPP pots the river, laying 2-1. I hold a bluff-catching type hand--middle pair or something. I believe OPP's value-betting range that beats me is X, and it contains let's say 40 combinations. As I'm getting 2-1, OPP would need to be bluffing with ~13 combinations (33% of his v-betting range) for me to be indifferent to calling or folding. If, by my estimations, he would bluff less than 13 combinations then I should fold; if I estimate he could be bluffing with more than 13, I should call.

I'm kind of beating this subject to death across my posts, but I think it's an important one and I want to ensure I fully understand it.