Balancing Bluffs vs Balancing Strategy

[leaponthis]

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p.s. leaponthis, please don't reply to my question.

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Looks like, to me, that no one replied to your question. I think it is because you are a buu hle (head). hey please don't reply to this. If you were a decent fellow you would have sent me a pm requesting I gnore your posty but beong a crappy guy like you are you don't havve the character to do so. It's the reason no one answered your question. I'm sure. Butt face.

this is leaponthis not replying to your question just telling you to f...koff.

[JocK]

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Playing optimally does not offer your opponents the opportunity to make mistakes (except for dominated decisions which are always availble no matter how you play).

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Although this might be true for games like Roshambo, this is not correct in general (but it depends a bit on what you mean by 'dominated decisions').

In more complex games strategies do exist that can lead to gains against certain of opponent's choices (i.e. these are non-dominated strategies), but the same strategies are dominated by the Nash strategies. Selecting such a strategy that is dominated by the opponent's Nash strategy would be a mistake.

In general it is true that Nash-strategies are not maximally exploitive towards opponent's errors, but they do exploit some of these errors.

[jogsxyz]

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Jerrod, Jared...this is getting confusing... [img]/images/graemlins/smile.gif[/img]

Anyways, this is about Jerrod's example of betting the turn with the "correct mix" of hands. I know how many pair-combinations I play in certain positions and I can ballance it by adding as many other combinations like 2-suited-card or offsuit-cards with max-stretch. Unfortunately I have no idea how often those 4-card draws and those made hand monsters come up on the turn, so all that knowledge doesn't help. If I bet everything just as it shows up, I am almost certain to have an incorrect mix.

It would have been nice to see some stats tables in the book and maybe one of example of how the ballancing is done, but that's of course missing....too bad I am not Brian Alspach.

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Well yeah, if we knew how to find "the correct mix" then we could easily find the optimal strategy. So we guess in an informed way, with an eye to making our distribution reasonable no matter what cards come on later streets. This isn't hard in holdem because you can easily mix together draws and made hands in all sequences. It's not so easy in stud, where if your board is 952 rainbow you just can't have much of a drawing hand. i don't know what the answer there is; mostly I just try to play a lot of hands in the same way so that I'm not very readable.

jerrod

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Don't know the correct mix? What's 1/(P+1)
and s/(1+s) all about? Isn't that the correct
mix? Or the more general b/(P+b), where P
is the pot and b is the bet. For every legit
bet or raise, bet b/(P+b) additional hands.

[Jerrod Ankenman]

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Jerrod, Jared...this is getting confusing... [img]/images/graemlins/smile.gif[/img]

Anyways, this is about Jerrod's example of betting the turn with the "correct mix" of hands. I know how many pair-combinations I play in certain positions and I can ballance it by adding as many other combinations like 2-suited-card or offsuit-cards with max-stretch. Unfortunately I have no idea how often those 4-card draws and those made hand monsters come up on the turn, so all that knowledge doesn't help. If I bet everything just as it shows up, I am almost certain to have an incorrect mix.

It would have been nice to see some stats tables in the book and maybe one of example of how the ballancing is done, but that's of course missing....too bad I am not Brian Alspach.

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Well yeah, if we knew how to find "the correct mix" then we could easily find the optimal strategy. So we guess in an informed way, with an eye to making our distribution reasonable no matter what cards come on later streets. This isn't hard in holdem because you can easily mix together draws and made hands in all sequences. It's not so easy in stud, where if your board is 952 rainbow you just can't have much of a drawing hand. i don't know what the answer there is; mostly I just try to play a lot of hands in the same way so that I'm not very readable.

jerrod

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Don't know the correct mix? What's 1/(P+1)
and s/(1+s) all about? Isn't that the correct
mix? Or the more general b/(P+b), where P
is the pot and b is the bet. For every legit
bet or raise, bet b/(P+b) additional hands.

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Well, this doesn't apply so easily to streets before the river. After all, some of the hands you are bluffing are semi-bluffs which have equity on the next street. So if you bluffed with a ratio of 1 to (p+1) value bets, you'd be bluffing too infrequently, as on the next street some of your bluffs would turn into value bets and you'd have too few bluffs. This would happen even if you incorporated "give up bluffs" like we discuss in the multiple street bet sizing examples into your turn strategy.

Not to mention that some of your hands will improve but still lose because your hand distributions aren't as bifurcated as they are in toy games, your opponent can raise and could potentially have all kinds of funky distributions coming into or going out of this street, and so on.

jerrod

[Jerrod Ankenman]

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If you are playing an optimal game without taking into account how your opponent is playing then you are playing an equilibrium stategy and breaking even before the rake. Playing at equilibrium means you force your opponents to break even no matter what action they take (unless they make mistakes by making dominated decisions -- like calling a bet on the river with the nut low). Playing optimally does not offer your opponents the opportunity to make mistakes (except for dominated decisions which are always availble no matter how you play). In order to offer your opponents the opportunity to make mistakes, you must deviate from the balancing point of optimal equilibrium -- you must tilt. To do so profitable requires that you tilt in a direction that exploits the direction in which your opponent is tilting, but in doing so you open yourself up for exploitation by another player.


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Someone else responded pointing out that this isn't true, but I wanted to comment specifically on the idea that your opponents have to employ dominated strategies in order for you to profit when you are playing equilibrium/optimally. It's true that you will sometimes benefit when they do this, but it's definitely not true that this is the only way.

Suppose we define "X makes a mistake" to mean "X takes an action x1 such that X has lower expectation against Y's equilibrium strategy than X would if X played the action from X's equilibrium strategy."

According to your statement above, against an opponent playing optimally, X can only make mistakes if he takes actions which have lower or equal equity against all possible Y strategies than his equilibrium action.

Hopefully it's clear that this isn't the case (simply imagine a guy who bluffs a little too much - bluffing with a hand close to the bluffing threshold clearly isn't dominated, as some Ys will play too tight).

Jerrod

[bbbushu]

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Authors,

i've got the book and have been reading it over (i'm thankful for the first chapter btw, i am taking full advantage of the refresher micro-course...) but i predict a fairly major issue with it that maybe this thread can help me flesh out.

while the book is loaded with somewhat intimidating-looking math, i believe i'm fully capable of processing the information and understanding the concepts but i think i'll have some trouble with the application to actual play. i play limit hold 'em (almost exclusively shorthanded and HU, if that matters) so i'm assuming whatever applications you guys make in the NLHE case study will be only partially useful for me. i understand this might be addressed in the book and if you feel i'll figure it out simply by reading the rest of the book, feel free to say so. i understand that the book is NOT a "formula" for winning hold 'em, etc. but i might struggle applying the ideas, themselves, to the play of hands.

another question that may be answered later in the book: does a player hafta choose between optimal and exploitive strategies while playing? can they be used to compliment each other or are they mutually excusive (and possible counterproductive when combined)?

thank you for starting this thread, it has already helped me out.

bbbushu

p.s. leaponthis, please don't reply to my question.

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[leaponthis]

lol. You are a spiffin joke.

leaponthis

[Jerrod Ankenman]

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Authors,

i've got the book and have been reading it over (i'm thankful for the first chapter btw, i am taking full advantage of the refresher micro-course...) but i predict a fairly major issue with it that maybe this thread can help me flesh out.

while the book is loaded with somewhat intimidating-looking math, i believe i'm fully capable of processing the information and understanding the concepts but i think i'll have some trouble with the application to actual play. i play limit hold 'em (almost exclusively shorthanded and HU, if that matters) so i'm assuming whatever applications you guys make in the NLHE case study will be only partially useful for me. i understand this might be addressed in the book and if you feel i'll figure it out simply by reading the rest of the book, feel free to say so. i understand that the book is NOT a "formula" for winning hold 'em, etc. but i might struggle applying the ideas, themselves, to the play of hands.

another question that may be answered later in the book: does a player hafta choose between optimal and exploitive strategies while playing? can they be used to compliment each other or are they mutually excusive (and possible counterproductive when combined)?

thank you for starting this thread, it has already helped me out.

bbbushu

p.s. leaponthis, please don't reply to my question.

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You don't necessarily have to choose between optimal play and exploitive play - I mean, you could play exploitively and then fall back on optimal if you think you're being out-exploited, for example.

As for how to apply this directly to play, it's not easy, and I wouldn't say that if you get farther in the book, there's just an easy method of understanding this difficult concept.

However, if you take the lessons about balance in the book to heart, and start to focus on the distribution you hold in each situation, and playing in a balanced manner, you'll likely be able to benefit. Another exercise worth doing is to try to exploit your own play.

jerrod

[bbbushu]

like, analyze my own common lines and figure out how a villain could win the max from me?

thanks for the response!

[jjacky]

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David,

It bothers me a little when you say "It might be better to play a hand differently almost every time from the way it should be played if it was the last hand of your life. For the sake of future hands. "

Game theoretically you should play the hand unpredictably if it's the last hand of your life as well. The reasoning has nothing to do with future hands.

Is this just an effective way of explaining game theory to people that you use because it's effective even though it isn't correct?

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It is correct. There is a difference between mixing up your play to optimize the value of that particular hand and mixing up your play to maximize the value of all your hands.

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Can you give an example simpler than poker where the game theoretic correct strategy is different for the last game you play than any game previous?

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no he can't. the nash equilibrium doesn't change in constant sum games*. no matter how many repetitions will be played out in the future (nor does the best response to any gives strategy).
the only reason not to play the overall strategy with the highest EV for the actual hand is to make the opponent to change his strategy. if he doesn't (or not in a manner that increases our EV in future hands), there is none.

*constant sum games are game theoretically equivalent to zero sum games.

for nit-picker: note that games with rake taken from the pot (as opposed to time fees, tournaments and rake free games) are not exactly constant sum games. but that is not the point of the discussion.
please also note that the conditions of future hands can be changed due to the developement of the stacks. that means single hands are not independent games in a game theoretical sense. if the game is limit (and the stacks are big enough) or if all the hands would start with a cap or the same amount of money, every hand would truely be independent beside the possible strategy changes of the competitors.