Balancing Bluffs vs Balancing Strategy
 

Now that the Mathematics of Poker is out there, it becomes necessary to distinguish between the concepts I write about and the concepts in that book. The blurb that is often used about me "greatest poker theoretician" or something like that, has always been slightly in error. Theory has been defined as the opposite of practice. But to be more precise it is necessary to change the word theory to general principles. An irrelevant fine point up to now.

Put another way, much of my stuff concerns advice of a general nature. What factors should you consider before you make your decision? It was less likely to recommend specific plays. However most of that advice did focus on exploiting other peoples mistakes. It did not go into detail about playing in such a way as to avoid being exploited yourself. I advocated mixing up your play a bit against tough players and mixing up your bluffs against most players, but there was no emphasis on "balancing" all your plays in one grand overall strategy. Bluffs maybe, but not anything else.

In other words if a certain hand figured to do better by playing it one way rather than another, I wanted you to realize that. And to play it that way unless decisons were close and/or your opponnents are tough.

In theory however the above approach could conceivably be wrong. 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. The Mathematics of Poker assumes you are taking this approach. And just like using Game Theory to bluff and call bluffs, using Game Theory to balance an overall strategy, practically guarantees a long term win. My experience tells me that the vast majority of games will be beaten for a greater amount if this approach is shelved for my more exploitive approach but time will tell.

All comments welcome.

Re: Balancing Bluffs vs Balancing Strategy
 

In your opinion, how close can the best pros play to optimally (in a game theory sense)? Put another way, when they play each other, what percentage of their game is based on "Don't be a sucker" as opposed to exploiting perceived leaks in each other's games? Does this vary between different games? E.g. is limit HE played closer to optimally than say Omaha PLO at the highest level?

These are vague questions, since nobody knows what an unexploitable strategy is for any form of poker. But I'd love to hear your informed speculation anyway.

Re: Balancing Bluffs vs Balancing Strategy
 

Are you saying your books have possibly taught us a suboptimal/wrong way of playing poker?

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Are you saying your books have possibly taught us a suboptimal/wrong way of playing poker?

[/ QUOTE ]

Yep. As long as you are playing 200-400 or higher.

Re: Balancing Bluffs vs Balancing Strategy
 

This reminds me of a topic that came up in Thoery a week or so ago.

Let's ignore the difficulty of creating a game-theoric type perfect strategy, and just assume you've got one. The question is when you use it vs. other exploitive sub-optimal strategies. I believe that an elegant solution to that very problem, on numerous levels, is represented in the Iocaine Powder Roshambo bot. http://ofb.net/~egnor/iocaine.html

It's got both a game-theoretic strategy (random play) and exploitive ones (history matching & frequency analysis). It then has two levels of meta-strategy to select between them. I'll let you read the details. I believe a similar meta-strategy could be adopted in poker. I don't know, however, the degree to which a player could mentally do the score keeping necessary to actually implement it.

Might be more of a feel thing to really make it happen. But at least knowing what you're trying to approximate could be valuable.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Now that the Mathematics of Poker is out there, it becomes necessary to distinguish between the concepts I write about and the concepts in that book. The blurb that is often used about me "greatest poker theoretician" or something like that, has always been slightly in error. Theory has been defined as the opposite of practice. But to be more precise it is necessary to change the word theory to general principles. An irrelevant fine point up to now.

Put another way, much of my stuff concerns advice of a general nature. What factors should you consider before you make your decision? It was less likely to recommend specific plays. However most of that advice did focus on exploiting other peoples mistakes. It did not go into detail about playing in such a way as to avoid being exploited yourself. I advocated mixing up your play a bit against tough players and mixing up your bluffs against most players, but there was no emphasis on "balancing" all your plays in one grand overall strategy. Bluffs maybe, but not anything else.

In other words if

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Now that the Mathematics of Poker is out there, it becomes necessary to distinguish between the concepts I write about and the concepts in that book. The blurb that is often used about me "greatest poker theoretician" or something like that, has always been slightly in error. Theory has been defined as the opposite of practice. But to be more precise it is necessary to change the word theory to general principles. An irrelevant fine point up to now.

Put another way, much of my stuff concerns advice of a general nature. What factors should you consider before you make your decision? It was less likely to recommend specific plays. However most of that advice did focus on exploiting other peoples mistakes. It did not go into detail about playing in such a way as to avoid being exploited yourself. I advocated mixing up your play a bit against tough players and mixing up your bluffs against most players, but there was no emphasis on "balancing" all your plays in one grand overall strategy. Bluffs maybe, but not anything else.

In other words if a certain hand figured to do better by playing it one way rather than another, I wanted you to realize that. And to play it that way unless decisons were close and/or your opponnents are tough.

In theory however the above approach could conceivably be wrong. 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. The Mathematics of Poker assumes you are taking this approach. And just like using Game Theory to bluff and call bluffs, using Game Theory to balance an overall strategy, practically guarantees a long term win. My experience tells me that the vast majority of games will be beaten for a greater amount if this approach is shelved for my more exploitive approach but time will tell.

All comments welcome.

[/ QUOTE ]

(sorry i'm on a bad internet connection, so a couple of posts have been cut off mid-way)..

One obvious example of this is the "arms race" on the turn in high limit LH games online. What developed there was a tendency after the sequence rc; kbrc; b? on two-flushed boards for people to semi-bluff raise liberally on the turn (including all flush draws, straight draws, and other weaker draws such as small pair+gutshot and the like).

The exploitive response to this that I observed was for original bettors to three-bet liberally, including hands as weak as middle pair in this sequence, because the number of semi-bluffs was just far too high compared to the number of value raises (as these players wouldn't adjust their value raise thresholds to balance). Against a properly balanced strategy, three-betting this liberally is a disaster. This also shows a clear example of why, contrary to some players' assertions, playing optimally or in a balanced manner isn't about equalizing all your opponent's actions -- just the ones that are on the borders.

End the cycle of exploitation!

jerrod

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
The Mathematics of Poker assumes you are taking this approach. And just like using Game Theory to bluff and call bluffs, using Game Theory to balance an overall strategy, practically guarantees a long term win. My experience tells me that the vast majority of games will be beaten for a greater amount if this approach is shelved for my more exploitive approach but time will tell.


[/ QUOTE ]

Using Game theory to the extent that you suggest above seems to me to be an attempt at fine tuning a very good strategy to ensure optimal play against the very best opponents. The only reason that I can think of to employ such a mythical strategy at present would be if you were playing in the only game in town and everyone in it was an expert. Could be that the 4-8k game in Vegas is such a game but from the take I've been given on some of the players in this game it hardly seems necessary nor practicle to employ nitty, game theoretical perfect poker, if there is such a thing, to win. If there is such a thing as game theoretical optimal strategy in poker it would dispel a lot of the current beliefs about how to win at poker through the use of skills such as game selection, reading your opponent, etc.. I doubt that without mastering these types of skills one could use a math strategy that would win at the highest levels of poker or any level for that matter. Poker skills are necesary for expert play. Game theory is just another tool for the expert. Talent for implimenting these defined poker skills, and not game theory, is the deciding factor on which experts win in the long run, now and in the future.

Your problem is that you can't see past the formula. You and all other math types attack poker as a mathematicl exercise when in fact it's a social exercise. It's a good thing Mason co-authored your books. I believe that he gives more credit to the talent of the player than you do.

leaponthis

Re: Balancing Bluffs vs Balancing Strategy
 

leaponthis,

You misunderstood the section you quoted. What do you think he meant by "more exploitive approach"? But half of what you said was wrong, anyway. The whole point of a game theoretic strategy is that it can't be a losing one, can't be exploited. That's it. The social stuff is part of exploitive play, which loops us back to the beginning of this paragraph.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
leaponthis,

what you said was wrong.

[/ QUOTE ]

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]


One obvious example of this is the "arms race" on the turn in high limit LH games online. What developed there was a tendency after the sequence rc; kbrc; b? on two-flushed boards for people to semi-bluff raise liberally on the turn (including all flush draws, straight draws, and other weaker draws such as small pair+gutshot and the like).

The exploitive response to this that I observed was for original bettors to three-bet liberally, including hands as weak as middle pair in this sequence, because the number of semi-bluffs was just far too high compared to the number of value raises (as these players wouldn't adjust their value raise thresholds to balance).

jerrod

[/ QUOTE ]

Jerrod,

I love this post. I've been trying to think about different situations like the one above (sequences of moves that occur regularly and help define your opponent's strategy) for some time, and your approach above is what I've been looking for.

In your book (I just ordered it tonight), do you list and analyze what you consider the most common betting sequences in limit and NL holdem? If not, do you do this as a way of improving your own play? How systematic are you? It seems that one approach to the game (not necessarily the best, but an instructive one at least) would be to exhaustively list these betting sequences, how often they came up, what their frequency should be and therefore how to exploit opponent's whose frequencies deviate from the optimal ones.

Thanks for any further thoughts,
gm

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
[ QUOTE ]


One obvious example of this is the "arms race" on the turn in high limit LH games online. What developed there was a tendency after the sequence rc; kbrc; b? on two-flushed boards for people to semi-bluff raise liberally on the turn (including all flush draws, straight draws, and other weaker draws such as small pair+gutshot and the like).

The exploitive response to this that I observed was for original bettors to three-bet liberally, including hands as weak as middle pair in this sequence, because the number of semi-bluffs was just far too high compared to the number of value raises (as these players wouldn't adjust their value raise thresholds to balance).

jerrod

[/ QUOTE ]

Jerrod,

I love this post. I've been trying to think about different situations like the one above (sequences of moves that occur regularly and help define your opponent's strategy) for some time, and your approach above is what I've been looking for.

In your book (I just ordered it tonight), do you list and analyze what you consider the most common betting sequences in limit and NL holdem?

[/ QUOTE ]

No, the book doesn't contain much specific advice on particular poker games (by design - we do consider a particular case study of NL - the BB vs an early raiser).

[ QUOTE ]
If not, do you do this as a way of improving your own play?

[/ QUOTE ]

Yes, and I recommend it to others.

[ QUOTE ]
How systematic are you?

[/ QUOTE ]

Not very, because I'm kinda lazy.

[ QUOTE ]
It seems that one approach to the game (not necessarily the best, but an instructive one at least) would be to exhaustively list these betting sequences, how often they came up, what their frequency should be and therefore how to exploit opponent's whose frequencies deviate from the optimal ones.

Thanks for any further thoughts,
gm

[/ QUOTE ]

I think that you could totally benefit from just looking at your action frequencies in the most important lines in headsup pots - ie, button raises, blind defends, check-bet, etc.

jerrod

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Theory has been defined as the opposite of practice.

[/ QUOTE ]

I don't want to hijack this thread, so please, nobody respond heavily to this.

This definition of theory has always bothered me, and I just wanted to get it off my chest after having been reminded of it here. I often hear somebody make an argument, to which somebody else will respon 'well, in theory that works, but not in reality.' This really irritates me. If something does not work in practice, it does not work in theory either. Rather, it means that there is something wrong with your theory. Something is being omitted or miscalculated.

For instance, if somebody says 'if everybody in the world did X, then Y would be the result' and another person replied, 'well, that works in theory, but not in reality' what they really mean is 'well, that works in your hypothetical but not in reality.' The words theory and hypothetical are not synonymous. A theory is an explanation of how different parts of a system work, and why those specific parts work the way they do. A hypothetical is a contrived system.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
using Game Theory to balance an overall strategy, practically guarantees a long term win

[/ QUOTE ]

[ QUOTE ]
The whole point of a game theoretic strategy is that it can't be a losing one, can't be exploited.

[/ QUOTE ]

I definitely understand that a game theoretical approach can't be exploited. The problem is that there is no game theoretical approach. Nor can any of these math guys come up with one that is workable. And that goes for heads up play also. If there existed a workable (winning) game theoretical strategy, guys like Sklansky and Fergusen and Weideman, etc.. would win all of the heads up championships. But they don't.

Sklansky has now stated that the strategy he (and Malmuth) have sold to the public is not a winning strategy. To beat high limits you must adjust that strategy with game theroy. He says that but where is the game theory adjustments of which he speaks? I'll tell you where they are. They are under development. Sure they are. My point about the social aspects of poker that Sklansky doesn't give much credence to are basic skills like reading your opponent, and understanding position. In poker there is such a thing as talent. Talent that allows a player to rise above his opponents and out play them. Out play - not out calculate. Sklansky disregards this in his theories because talent does not lend itself to logical analysis.

leaponthis.

Re: Balancing Bluffs vs Balancing Strategy
 

Game theory uses randomness to choose an action. This works for bluffs when your opponent doesn't see a part of your hand.
If he gets to see the river card that you choose to bluff on (like your example in the theory of poker, but now it's holdem) he knows it is more likely you are bluffing if it's a blank than if it might have made your drawing hand. So game theory is flawed here.
The same applies to strategies. Your strategy reveales itself a bit by your actions on previous streets like that rivercard revealed your bluff. I think that if you'd randomise your strategy every hand, it's very, very hard to determine that strategy for your opponents. It will probably work great for most players, but real good players might have better results by choosing their strategy by judgement of the situation/game.

Re: Balancing Bluffs vs Balancing Strategy
 

Jerrod,

[ QUOTE ]

Playing optimally or in a balanced manner isn't about equalizing all your opponent's actions -- just the ones that are on the borders.


[/ QUOTE ]

What does this mean with regard to your example? It's important to make sure your opponent can't profit by 3betting all of his hands (or close) at a certain point in a sequence?

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Game theory uses randomness to choose an action. This works for bluffs when your opponent doesn't see a part of your hand.

[/ QUOTE ]

The "randomizing" aspect of game theory is pretty unimportant in poker compared to the "maximizing" aspect. Many people have written about randomizing their play with their watches or whatever, but this type of thing is only a very small part of playing optimally - in fact, you generally should not randomize your bluffing by selecting some random card to bluff on. Instead, you should use card removal effects to decide what the best hands to bluff on are, and use those. The only thing that really needs to be randomized are hands that require mixed strategies, and there are quite likely to be very few of those.

[ QUOTE ]
If he gets to see the river card that you choose to bluff on (like your example in the theory of poker, but now it's holdem) he knows it is more likely you are bluffing if it's a blank than if it might have made your drawing hand. So game theory is flawed here.

[/ QUOTE ]

This is quite untrue - game theoretic strategies have a mixture of bluffs and value bets on *every* river card.

[ QUOTE ]
The same applies to strategies. Your strategy reveales itself a bit by your actions on previous streets like that rivercard revealed your bluff. I think that if you'd randomise your strategy every hand, it's very, very hard to determine that strategy for your opponents. It will probably work great for most players, but real good players might have better results by choosing their strategy by judgement of the situation/game.

[/ QUOTE ]

"Randomizing strategies"(ie playing a different strategy on each hand) isn't what we're talking about at all.

jerrod

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Jerrod,

[ QUOTE ]

Playing optimally or in a balanced manner isn't about equalizing all your opponent's actions -- just the ones that are on the borders.


[/ QUOTE ]

What does this mean with regard to your example? It's important to make sure your opponent can't profit by 3betting all of his hands (or close) at a certain point in a sequence?

[/ QUOTE ]

Yeah. Imagine the other guy's strategy as like a series of regions (the value raise region, the value call region, the semi-bluff region region, the drawing call region, and so on). Now if there weren't card removal effects (like this were some kind of idealized game), the only hands that would be mixed strategies would be hands on the border, which are mixed to make the overall frequencies right.

In real poker there are card removal strategies and in order to balance for new public information (like the community cards to come) there is probably a little mixing for several hands around. But almost certainly many hands use pure strategic options. (this means they do one thing or another 100% of the time)

In general, when a player deviates from a strategic option that is pure, he will often lose value.

jerrod

Re: Balancing Bluffs vs Balancing Strategy
 

To give a specific example of what I was talking about, take the chapter in our no limit holdem book where we recommend limping with specifically two eights with a certain stack size. The Mathematics of Poker seems to make reference to this play and states that any small gain from limping would be negated by the fact you are not playing preflop in a consistent way and could thus be more easily read. Whether that is true depends on the game.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
And just like using Game Theory to bluff and call bluffs, using Game Theory to balance an overall strategy, practically guarantees a long term win. My experience tells me that the vast majority of games will be beaten for a greater amount if this approach is shelved for my more exploitive approach but time will tell.

All comments welcome.

[/ QUOTE ]

When this statement becomes false, the games will no longer be beatable. No one will be able to overcome the hefty expenses.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
The Mathematics of Poker seems to make reference to this play and states that any small gain from limping would be negated by the fact you are not playing preflop in a consistent way and could thus be more easily read. Whether that is true depends on the game.

[/ QUOTE ]

If Sklansky is correct here, and as usual he usually is, his statement indicates that the authors of this math book are a bit flawed in their thinking. Perhaps this book is not what many here make it out to be. Be careful.

leapopnthis

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Yeah. Imagine the other guy's strategy as like a series of regions (the value raise region, the value call region, the semi-bluff region region, the drawing call region, and so on). Now if there weren't card removal effects (like this were some kind of idealized game), the only hands that would be mixed strategies would be hands on the border, which are mixed to make the overall frequencies right.

[/ QUOTE ]

This mechanical method of optimal play seems to lend itself to being programmable in a computer. Have you run a computer simulation? Does Turbo Texas Holdem employ this optimal game theory strategy?

leaponthis

Re: Balancing Bluffs vs Balancing Strategy
 

David. It's obvious game theory is best only when your opponent is tough. If you know the guy is going to pick scissors no matter what, you pick rock every time, you don't do better by using game theory and picking 33% each.

You explained this in the theory of poker.

What's your need to go over this here?

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
on two-flushed boards for people to semi-bluff raise liberally on the turn (including all flush draws, straight draws, and other weaker draws such as small pair+gutshot and the like).

The exploitive response to this that I observed was for original bettors to three-bet liberally, including hands as weak as middle pair in this sequence, because the number of semi-bluffs was just far too high compared to the number of value raises (as these players wouldn't adjust their value raise thresholds to balance). Against a properly balanced strategy, three-betting this liberally is a disaster. This also shows a clear example of why, contrary to some players' assertions, playing optimally or in a balanced manner isn't about equalizing all your opponent's actions --just the ones that are on the borders.


[/ QUOTE ]

If I read this correctly the semi-bluffing liberal raiser was raising so frequently with draws that he was being exploited via three bets from his opponent. So you propose balancing your semi-bluff raises via a game theory (randomized) approach that takes into account value raising your good hands.

I can see where a randomizing approach is certainly preferable to consistently semi-bluff raising in the face of a consistent three bet. Are you proposing that whenever one finds themselves in a potential semi-bluff situation that one semi-bluff on a randomized basis? The semi-bluff concept includes some liklihood that your opponent will fold. If done without this in mind then the raiser is making a mistake. This liklihood leads to one having knowledge of their opponent. So if done correclty one would only semi-bluff in situations where there is a good chance that it will produce the desired results. Randomizing would mean that you would sometimes be semi-bluffing knowing that there was no chance of obtaining the desired results. Sure you would nulify the consistent three betters exploitation of a semi-bluff but so what you would now be making semi-bluffs knowing they were not suited to the situation.

leaponthis

Re: Balancing Bluffs vs Balancing Strategy
 

leaponthis,

Optimal play is waaay too complicated to be calculated in real-time by any computers currently in existence. (I might have some vocabulary wrong here, but the idea is sound.) So no, Turbo Texas Holdem != optimal.

Re: Balancing Bluffs vs Balancing Strategy
 

"In poker there is such a thing as talent. Talent that allows a player to rise above his opponents and out play them. Out play - not out calculate. Sklansky disregards this in his theories because talent does not lend itself to logical analysis."

David has written:

"The fact is that many of the superstars are freaks. They have an inborn talent for the game as most champion athletes do. It is safe to assume that most readers do not have this talent. They thus cannot hope to achieve top level play without a lot of help. . . .

"Being good at poker is something like being good at bowling or golf. You need talent to become a superstar no matter how much you know. However with proper coaching, practice, and study most people shoud be able to achieve one notch below superstar status. Most people can become 190 bowlers or shoot 77 in golf if they have a coach who can show them all the fundamentals. It is not necessary that they have that much talent. With proper coaching, practice, and study they can frequently surpass people who have much more talent but who don't want to study and practice the fundamentals.

"Thus, I would like you to consider me your poker coach. I might only be able to get you to be a 77 shooter but this is good enough. Even if you can't get on the pro tour with this score, there is plenty of money to be made if you're this good. This is especially true in poker. There are a lot of 90 shooters out there just waiting to give you their money. Let me help you take it."

David recognizes that his audience likely has less talent than the superstars and writes for that audience.

Re: Balancing Bluffs vs Balancing Strategy
 

"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."

But eventually that future has to come to be the present. When is the point at which we stop playing the hand differently and start playing it Sklansky-optimally?

I think what you mention in one of your other posts in this thread is correct: basically, you do better playing every hand like it was the last hand of your life up to a certain stakes level.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
In poker there is such a thing as talent. Talent that allows a player to rise above his opponents and out play them. Out play - not out calculate. Sklansky disregards this in his theories because talent does not lend itself to logical analysis."

David has written:

"The fact is that many of the superstars are freaks. They have an inborn talent for the game as most champion athletes do. It is safe to assume that most readers do not have this talent

[/ QUOTE ]

So sue me.

laponthis

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]


In real poker there are card removal strategies and in order to balance for new public information (like the community cards to come) there is probably a little mixing for several hands around. But almost certainly many hands use pure strategic options. (this means they do one thing or another 100% of the time)

In general, when a player deviates from a strategic option that is pure, he will often lose value.


[/ QUOTE ]

Jerod, aren't you equating real poker with something like your 0-1 games which result in pure strategies? In actuality aren't there groups of hands that are broadly equivalent - e.g. all flush draws? If this is the case, then real poker is similar to the AKQ game which requires a mixed strategy.

Or were you talking about pre-flop play specifically.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
If there existed a workable (winning) game theoretical strategy, guys like Sklansky and Fergusen and Weideman, etc.. would win all of the heads up championships.

[/ QUOTE ]
You are insane.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
You are insane.

[/ QUOTE ]

And you are... the brightest bulb on the tree?

leaponthis

Re: Balancing Bluffs vs Balancing Strategy
 

The brightest? Dunno. Bright enough to understand that "a winning strategy" does not guarantee a win in a particular session? Yes.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
[ QUOTE ]


In real poker there are card removal strategies and in order to balance for new public information (like the community cards to come) there is probably a little mixing for several hands around. But almost certainly many hands use pure strategic options. (this means they do one thing or another 100% of the time)

In general, when a player deviates from a strategic option that is pure, he will often lose value.


[/ QUOTE ]

Jerod, aren't you equating real poker with something like your 0-1 games which result in pure strategies? In actuality aren't there groups of hands that are broadly equivalent - e.g. all flush draws? If this is the case, then real poker is similar to the AKQ game which requires a mixed strategy.

Or were you talking about pre-flop play specifically.

[/ QUOTE ]

Flush draws aren't equivalent. Some have showdown value, others have almost none. Some have stronger pair draws than others. Some block the opponent from having random gutshots and some don't, etc. All of these are selection factors for playing them in different ways - if it's necessary to do so.

It's probably true that there is a little bit of blurring near the threshold hands, to prevent the opponent from exploiting cards that come on future streets. This is probably limited to just a few hands. But my opinion is that the bulk of hands throughout the tree are pure. The reason is that if a hand is mixed, then playing it both ways has to have equal equity, and I just don't think that broad swaths of hands are indifferent between two actions.

jerrod

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
The brightest? Dunno. Bright enough to understand that "a winning strategy" does not guarantee a win in a particular session? Yes.

[/ QUOTE ]

I fell over laughing myself when I read this:

[ QUOTE ]
If there existed a workable (winning) game theoretical strategy, guys like Sklansky and Fergusen and Weideman, etc.. would win all of the heads up championships. But they don't.

[/ QUOTE ]

That's the kind of mistake a novice would make. On second thought, I take that back--most novice's know better.

Re: Balancing Bluffs vs Balancing Strategy
 

David ~ Being a woman (and a young woman at that)... I find it difficult to bluff. Men tend to call me down with anything, or check-raise me with nothing (and then show me their cards to rub it in). I've found that my best way to make money is to wait for position and good starting hands. Sometimes if I've won a huge pot, and have played very little hands... I am able to bluff. But most of the time, guys will say something like "I wanna see what the little lady has" and call me down ~ no matter the size of the bet, the odds they are getting, or whether they have anything on the board or not.
The only problem with this, is that sometimes the cards don't come. For example, I just started playing again Thursday night. I sat down short stacked at a 2-4 game. The action was insane. Almost every hand was $50 preflop with 3 to 4 callers. Because of my stack size and to analyze my opponents, I waited for top hands. During that hour, I was lucky enough to get pocket jacks and call the $50 preflop bet. There were 3 other callers and I was in mid position. The flop came down J A J giving me quads. The first hand I played!! Of course, I ended up tripling my money when one guy made a huge bet, another went all in, I called, the initial bettor folded. Piece of cake. During the next round, I re-raised to $30 (it was $15) with AXs in late position. I once again had several callers. The flop came all diamonds, giving me nut flush. I was able to get another all in on that hand too.
But even after only playing the nuts, every time I got into a pot I would be bluffed out. I folded the better hand quite a few times, because there were too many things that could have beaten me and I wasn't getting the proper odds to call. (For example AJs, would flop top pair and get pushed out of the pot with A2.) You'd probably say that I should know how these guys play ~ and I did ~ But I didn't want to make a call without the right odds holding only top pair ~ when these guys could be playing any two cards (in fact, they played almost every hand) and it was more than possible I was up against 2 pair or even a straight.
So by the time my stack got down to $350, I stopped playing hands. I waited for hours (somewhere between three and four) with patience. Flirting with the guys and talking them into drinking more. Then, I started playing again. In less than two hours, I got my stack well over $1200. By that time they were getting tired and not betting as much. Then I left.
I always tend to do very well in the games I play and ~ when I'm deep stacked ~ also mix up my play and variate my bet sizes so that no one can put me on a hand. But it aggravates me sometimes that I'm almost always called down and have to wait so long for cards.
I know you're not a woman, but do you have any advice???

~ Brandi

Re: Balancing Bluffs vs Balancing Strategy
 

By the way, I wanted to say thank you for writing you NLH Theory and Practice book... I did well even when I first started, but understanding the mathematics of poker has greatly improved my game. Things that I normally would not have called, lately I have been ~ because I am getting the right odds ~ and what's more, is that I've had the winning hand. I also do not go on tilt anymore or get upset when someone makes a bad call and then outdraws me. Instead, I've simply said "Nice Hand" and waited ~ knowing that if they were going to make bad calls, I was glad to have them sitting at my table, and that I would get all their money and more on another hand.
So thank you, thank you, thank you. Best book ever. [img]/images/graemlins/heart.gif[/img] [img]/images/graemlins/heart.gif[/img]

Re: Balancing Bluffs vs Balancing Strategy
 

welcome back brandi, i'm sure 2007 will be your year!

Re: Balancing Bluffs vs Balancing Strategy
 

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?

Re: Balancing Bluffs vs Balancing Strategy
 

It's possible no optimal strategy exist from
street to street. Let's start the game from
the turn.
Two person fix limit game. Pot is P after the
flop action. Each bet is 1 unit.
You hold TPTK on the turn.
Opponent checks. You bet. Opp check/raises.
Now your options are fold, call, reraise. If
you reraise, opp has options of fold, call, cap.
Now you have fold and call options.

You---fold----call-----RR-----fold-----call
Opp
fold___-1_____M1____P+2_____xx_____xx
call___xx_____xx_____M2_____xx_____xx
cap___xx_____xx_____xx_____-3_____M3

In matrix M1 the new pot size is P+4.
M2 is P+6. M3 is P+8.

Many of the cells are empty. Other cells
lead to another matrix. The river matrices
must be solved to have values to enter
into those cells. Only then can the
indifferences between line strategies be
solved.
Your linear hand strength will change from
the turn to the river dependent on the river
card. So instead of one M1 matrix, there
may be 46 M1 matrices. This matrix may be
unsolvable. Optimal strategy may not exist.

Re: Balancing Bluffs vs Balancing Strategy
 

[ QUOTE ]
Bright enough to understand that "a winning strategy" does not guarantee a win in a particular session? Yes.

[/ QUOTE ]

You call me insane...o.k. I might be..but for sure you are a nut case. The heads-up championships of which I spoke...were just examples (they are actually tournaments). Yes a particular strategy cannot garauntee winning a particular session but a strategy of the type these math wizs speak does predict dominance by those that employ it over those that don't. If you don't believe this just ask them.

leaponthis