The evolution of the mid-high stakes forum

[elindauer]

Ok, boys. This is the mid-high forum. It's time for us to take the next step in poker analysis.

You may have noticed that SO many threads talk about points that are very close in EV. Most threads, and all good threads, have heated arguments back and forth. It's a call. It's a fold. It's a raise. Frequently, nobody convinces anybody, and everybody has a good argument for their position. Fold, because he'll never check-raise with a weaker hand. Call, because if you fold he can run you over. You get the idea.

Well, the reason for much of the debate is that there's a fourth option we're ignoring: none of the above.


What do I mean? What is this fourth option? The fourth option is a probability triple, which indicates that you should take each of the three possible actions some percentage of the time. I suggest we write these triples this way:

{fold, call, raise}


Up to now, this forum has allowed only three options:

Fold: {100, 0, 0}
Call: {0, 100, 0}
Raise: {0, 0, 100}


When the answer to the OP is some triple like {15, 80, 5}, as it so often is, then we end up yelling at each other about how clearly our answer is right and the other guy's answer is wrong, and how if you think that, let's play heads up some time, fish.


Here's an example. You raise KQ and are called by the big blind, who is a good player. You flop top pair and bet all the way, and only to sadly get check-raised on the river. What should you do?

Well, this answer is almost always going to invlove a probability triple. Any answer of always folding, calling, or raising represents an exploitable strategy. Some are more exploitable than others, but all of them miss the mark of the perfect strategy.


We're playing mid and high stakes poker, so it is inevitable that we are going to have to deal with good players. Even against bad players, situations where triples are important arise all the time. Even a bad player is capable of noticing that you have been folding to river raises a lot, right?



So, from now on, please consider answers in the form

{fold, call, raise}

to be valid. These will be most common when the hand involves an opponent who is tricky, so he doesn't play exactly the same way every time with the same hand, and is capable of some adjustments to our play. Hopefully, we can start dialing in some of these triples for common situations, and talk about simple ways to make the random selection at home.


good luck.
Eric

[elindauer]

hi all,

Tommy suggests an alternate form to the triple {fold, call, raise} format I suggested. Specifically, if there is no action yet to you, suggestions might also have the form {check, bet}.

In my first attempts at using this notation tonight, I handled this with the triple {-, check, bet}, which I think is awkward. I support Tommy's improved notation.

thanks,
eric

[1800GAMBLER]

With KQ betting all the way and getting raised on the river in games less than 50/100 paying a whole 1BB in calling to not be exploitable when there's a player pool of 1000s is crazy. Which is true for most threads around here. In the 30/60 game against the majority of players there's very little point in paying off, and when there is a chance of being exploited it's better to fold then call your next hand rather than to randomise your calls/folds.

[elindauer]

[ QUOTE ]
With KQ betting all the way and getting raised on the river in games less than 50/100 paying a whole 1BB in calling to not be exploitable when there's a player pool of 1000s is crazy.

[/ QUOTE ]

So, isn't it still applicable to hands played against known opponents who know you, like in high stakes games, like the ones discussed in this forum? I posted this here for a reason. I agree that it has less use in the lower stakes games.

Further, when your opponent is unknown, it's perfectly reasonable, especially as the limits go up, to handle these decisions with game theory. It's perhaps a defensive strategy, but it's sound, and gets more and more sound as the limits go up. You then can adjust from the "basic strategy" of game theory triples as you learn more about how he plays.

Further, just because the player pool is large does not mean that there aren't lots of good players around who know who you are. Datamining has taken on an art form these days. pokeredge supplies tons of data about players you've never played against. Assuming that your unknown opponents doesn't know you is dangerous.

Finally, I think it's important to know how the game would be played if your opponent played perfectly. This gives you a framework to adjust as you get information about your opponent. Maybe you never 3-bet for value and then fold to a 4-bet on the river, but it's still useful to know that in a perfectly played game, this should happen. If you start writing out triples and see that you are suggesting a 3-bet but would never fold to a 4-bet, then you are forced to ask yourself what mistake your opponent is making that is allowing you to get away with this.

[ QUOTE ]
Which is true for most threads around here. In the 30/60 game against the majority of players there's very little point in paying off, and when there is a chance of being exploited it's better to fold then call your next hand rather than to randomise your calls/folds.

[/ QUOTE ]

There is plenty of room within a triple-based solution for you to apply your own judgment about when to fold and when to call. You like to fold early and call later. That's a fine strategy. Other times it may not be appropriate though, like when we have an extensive history with the villain.

You also seem to think that in your games, the way they are played today, in the particular situation I described, that you should never fold. Fine. That doesn't mean that a mixed strategy will never be appropriate in a different game, or at a different time, or in a different situation.

I write this post because, to read 2+2, you might conclude that every decision in a poker game had one correct answer. Mixed solutions are almost never suggested or discussed. In fact though, in a perfect game they would be absolutely commonplace, covering virtually every decision made! It seems absurd to think that our opponents are so bad, so predictable, even in the highest limits discussed here, that we still can get away with a definite fold or call or raise answer every time.

good luck.
eric

[1800GAMBLER]

Some good stuff in that post.

[AceHigh]

[ QUOTE ]

So, from now on, please consider answers in the form

{fold, call, raise}

to be valid.

[/ QUOTE ]


I think this implies a level of precision that just doesn't exist, at least not for most players. I'd rather see someone respond:

"You are almost never good here, I would fold. The pot would have to twice as big for me even to consider calling."

Or

"I'd call. If the pot was smaller, say 7BB, it's a fold, but I think you will be good more than the 13:1 you are getting".

etc.

[mterry]

Are you advocating using probability triples at the table? I feel with little time to think and only subjective source of randomness, pts will have less value. However, after the hand I agree they provide a good way to quanitfy how we should've mixed up our play at a certain point.

[elindauer]

[ QUOTE ]
Are you advocating using probability triples at the table? I feel with little time to think and only subjective source of randomness, pts will have less value. However, after the hand I agree they provide a good way to quanitfy how we should've mixed up our play at a certain point.

[/ QUOTE ]

I assume you are talking to me.

Yes, I advocate them, the same way I advocate using the complex math we often do at the table. You do it precisely away from the table, and then you do it intuitively at the table.

As far as randomness, my NL friend uses dice when he plays online against tough opposition. Doing it live would be trickier of course, but the old second-on-the-watch trick can work, among others.

good luck.
eric

[1800GAMBLER]

I don't think there is much reason at the 30/60 to use 'the triple', if i'm against someone i'm going to play 1000+ hands against over the next few months then metagame considerations become important. I think the most important metagame strategy against these players is putting them on the back foot. Some turn bluff raises, some flop draw caps, etc, find their exploitable strategies. I've labelled finding their exploitable strategies as 'get shania wide', by this i mean, playing legit against unknowns but watching if they fold the river for 1 bet in sitations, or fold to turn raises, then increase your range of hands against them to include bluffs and put them to the zero expectation calls.

Again though, this is against the regulars only. By that i mean, i will turn bluff raise against anyone if i think it is +EV for this hand, but for the regs i will do it if i think it is -EV right now but worth more later on. FWIW, i can only think of about 5 players i do this against in the 30/60 limit, but there are a lot i do it against in the 10/20 nl.

The parts of the last post i think were really good for the forum was,

[ QUOTE ]
Finally, I think it's important to know how the game would be played if your opponent played perfectly. This gives you a framework to adjust as you get information about your opponent. Maybe you never 3-bet for value and then fold to a 4-bet on the river, but it's still useful to know that in a perfectly played game, this should happen.

[/ QUOTE ]

If your opponent played perfectly then they bluff 10:1 on their 10:1 bets, or 5:1 on their 5:1 bets, or (like in NL) 2:1 on their 2:1 bets. Knowning this you can, find the ones who aren't doing it. Good example is 88 overpair vs limper who called a low flop who you know has overcards then the Q comes. Some posters, wont think and just bet, some wont bet against some players because they will bluff raise, yet hardly any posters say 'i bet here because he will bluffraise too often, so it's not a tough decision it's a good decision' i think those are the only metagame game theory/percentage plays that have much value in the 30/60.

Plus _considerating_ all plays such as 3 bet and fold for 4 is good poker, but JASucker has said way way enough on that for us all.

[elindauer]

Hi gambler,

Despite your kind words on part of my post, I get the impression that you consider the idea of a mixed strategy to be rather theoretical and not of much practical value. I'd like to point out that doing this:

[ QUOTE ]
Some turn bluff raises, some flop draw caps, etc, find their exploitable strategies

[/ QUOTE ]

is just a more hand wavy way of saying that you would employ a mixed strategy of sometimes raising and sometimes calling with the same hand in the same spot. All I'm saying is that we should start addressing these critical ideas more precisely, by trying to figure out how often you should cap a draw HU, how often you bluff raise the turn, etc. We should start putting these numbers on specific boards, with particular textures and given actions, against particular known opponents.

[ QUOTE ]
... watching if they fold the river for 1 bet in sitations, or fold to turn raises ...

[/ QUOTE ]

Surely you don't mean that you'll either always raise the turn or never raise the turn, right? Welcome to the land of mixed strategy, where {20, 60, 20} is a perfectly legitimate answer and may be clearly better than any of {100, 0, 0}, {0, 100, 0}, or {0, 0, 100}.

I think we all understand this intuitively and mix up our play accordingly, but we don't ever talk about here. Doesn't anybody think that those changeup plays we all just make on our own intuition deserve any recognition? How often should we make them. On what boards? Against what opponents?

So often the changeup is the most interesting part of the hand, but we blow by it and just say, eh, let's not talk about the preflop. I was mixing up my play. Now, about that turn decision... tell me the answer. Call, raise, or fold?

-Eric

[1800GAMBLER]

[ QUOTE ]
I get the impression that you consider the idea of a mixed strategy to be rather theoretical and not of much practical value.

[/ QUOTE ]

[ QUOTE ]

is just a more hand wavy way of saying that you would employ a mixed strategy of sometimes raising and sometimes calling with the same hand in the same spot.

[/ QUOTE ]

I know that. There are two places to mix range your plays, on the offensive and on the defensive. You give the KQ example which was on the defensive so i took the majority of the time you do this strategy to be on the defensive, which is when i think it has very very little value because our opponents are playing so far away from perfect.

However, i still don't think the mix strategy will come to this board. This board is how to play one hand, we don't post 100 hand sessions or long history, only schiends does that with his 100/200 HU sessions which i think are great for the forum.

[ QUOTE ]
Surely you don't mean that you'll either always raise the turn or never raise the turn, right?

[/ QUOTE ]

Yes, i did. There are just so many plain situations in which i have no reason to mix it up. I raise AA preflop. Big blind calls. flop comes Jxx. i get checkraised. There is pretty much never a reason to mix my strategy up here; never am i calling down and never am i raising the flop. The only time i will ever mix it up is if i do it and BB folds, the next time around or the next time after that he gets AK added to my range, which bluff theory wise would be over adjusting to his fold, since it's about 24 legit combos and 16 bluff combos in a roughly 4:1 bluff.

[Chris Callahan]

[ QUOTE ]
Here's an example. You raise KQ and are called by the big blind, who is a good player. You flop top pair and bet all the way, and only to sadly get check-raised on the river. What should you do?

Well, this answer is almost always going to invlove a probability triple. Any answer of always folding, calling, or raising represents an exploitable strategy. Some are more exploitable than others, but all of them miss the mark of the perfect strategy.

[/ QUOTE ]

Your idea might be good, but I think this example is wrong. When defending against this raise, you should consider the whole range of hands you can hold at that point, and then call the correct percentage of the time. There will be a cutoff hand which will be the worst one you call with, and this hand is the only one that might need a mixed call/fold strategy. It makes no sense calling with KJ some of the time and folding KQ some of the time.

[ QUOTE ]
Ok, boys. This is the mid-high forum. It's time for us to take the next step in poker analysis.

You may have noticed that SO many threads talk about points that are very close in EV. Most threads, and all good threads, have heated arguments back and forth. It's a call. It's a fold. It's a raise. Frequently, nobody convinces anybody, and everybody has a good argument for their position. Fold, because he'll never check-raise with a weaker hand. Call, because if you fold he can run you over. You get the idea.

Well, the reason for much of the debate is that there's a fourth option we're ignoring: none of the above.


What do I mean? What is this fourth option? The fourth option is a probability triple, which indicates that you should take each of the three possible actions some percentage of the time. I suggest we write these triples this way:

{fold, call, raise}


Up to now, this forum has allowed only three options:

Fold: {100, 0, 0}
Call: {0, 100, 0}
Raise: {0, 0, 100}


When the answer to the OP is some triple like {15, 80, 5}, as it so often is, then we end up yelling at each other about how clearly our answer is right and the other guy's answer is wrong, and how if you think that, let's play heads up some time, fish.


Here's an example. You raise KQ and are called by the big blind, who is a good player. You flop top pair and bet all the way, and only to sadly get check-raised on the river. What should you do?

Well, this answer is almost always going to invlove a probability triple. Any answer of always folding, calling, or raising represents an exploitable strategy. Some are more exploitable than others, but all of them miss the mark of the perfect strategy.


We're playing mid and high stakes poker, so it is inevitable that we are going to have to deal with good players. Even against bad players, situations where triples are important arise all the time. Even a bad player is capable of noticing that you have been folding to river raises a lot, right?



So, from now on, please consider answers in the form

{fold, call, raise}

to be valid. These will be most common when the hand involves an opponent who is tricky, so he doesn't play exactly the same way every time with the same hand, and is capable of some adjustments to our play. Hopefully, we can start dialing in some of these triples for common situations, and talk about simple ways to make the random selection at home.


good luck.
Eric

[/ QUOTE ]





"if you think that, lets play heads up some time, fish"


that was classic....PURE [censored] COMIC GENIUS.

I am still laughing.


God that was funny.


AND ACCURATE, TOO.....

[tonysoldier]

I absolutely agree with you, I tried to start a thread on this a few months ago, but nothing happened, I hope that this one is good. I give some more of my thoughts when I read the thread.

[jba]

this is very similar to a book I have been reading, How Good is Your Limit Holdem. In that book he has multiple choice quizzes, each answer is worth a certain amount of points. In OP's KQ example he might say ok the guy just check/raised you, what do you do?

A. reraise
B. call
C. fold

In the answers you would get 0 pts for answering A, 10 for B, 7 for C (he goes into much more detail about villain, prev hands, etc). The explanation will be "yadda yadda against many opponents this is an easy fold but because of X it isn't go great here".

I think it's definitely the right way to think about things and your tuple method is better than the currently very crude "X and it isn't close" / "it's closer than most are making it out to be".

so basically, that was a pretty long way to say I like it.

[elindauer]

[ QUOTE ]
However, i still don't think the mix strategy will come to this board. This board is how to play one hand, we don't post 100 hand sessions or long history, only schiends does that with his 100/200 HU sessions which i think are great for the forum.

[/ QUOTE ]

But this is my point. Let's say a hand has an opportunity to semi-bluff. What you are saying is that your answer to what you would do in a post will be either fold, call, or raise, but that, at the table, this isn't how you would play at all. You would play a mixed strategy designed to keep him guessing, involving semi-bluff raising. How often should you semi-bluff raise over the hands that look like this? That's an interesting question we should be discussing, but aren't.

How you play and how you post are different. In the mid high stakes forum, this shouldn't be the case. We should have a vocabulary for describing what we really would do, which is not any of fold, call, or raise.

I agree that it might not catch on. It's different and it's challenging. We're not used to thinking this way. In my mind, the fact that it would be so hard to put anything but a broad range of numbers on these triples suggests just how much room there is for us all to improve.

[ QUOTE ]
There are just so many plain situations in which i have no reason to mix it up. I raise AA preflop. Big blind calls. flop comes Jxx. i get checkraised. There is pretty much never a reason to mix my strategy up here; never am i calling down and never am i raising the flop.

[/ QUOTE ]

Well, that is your opinion. I personally feel that in this exact situation, a triple is absolutely necessary against any decent opponent. If you never reraise overpairs, then he can know that when you do reraise, you don't have a particularly strong hand. Further, by always playing your big hands slow, you give him more incentive to take shots at the pot with draws, since he knows he's unlikely to be forced to pay 3 bets to see the turn. He can just check the turn if he mises his draw and you call the flop.

AA is a particularly strong overpair that doesn't fear free cards generally, so I like the smooth call play often with that hand. Maybe {0, 80, 20}. But you see what's happening here? Talking about triples forces us to confront two questions. First, how should we play this hand while considering questions like metagame, etc. Not just this one hand in a vaccuum, but this hand in the context of many hands. Second, it forces us to consider how our strategy with this hand interacts with our strategy for playing other hands. If we always call, what hands does that leave us 3-betting? How can our opponent take advantage of this? Will he take advantage of this? What mixed strategy would be the "default" that could not be exploited? Would it ever include folding?

[ QUOTE ]
The only time i will ever mix it up is if i do it and BB folds, the next time around or the next time after that he gets AK added to my range, which bluff theory wise would be over adjusting to his fold, since it's about 24 legit combos and 16 bluff combos in a roughly 4:1 bluff.

[/ QUOTE ]

Without getting into the specifics, this is precisely the kind of discussion we should be having in the mid high forum. Exactly like this. How to play the hand, then adjust our mixed strategy based on that play and our assumptions about their assumptions...

It all gets very complicated and very interesting fast. Let's save the "fold preflop" stuff for the low stakes tables, and move on.

Thanks for the discussion, you make well thought out points. I think our views of the world are closer than it would seem given that we appear to be disagreeing.

-Eric

[elindauer]

Hi Chris,

You're right and this is a very insightful post. I might disagree with your contention that folding KQ and calling KJ must be wrong. These hands are virtually identical in quality facing a check-raise, so our feelings about whether or not top pair is good at this particular time is much more important than the pip in kicker.

If you are not going to use judgment to make these decisions, ala Gambler's suggestion that you fold early and call late in the session, then yes, I agree that you should fold the weakest hands and call the strongest hands, using triple concept to discuss what percentage of your hand range to fold. I think you'll find that with any decent percentage, you're probably going to have to fold some pairs though. Maybe not, it depends on how much bluffing you do. See how we're talking about your whole strategy again? You have to for there to be any reasonable discussion of whether or not you should fold, yet this is almost never acknowledged in this forum. I think this is because we have, until now, lacked the vocabulary to begin the discussion.

-Eric

[elindauer]

[ QUOTE ]



[ QUOTE ]

So, from now on, please consider answers in the form

{fold, call, raise}

to be valid.

[/ QUOTE ]


I think this implies a level of precision that just doesn't exist, at least not for most players. I'd rather see someone respond:

"You are almost never good here, I would fold. The pot would have to twice as big for me even to consider calling."

Or

"I'd call. If the pot was smaller, say 7BB, it's a fold, but I think you will be good more than the 13:1 you are getting".

etc.

[/ QUOTE ]

Hi AceHigh,

Your statement is clearly true, right now. Does that mean that, with the great poker talent and minds available on this board, we cannot change this?

I'd speculate that few players have ever spent much time thinking about this, and there's very little written in the literature. It's not surprising that we have no feel for the numbers. We have to start thinking and playing this way and getting experience and refining and playing and thinking... just like when we were working on the simple fold or call or raise model that has served us so well to this point.

Time to take the next step. We'll have stupidly broad ranges in the beginning. It won't be easy. That doesn't mean we shouldn't try.

By the way, the painfully bad (IMO) and hand waving analysis of DERB's play would be helped immensely by discussions like this. I happen to believe we're going to find that mixed strategies against good players are going to involve 3-betting some medium pairs on the turn, to try to exploit their tendency to fold to raises... Or, perhaps better, because they don't have the leak of never folding to raises, we have to stop leaking by never semi-bluff 3-betting. Or, perhaps, because they fold to raises too much, we must semi-bluff 3-bet more... or... well, what is it? How often should you muck AK unimproved to a turn donk bet? How often should you call? Raise? And how often DO you do it?


-Eric

[Chris Callahan]

[ QUOTE ]
You're right and this is a very insightful post. I might disagree with your contention that folding KQ and calling KJ must be wrong. These hands are virtually identical in quality facing a check-raise, so our feelings about whether or not top pair is good at this particular time is much more important than the pip in kicker.

[/ QUOTE ]

I agree with this, but now you are talking about reads and psychology. It's not what's implied by the {fold,call,raise} notation. The way I see it, it says that you should randomize your action after you have taken all information into consideration. But it cannot be correct to use {50,50,0} for KQ and {50,50,0} for KJ, because you could simply improve on this by using {0,100,0} for KQ and {100,0,0} for KJ.

In terms of game theoretic optimal strategies it might not matter if you fold KQ and call KJ because it might not be exploitable (meaning that even if you do this it's never correct for your opponent to check-raise KQ or KJ). But in choosing between two optimal strategies we should of course use the one that has the potential to exploit mistakes (in this case raising with a hand that he should always just call with).

[Spicymoose]

The reason you need to vary your play is so that you are not predictable, and cause your opponents to put you on hand ranges as different as possible from what you actually have later on. If you have a hand where you want to {20,60,20}, I think randomly choosing your 3 options based on the percentages is ok, but I think it is better to consciously choose which option, after you have your mixed strategy.

The reason for this is because you currently have some image at the table. Lets say that your image is extremely tight, only bet good hands, never bluff. In this case, you want to people to keep that image, so your likely actions should be more inclined to do things that look weak/tight. Now, if you have something like {50,50,0}, maybe you will be more inclined to fold, to keep your image as is, rather then let people know that you might call down semi-loose. This can only be taken to an extent though, if you are pondering a {10,90,0}, then you can't just automatically fold to keep your image as is.

Basically my point is that when using a mixed strategy, you should be thinking about what your current image is, and where you want your image to go, and have that have at least some influence on your mixed strategy.

[DeeJ]

Eric
I have been surprised that I'm usually one of the few people to say "I call 50%, fold 50%" or something like that. Maybe it's not having played for long enough to be sure of any particular recommendation it's also a good way of hedging my bets /images/graemlins/grin.gif

edit: I've become Pooh. Bah!

[elindauer]

[ QUOTE ]
I agree with this, but now you are talking about reads and psychology. It's not what's implied by the {fold,call,raise} notation.

[/ QUOTE ]

This is your assumption. I think {50, 50, 0} simply says that over your career in this situation, you should fold half the time and call half the time.

Now, if you don't think you can better judge these things than your opponent, then yes, you can use dice and randomize the decision that way. In the KQ vs KJ hand, I agree that always calling the KQ and always folding the KJ is a good way to use the cards to make the decision random for you.

However, many players feel that they CAN outguess their opponent, or at least that they would like to try. Maybe they fold the 50% of bets that seem to come the fastest, for example. Or maybe they fold the 50% of bets where their opponents put their chips into the pot in the most unusual way. Whatever. Your holding a Q kicker or a J kicker may not be the best way to ensure that your calls have the highest win rate.

By the way, folding the KJ always and the KQ never is in fact somewhat exploitable, in that if your opponent knows exactly what you are doing, he can profit by bluffing a little more any time he holds a queen. From a purely theoretical view, you have to call the KJ just as often as the KQ.

-Eric

[elindauer]

Hi SpicyMouse,

I agree completely that a good player will not want to use dice to randomize the selection, but should instead use his judgment to try to make the best choice available right now.

This of course comes with the caveat that if the choice is {50, 50, 0}, he cannot use his judgment to constantly decide to fold. This implies that he needs to find a way to keep track of his history somehow, to make sure that he isn't judging his way into a {90, 10, 0}, making his game exploitable without realizing it.

We're also assuming that this player is in fact better than his opponets, aren't we? He should only use his judgment if he feels he can outguess the opposition. Maybe he's sitting in a game with three bad players, five average, but one outstanding, world-class player. The game may be good, but against the world-class player, he should not try to use his judgment to decide whether to call or fold. He should flip the coin. This will help him defeat the good players edge on him in those pots where they face each other.

But first he has to know the percentages, so let's start working on them. /images/graemlins/smile.gif

-Eric

[Paluka]

I think this usage of the triple {} thing is pointless. Most people usually say stuff like "I call here. If X were true I would raise, if Y were true I might fold. This is a spot where I might vary my play if I was playing against a guy I play against every day." This is way more useful than just trying to be ultraprecise and put some numbers out there.

[DrSavage]

Usually people balance their play with hand ranges and not probabilities of action with a given hand. In your KQ example, the correct action against a good opponent is mostly a function of your hand range with which you bet the river, you can easily construct a range in which always calling will be correct, another one where always folding will be correct and another one where always reraising will be correct. Your actual decision will almost always depend on specific hand you have and you will use game theory here
practically never. Also, trying to use game theory in "calling" problems is just wrong, either your opponent's range is small enough so you can always fold or it's wide enough so you can always at least call or it's just enough so it's not really correct to do either, in which case it doesn't matter what you do. It's absolutely never a correct strategy to call X% and fold Y% for any given opponent, it's either always call or always fold or you are [censored] either way.

[elindauer]

[ QUOTE ]
Eric
I have been surprised that I'm usually one of the few people to say "I call 50%, fold 50%" or something like that. Maybe it's not having played for long enough to be sure of any particular recommendation it's also a good way of hedging my bets /images/graemlins/grin.gif

edit: I've become Pooh. Bah!

[/ QUOTE ]

I feel a certain sense of honor that you made your pooh-bah post in my thread. I'm pretty sure that makes me quite a dork. :P

So does using that little :P symbol just now. Man, my ego is taking a beating tonight!

-Eric

[elindauer]

[ QUOTE ]
I think this usage of the triple {} thing is pointless. Most people usually say stuff like "I call here. If X were true I would raise, if Y were true I might fold. This is a spot where I might vary my play if I was playing against a guy I play against every day." This is way more useful than just trying to be ultraprecise and put some numbers out there.

[/ QUOTE ]

Well, that's one attitude. My own feeling is that more precise answers are better than less precise answers.

I think you may be saying that you don't like someone writing {35, 50, 15} because no one can be that exact. I have two thoughts on that.

First, many game theory problems are fundamentally solvable, so it is not so ridiculous, when crafting a strategy that we are going to employ, that we could in fact be that exact.

Second, I have no problem with a notation that allowed for ranges. Already I've seen someone post something like {20-30, 50-60, 20-30} which only suggests ranges. This, to me, has much more merit than "sometimes do it", or "if I'm mixing up my play I do it" or the other highly vague notions that we use those times we do address this issue.

I agree that at the start, we'll suck at putting down the numbers. It will be awkward for experienced players who are used to knowing the answers to fumble with these numbers and admit that they really don't know the answer. My fear is that this might dissuade some people, perhaps some of the best players, from even trying.

My hope is that it won't.

-Eric

[elindauer]

[ QUOTE ]
Usually people balance their play with hand ranges and not probabilities of action with a given hand.

[/ QUOTE ]

Before I go any farther, I wanted to highlight this sentence as being very insightful and absolutely true. There are many situations where this works well. Obviously, because that's all we talk about here at 2+2 and some of us have in fact been known to do quite well at this game. /images/graemlins/smile.gif

[ QUOTE ]
In your KQ example, the correct action against a good opponent is mostly a function of your hand range with which you bet the river ... you will use game theory here
practically never.

[/ QUOTE ]

Well, not so fast. It's really about the comparison between the range our opponent will raise and the range we hold. You can't just construct a range where you should always call. It's always going to be opponent-dependent.

But, in many cases, our opponents range depends on whether or not we will call. Some players are good enough to adjust to what we are doing, just the way we try to adjust to what they are doing. Just looking at your own hand for the decision is what rookie's do.

[ QUOTE ]
Also, trying to use game theory in "calling" problems is just wrong, either your opponent's range is small enough so you can always fold or it's wide enough so you can always at least call or...

[/ QUOTE ]

This is a very eloquent statement of what I think is a widespread misconception on these boards. On the surface, your argument makes sense. Either it's right to call, or it's wrong.

Your mistake is in the subtle assumption that we can know our opponents hand range. Can we? Against a good opponent, this will be very difficult. He can change gears silently without our knowledge. He can adjust to the way we are playing him without our knowledge. He can be an unknown to us. He may be much better than us and understands the way we are thinking, perhaps because we post all of our thoughts on message boards for anyone to see. /images/graemlins/smile.gif

In all of these cases, the safest choice for our strategy is to use a mixed strategy until we have more information suggesting we should try to outguess him.

[ QUOTE ]
It's absolutely never a correct strategy to call X% and fold Y% for any given opponent, it's either always call or always fold or you are [censored] either way.

[/ QUOTE ]

Are you sure? How about if I describe the following opponent: she is smarter than you. she is able to judge whether or not you are going to think she will bluff. she recognizes the kinds of boards you think are "unbluffable", and the kind you don't. How should you decide whether or not to call? Do you want to go on trying to outguess her, when you know she is better than you?

Think this person doesn't exist? Don't you think this about yourself relative to your weaker opponents?

Here's another opponent: good, solid, winner. Very observant and able to adjust to her opponents. You know you are going to have to play with her often, because the player pool for this game is very small. Perhaps you are playing the big game at the Bellagio.

You've made a few big river laydowns today. You don't know if she thinks you're playing weak today, or if she'll recognize that you're just playing the opponent. You get check-raised by her in a spot where she usually has you beat, but it's close. Call or fold?

good luck.
eric

[Paluka]

[ QUOTE ]
[ QUOTE ]
I think this usage of the triple {} thing is pointless. Most people usually say stuff like "I call here. If X were true I would raise, if Y were true I might fold. This is a spot where I might vary my play if I was playing against a guy I play against every day." This is way more useful than just trying to be ultraprecise and put some numbers out there.

[/ QUOTE ]

Well, that's one attitude. My own feeling is that more precise answers are better than less precise answers.

I think you may be saying that you don't like someone writing {35, 50, 15} because no one can be that exact. I have two thoughts on that.

First, many game theory problems are fundamentally solvable, so it is not so ridiculous, when crafting a strategy that we are going to employ, that we could in fact be that exact.

Second, I have no problem with a notation that allowed for ranges. Already I've seen someone post something like {20-30, 50-60, 20-30} which only suggests ranges. This, to me, has much more merit than "sometimes do it", or "if I'm mixing up my play I do it" or the other highly vague notions that we use those times we do address this issue.

I agree that at the start, we'll suck at putting down the numbers. It will be awkward for experienced players who are used to knowing the answers to fumble with these numbers and admit that they really don't know the answer. My fear is that this might dissuade some people, perhaps some of the best players, from even trying.

My hope is that it won't.

-Eric

[/ QUOTE ]

But the real problem is that proper balancing strategies will vary widely based on the situation. If we try and do this every thread will have to answer a) was it live or online b) did the player know you and did you know him c) did you have a history against each other blah blah blah. So all the poker strategy will become muddled by everyone's interpretation of the relationship between the two players. Now combine that with the fact that a) a very small percentage of my online opponents pay enough attention to make me want to vary my play with b) the precision of our answers is going to be awful and I think this is fairly pointless. I'd much rather get an explanation like the one I alluded to in my first post. You say you want precision, but what you are trying to do is measure something with a ruler and give an answer in 1000ths of an inch.

[w_alloy]

Elindaur, I really like most of your posts in this thread. But I think you are making a key mistake in part of your reasoning which I am surprised noone else has pointed out (maybe I am making the mistake, or someone pointed it out and i didnt see?).

We do not necessarily have to balance our strategy when we have top pair and get raised on the river in your example. We only need to balance our strategy for calling with a hand a % of the time we take the raise bet bet bet line and get raised on the river with this board against the BB. It is less relevent the actual hand we hold, because our opponent doesnt know when he raises the river after he takes that line.

Put another way, our weighted range of possible hands needs to have balanced actions, based on the action in the hand up to this point and our tendancies. So, for example, in the example KQ hand lets say we only take this line when we have exactly KdQc or better then top pair. We can then always fold KdQc (if we call with better then top pair) because we will call enough with our range to make his bluff unprofitable.

It may seem like this doesnt contradict any of your points, and that this is meerly a small point, but this is not so. Most players, instead of using triples for specific hands, choose to balance their lines and therefor possible hand ranges to optimal levels. Triples are sometimes required to balance lines, but usually only on earlier streets. This brings us to a more relevent point: Where one person may require a triple for a given spot, others will have balanced that line on earlier streets for that board. It becomes required to know that persons exact wighted hand range to know if a triple is required. This is all rediculously complex for normal internet message board advice, and furthermore assumes your opponent is astute enough to recogonize holes and exploit them (this has been discussed at length already in this thread).

I think triples are a good idea, but should only be used when the opponent is a true expert and very familiar with hero's play, hero's hand range is well defined, and we know what hero will do with his other holdings in this spot on this board (or we need to state it with our triple).

[DrSavage]

[ QUOTE ]

Are you sure? How about if I describe the following opponent: she is smarter than you. she is able to judge whether or not you are going to think she will bluff. she recognizes the kinds of boards you think are "unbluffable", and the kind you don't. How should you decide whether or not to call? Do you want to go on trying to outguess her, when you know she is better than you?


[/ QUOTE ]

I'm sure as hell am not flipping a coin to see if i should call or not.

[ QUOTE ]

You've made a few big river laydowns today. You don't know if she thinks you're playing weak today, or if she'll recognize that you're just playing the opponent. You get check-raised by her in a spot where she usually has you beat, but it's close. Call or fold?


[/ QUOTE ]

Call if i think I can be bluffed here a larger percentage of the time than my pot odds, fold otherwise.

It seems to me that you somehow think that if someone will bluff me 10% of the time amd the pot is offering me 9 to 1 i should call him 90% and fold 10%. That's just wrong.

[DeeJ]

[ QUOTE ]
It's absolutely never a correct strategy to call X% and fold Y% for any given opponent, it's either always call or always fold or you are [censored] either way.

[/ QUOTE ]

This is not my understanding of game theory (or practical poker). You are saying that one should play more predictably? (as opposed to solidly?)

I think when it gets very shorthanded and there's more aggression and bluffs this is more relevant. Full tables do play more by what you hold, but what is often important is what your opponents think you hold (which table image, shania, meta game history) & plays a part in determining the optimum frequency of your decisions. If a certain villain has been bluffing at you, you will call more. That's a judgement more based on game theory, than a precise hand holding.

Corollary - if villain to your left spots that you 'always fold' in a certain situation, (eg when Ace is on the turn, you check) he then bets into you and you can't beat a pair of aces, he'll do this to you more often h/u because the only time you'll defend is when you have at least a pair of Aces yourself, which is <50% of the time.

If you're playing people who don't know you and you don't know them, sure, play optimal solid poker. But even that means you might be bluffing sometimes (X% rather than predictably) to extract the max, against certain players.

Dan Harrington also says he mixes up his play in NL to avoid giving too much information about his hand holdings, and uses approximate percentages to do stuff at random.

[DrSavage]

[ QUOTE ]
[ QUOTE ]
It's absolutely never a correct strategy to call X% and fold Y% for any given opponent, it's either always call or always fold or you are [censored] either way.

[/ QUOTE ]

This is not my understanding of game theory (or practical poker). You are saying that one should play more predictably? (as opposed to solidly?)

I think when it gets very shorthanded and there's more aggression and bluffs this is more relevant. Full tables do play more by what you hold, but what is often important is what your opponents think you hold (which table image, shania, meta game history) & plays a part in determining the optimum frequency of your decisions. If a certain villain has been bluffing at you, you will call more. That's a judgement more based on game theory, than a precise hand holding.

Corollary - if villain to your left spots that you 'always fold' in a certain situation, (eg when Ace is on the turn, you check) he then bets into you and you can't beat a pair of aces, he'll do this to you more often h/u because the only time you'll defend is when you have at least a pair of Aces yourself, which is <50% of the time.

If you're playing people who don't know you and you don't know them, sure, play optimal solid poker. But even that means you might be bluffing sometimes (X% rather than predictably) to extract the max, against certain players.

Dan Harrington also says he mixes up his play in NL to avoid giving too much information about his hand holdings, and uses approximate percentages to do stuff at random.

[/ QUOTE ]

Game theory comes into play in bluffing decisions, not in calling ones. You are not getting any edge by calling 90% of the time and folding 10% randomly.

[TStoneMBD]

to clear confusion for the time being if people actually like using this system, i think you should be expressing frequencies in the following format:

FCR{xx, yy, zz}

by putting FCR before the {} you distinguish the variables.

CB{xx, yy} resembles check/bet.


dont know if that helps at all. keep it up elindauer youre a great poster and i think evolving our form of discussion into frequencies is the way to go.

[DMBFan23]

maybe it's that for a given range we should take lines with the frequencies FCR{x,y,z} but for each individual hand in the range there is an action you should take every single time, and we should be thinking about what hands we add to or subtract form the range, as opposed to adjusting the frequencis of the individual hands, which are fixed. that seems to be what Dr. Gutshot is implying. Of course, the frequencies for each hand would depend on the other hands in your range as well, and it would depend on the opponent's range, so yeah.

But it could also be the case that there is a mixed strategy for each individual hand. I think this is how pokibot works, for example, and seems to be eric's stance.

if I knew the answer I'd be playing a lot higher.

[brick]

Hey Eric,
Nice website btw.

I play in live game here in Seattle with a lot of regular players who are good hand readers and seem to be able to put me on a hand farily easily.
I've been thinking about playing every tenth round using a "tricky or different" style than the other 9 rounds. I would use some method to keep track of the number of rounds I've played.
I would try to use this tricky strategy only when the EV loss on that play was small. (ie. I would not forgo raising AA after a few limpers to try to mix up my play.)

Do you think 10% is enough, but not too much, mixing it up to be effective?

[w_alloy]

[ QUOTE ]

Game theory comes into play in bluffing decisions, not in calling ones. You are not getting any edge by calling 90% of the time and folding 10% randomly.


[/ QUOTE ]

This is wrong. If your opponent is bluffing at optimal levels and assumes you are calling at optimal levels, it doesnt matter what you do. Besides that, I have no clue what you are talking about.

[elindauer]

Hi DMBFan23,

You understand the situation quite well. It's an excellent idea to use the following balancing technique:

1. Decide how often you need to be calling, folding, and raising in the given situation.

2. Look at your hand range and choose the best hands for raising, the mediocre hands for calling, and the worst hands for folding


This provides a mixed overall strategy that is hard for your opponents to handle. I see two issues with this approach as it is currently implemented in our discussions:


1. We don't do this! At least, not explicitly. No one ever discusses anything like the total hand range you could hold at this point, what percentage of hands would be reasonable to fold, and what hands that would be on this board after this action. If we did, we'd recommend those "big folds" much less often. When we did recommend them, we'd have to justify it by talking about hand ranges and how often we're folding and that's ok because we don't think he'll notice because it's not that much more than we should be, etc etc.

At the lower limits this kind of discussion isn't as relevent, because the players don't notice things as often. As you go up in limits, this kind of thinking becomes important to really beating the games well, I suspect.

2. Sometimes the percentages are not going to line up crisply between hands in your range. If you want to fold 5% of your hands, for example, and your hand range is fairly tight for the situation (imagine the river after lots of action), then that may mean folding TT and half the time you have JJ.

3. It's not unusual for the many hands to have essentially the same chance of winning against the hand your opponent is representing. For example, you check check-raised after the top card on the board pairs, against an opponent who always 3-bets premium pairs but didn't this time. Well, QQ, JJ, and TT might all look quite similar in their winning chances to you. If you were going to fold 10% of the time (say) with these hands, you might want to fold each of them 10% instead of never the Qs and Js and sometimes the Ts. This would let you base your decision on other factors, like whether or not his hand is trembling and how much time he spent thinking before he bet, which are probably going to be more highly correlated with whether or not he has trip 8s then is your own hand strength.

-Eric

[elindauer]

[ QUOTE ]
You say you want precision, but what you are trying to do is measure something with a ruler and give an answer in 1000ths of an inch.

[/ QUOTE ]

And I would say that you have a ruler available, and are choosing to ignore it, prefering to guesstimate your answer in yards.

I think this conversation reduces to a difference of opinion on how precise we can be, and whether or not it is worth trying. I certainly agree that being more precise is hard. I don't agree that it can't be worth done, or that it's not worth trying.

If you want to continue, let's switch to some other part of this thread where the specific merits of the system are being discussed.

-Eric

[elindauer]

[ QUOTE ]
Game theory comes into play in bluffing decisions, not in calling ones. You are not getting any edge by calling 90% of the time and folding 10% randomly.

[/ QUOTE ]

This just isn't accurate mathematically. Here's a simple example to prove the case:

You are playing a game where you and your opponents both flip coins. You both build an initial pot, and he acts first. His options are to check or bet 1/2 the pot. Your options are then to either call his bet, or fold. If he checks, you check. No betting or raising in this game for you. Heads beats tails.

How do you play? When you have the nuts, you always call of course. What about tails? Should you ever call with tails? You seem to argue that we must either always call, or always fold, that calling cannot be correct with game theory. This isn't the best answer though, and here's why:

if we always fold: our opponent will now always bet. He wins the pot 1/2 the time because you are "dealt" tails. The other half, he chops half the time and loses the pot half the time. He takes down 5/8 (62.5%) of every pot.

He has a lot of advantages though, he's probably entitled to a profit. Maybe this is the best we can do... let's look at always calling:

if you always call, he never bets tails. So, half the time he is dealt tails, and he chops the pot half of those times because you also get tails. The other half, he is dealt heads, and he bets the pot. You always call, so he wins 1.5x the pot 1/2 the time, 1/2 the pot the other half (a confusing sentence, but I think you'll see what I mean if you work it out). Results:

1/2 ev (tails) + 1/2 ev (heads) = dealt tails --> 1/2 (win half the pot --> 1/2 * 1/2 the time --> 1/2) + dealt heads --> 1/2 (win pot + your call --> 1.5 * when you are dealt tails --> 1/2 + chop the pot --> 1/2 * you are dealt heads --> 1/2) = 5/8, or 62.5% of the pot.


Sounds familiar. Maybe he just has an edge, and the rules give him 62.5% equity in this pot. Wrong. We can improve our results by using game theory to handle our calling frequency with tails.


When our opponent is trying to decide whether or not to bluff with tails, our strategy is critical. If we always call with tails, his decision is easy. Don't bluff. If we never call with tails, our decision is also easy, always bluff. But if we sometimes call, and if he can't predict when, then he has a harder decision. Our ideal calling frequency would be the one where it didn't matter whether or not he bluffed or checked when he got tails.

I'll spare you the math and just tell you that this calling frequency is 50%. How do are our results now?


if he chooses to bluff tails...

25% we both get heads, he bets we call. we win 1/4 pot
25% he gets tails, bluffs, and we call with heads. 1.5 pot for us.
12.5% he gets heads, bets, we call with tails. we lose .5 pot
12.5% he gets heads, bets, we fold tails. 0
12.5% he gets tails, bluffs, we call with tails and chop. .25 pot
12.5% he gets tails, bluffs, we fold tails. 0

Add it all up, an answer that is just slightly better than the 3/8 we expected to win by always calling with tails or always folding tails...

3/8 + 1/32

Since his bluffs are 0 EV, you get the same answer if he never bluffs tails, or if he bluffs with some mixed strategy.

All we have to assume is that our opponent is observant enough to adjust to what we are doing, and a mixed strategy for calling decisions becomes correct in this game. The same is true in poker.

good luck.
Eric

[elindauer]

hi w_alloy,

you make a good and true point. You can sometimes, perhaps even often, balance your strategy by using your cards to do the randomization for you.

Very insightful. Others have said this as well though, and I've explained why this is part of the answer, but isn't enough. In high limit games, we simply are forced to face off with experts who are capable of adjusting to our play, so we must go further in many situations. To sum up, these are:

- when your hand ranges don't happen to line up well with percentages you want to fold / call / raise in the situation
- when many hands have similar odds of winning against what your opponent is representing, so that they can be essentially chunked together as 1 hand

Sadly, these cases are very common in heads up pots, and heads up pots dominate the action in high limit games. Therefore, we need to look at this stuff to better handle these critical and common decisions.

Case in point: there's a thread right now with this action... you steal raise. Big blind calls. Flop J55. He bets. What do you do? Without a priori knowledge of what range he will donkbet, and recognizing that this range may well depend on how we react to his bets, the only starting point for this discussion is, in my opinion, a game theory discussion about how often we should call, fold, and raise. Then we can look at hand ranges, see which ones are similar in value, and start chopping it up among the hands. What you do depends greatly on your steal percentage, after all. Some of the hands right on the border are going to be so similar in value that we may decide to split calls and folds between them, to give ourselves some room to take into account our current table image, what the opponent has been doing the last few hands, etc. AK / AQ comes to mind here, as a good spot for treating to hands similarly to leave room for our expert judgment.

-Eric

[elindauer]

I like this notation. Another poster suggested something similar in private. I support this system 100%, and will start using it myself immediately.

thanks,
Eric

[elindauer]

Hi brick,

I think your posts shows a common use for mixed strategies, the game against well known opposition. Mixing up your preflop play, and trying to get a feel for how often to do this, is a noble endeavor.

In short, I think 10% sounds good. I don't want to get too much into the particulars though, as this kind of discussion really belongs in a different thread.

good luck.
eric

[DeeJ]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
It's absolutely never a correct strategy to call X% and fold Y% for any given opponent, it's either always call or always fold or you are [censored] either way.

[/ QUOTE ]

This is not my understanding of game theory (or practical poker). You are saying that one should play more predictably? (as opposed to solidly?)

I think when it gets very shorthanded and there's more aggression and bluffs this is more relevant. Full tables do play more by what you hold, but what is often important is what your opponents think you hold (which table image, shania, meta game history) & plays a part in determining the optimum frequency of your decisions. If a certain villain has been bluffing at you, you will call more. That's a judgement more based on game theory, than a precise hand holding.

Corollary - if villain to your left spots that you 'always fold' in a certain situation, (eg when Ace is on the turn, you check) he then bets into you and you can't beat a pair of aces, he'll do this to you more often h/u because the only time you'll defend is when you have at least a pair of Aces yourself, which is <50% of the time.

If you're playing people who don't know you and you don't know them, sure, play optimal solid poker. But even that means you might be bluffing sometimes (X% rather than predictably) to extract the max, against certain players.

Dan Harrington also says he mixes up his play in NL to avoid giving too much information about his hand holdings, and uses approximate percentages to do stuff at random.

[/ QUOTE ]

Game theory comes into play in bluffing decisions, not in calling ones. You are not getting any edge by calling 90% of the time and folding 10% randomly.

[/ QUOTE ]

Eric posted a good response to this, but I'll call David Sklansky to my aid - Theory Of Poker, p188, Using Game Theory to Call Possible Bluffs. He concludes that you still need sound judgement, which is more or less what I was saying. Obviously if you have a read or other clue as to which is the more profitable action, you can and should go with that. Sometimes you will need to call, with a less than ideal hand - infrequently - to keep the bluffer 'honest'.

[DrSavage]

[ QUOTE ]

I'll spare you the math and just tell you that this calling frequency is 50%. How do are our results now?


[/ QUOTE ]

Please don't spare me the math, I can handle it.

Unless i'm severely mistaken in the calculation, our EV for this game is EV = -0.25*POT*(-0.5 x -0.5 y +x*y), where x is probability of him bluffing tails and y is probability of us calling with tails. You are correct in a sense that:

1) If we set y at 0.5 our EV is set at -1/16 POT no matter what his bluffing frequency is.
2) If we choose any number other than 0.5 and he knows what this number is our EV is -1/16 POT - 1/8*abs (0.5 - y) POT, also note that the optimal strategy for our opponent in this case would be to always bet tails if y is < 0.5 and always fold tails if y > 0.5
3) However, the same is true another way. Our opponent can also lock the profit at 1/16 POT by always bluffing 50% , and once he's done that it's irrelevant what we do, and we might as well always call or always fold if that pleases us, as long as he's locked at 50% we don't gain nothing by flipping a coin or choosing to call or fold in advance. That was the reasoning for my original statement. Having actually done the math, I now agree that it's not really correct the way I phrased it .
4) Back to poker and KQ example, i still say that I wouldn't want to be flipping coins with KQ here. There are many hands I could be betting on the river here, some just pure bluffs and some a top set. It seems like all I have to do is at least call with a certain top % of hands (let's say I call with AK, AA and sets and fold the rest) and have the % of me calling sort themselves out.

[elindauer]

Very nice post DrSavage. Responses below.

[ QUOTE ]
[ QUOTE ]

I'll spare you the math and just tell you that this calling frequency is 50%. How do are our results now?


[/ QUOTE ]

Please don't spare me the math, I can handle it.


[/ QUOTE ]

I didn't think it was relevent. I just wanted to show that there was some calling percentage that was better than 100% or 0%. Obviously, you have the math skills to figure out the optimal answer for yourself. Well done.

[ QUOTE ]
Unless i'm severely mistaken in the calculation, our EV for this game is EV = -0.25*POT*(-0.5 x -0.5 y +x*y), where x is probability of him bluffing tails and y is probability of us calling with tails. You are correct in a sense that:

1) If we set y at 0.5 our EV is set at -1/16 POT no matter what his bluffing frequency is.
2) If we choose any number other than 0.5 and he knows what this number is our EV is -1/16 POT - 1/8*abs (0.5 - y) POT, also note that the optimal strategy for our opponent in this case would be to always bet tails if y is < 0.5 and always fold tails if y > 0.5
3) However, the same is true another way. Our opponent can also lock the profit at 1/16 POT by always bluffing 50% , and once he's done that it's irrelevant what we do, and we might as well always call or always fold if that pleases us, as long as he's locked at 50% we don't gain nothing by flipping a coin or choosing to call or fold in advance. That was the reasoning for my original statement. Having actually done the math, I now agree that it's not really correct the way I phrased it .


[/ QUOTE ]

You got it. We can use game theory on his side to see that he should bluff with a frequency as well, and that frequency is not 100% or 0%, but 50%. It works both ways. Like in poker. Every decision we make can be attacked with game theory.

[ QUOTE ]

4) Back to poker and KQ example, i still say that I wouldn't want to be flipping coins with KQ here. There are many hands I could be betting on the river here, some just pure bluffs and some a top set. It seems like all I have to do is at least call with a certain top % of hands (let's say I call with AK, AA and sets and fold the rest) and have the % of me calling sort themselves out.

[/ QUOTE ]

Totally reasonable argument which I've discussed now many times in other spots in this thread. Pat yourself on the back for recognizing that you can go a long ways in your randomization by using your own card strength to make the decisions. That's how we all got this far.

There are other times when you can't do this, or at least, it's not nearly as effective. For those times, we need game theory, and they tend to be more and more common as the limits go up. That is, they tend to crop up most in heads up pots where our opponents are either unknown or good enough to adjust to what we are doing. Playing 100/200? Get ready to see this a lot.

nice job.
-Eric

[elindauer]

So, we've concluded that in the mock coin flipping game, the optimal basic strategy is for the first player to act to always bet heads, and bluff with tails 50% of the time. The second player should now call 50% of the time. If either player uses this strategy, it doesn't matter what the other guy does.

We might have the good fortune to play this game against someone who doesn't know this though, right? Like in poker, not everyone knows the perfect strategy. But isn't it critical for us to understand what the basic strategy is before we go off trying to outplay our opponent?

This is the critical step that I think we are often times missing on these boards. We know that our opponent probably isn't playing a game-theory perfect game. So we know that it probably does matter what we do. So we are intent on finding out what that thing must be, and we feel that the only possible answer is fold, call, or raise. There must be 1 answer and it must be right.

We need to accept that many times we cannot find this answer. Look for the posts that put you in a tough, common, heads up situation. I steal raise, he donk bets, what now? I raise, he 3-bets and leads xyz flop. What now? They rarely get many responses unless very detailed reads are given. These posts are perfect for working out the basic game theory answer that we all should know cold for virtually every possible heads up blind steal line, ie

How often do you play when he donk bets? When he check-raises? How often do you cap preflop when he 3-bets? How often do you play when he 3-bets and leads?

Similar ideas for the turn and river. Think that's a lot of stuff to know. Hell yeah it is. It would take days or maybe weeks to go through all the math. But imagine the confidence you'd have stealing the blinds at that point. You'd have your game theory options all nailed down, and you'd know you could not be beaten playing that way. Then you could adjust from there any time you felt you knew your opponent well. And with the game theory basic strategy all hammered out, you'd have no problem knowing what it meant to make a small adjustment, or a big one, based on the tendencies of your opponents. You'd know just exactly the hands to change up with, and how often to do it.

Rather then swimming randomly through a sea of choices, you could conceivably come up with precise ways to handle virtually every hand, and certainly have enough general understanding to play in an unbeatable way virtually all the time.

Anybody interested in that? Think that would be useful for playing 100/200 heads up?

good luck.
eric

[elindauer]

I think you may be unwilling to acknowledge that you may be wrong here, DrSavage. Try to open your mind as you read the thoughts below...

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Are you sure? How about if I describe the following opponent: she is smarter than you. she is able to judge whether or not you are going to think she will bluff. she recognizes the kinds of boards you think are "unbluffable", and the kind you don't. How should you decide whether or not to call? Do you want to go on trying to outguess her, when you know she is better than you?


[/ QUOTE ]

I'm sure as hell am not flipping a coin to see if i should call or not.


[/ QUOTE ]

So, facing an opponent who you know to have superior judgment, who is able to outguess you, you are going to stubbornly refuse to randomize your play and continue to try to feebly outguess her?

I admire your determination, but not your utter disdain for money, or your refusal to even acknowledge that your own judgment is not always the best choice available.

[ QUOTE ]

[ QUOTE ]

You've made a few big river laydowns today. You don't know if she thinks you're playing weak today, or if she'll recognize that you're just playing the opponent. You get check-raised by her in a spot where she usually has you beat, but it's close. Call or fold?


[/ QUOTE ]

Call if i think I can be bluffed here a larger percentage of the time than my pot odds, fold otherwise.


[/ QUOTE ]

The whole point is that you can't possibly know this. How in the world are you actually going to make this decision??

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It seems to me that you somehow think that if someone will bluff me 10% of the time amd the pot is offering me 9 to 1 i should call him 90% and fold 10%. That's just wrong.

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Are you sure? I believe that if calling and folding are both 0 EV, then it doesn't matter what we do. In that case, wouldn't it make sense to call at the game theory optimal strategy, so that we minimize our opponents profits just in case our estimate of the odds is wrong? Surely you can accept that if we estimate the odds at 9:1 against, there is some room for doubt in either direction.

In fact, this is the best way to go and is exactly what you should do, bankroll variance considerations aside.

If you disagree, please give more logic then "this is just wrong", as your simply saying so doesn't make it true.

good luck.
eric

[DrSavage]

[ QUOTE ]
I think you may be unwilling to acknowledge that you may be wrong here, DrSavage. Try to open your mind as you read the thoughts below...


[/ QUOTE ]

I've already acknowledged that I was not correct in my wording in my last post.
[ QUOTE ]

Are you sure? How about if I describe the following opponent: she is smarter than you. she is able to judge whether or not you are going to think she will bluff. she recognizes the kinds of boards you think are "unbluffable", and the kind you don't. How should you decide whether or not to call? Do you want to go on trying to outguess her, when you know she is better than you?
So, facing an opponent who you know to have superior judgment, who is able to outguess you, you are going to stubbornly refuse to randomize your play and continue to try to feebly outguess her?
I admire your determination, but not your utter disdain for money, or your refusal to even acknowledge that your own judgment is not always the best choice available.


[/ QUOTE ]

Why do you always refer to the opponent as "she" ? I'm pretty sure males play poker too. This is pure discrimination.

In this particular situation my decision would be based on strength of my hand. We have discussed this already.



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It seems to me that you somehow think that if someone will bluff me 10% of the time amd the pot is offering me 9 to 1 i should call him 90% and fold 10%. That's just wrong.

[/ QUOTE ]
Are you sure? I believe that if calling and folding are both 0 EV, then it doesn't matter what we do. In that case, wouldn't it make sense to call at the game theory optimal strategy, so that we minimize our opponents profits just in case our estimate of the odds is wrong? Surely you can accept that if we estimate the odds at 9:1 against, there is some room for doubt in either direction.


[/ QUOTE ]

No, I'm not sure, I've admitted that in the previous opt already after having done the math. I would still make the decision based on the strength of my own hand. There are lots and lots of hands I would be betting here and quite a few I'd be calling a check/raise with.

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In fact, this is the best way to go and is exactly what you should do, bankroll variance considerations aside.


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I wouldn't fold top set here. I would fold queen high. Everything in between would go one way or the other based on my personal history against this opponent.

[elindauer]

[ QUOTE ]
I've already acknowledged that I was not correct in my wording in my last post.

[/ QUOTE ]

ok, perhaps I misread the strength of your convictions in your prior post. Apologies.


[ QUOTE ]
Why do you always refer to the opponent as "she" ? I'm pretty sure males play poker too. This is pure discrimination.

[/ QUOTE ]

I'm going to give you the benefit of the doubt and assume you are joking here. Just in case... would you have said anything if I'd used "he" every time? Think about it, and you may begin to understand how the common use of "he" encourages women to feel that a male is the standard, and women are somehow exceptions that must be explained. I'm just doing my little part to balance the usage of "he" and "she" as gender-neutral adjectives in our society.


On everything else, I can see that I won't convince you, and I'm afraid we've reached an impasse.

good luck.
Eric

[2ndGoat]

My thoughts... without reading this whole thread.

1) I think people have considered this before under the label of "metagame." "It may generally be best to fold here, but if you've been folding a lot you need to call." That's a rough approximation of "You need to fold 80% of the time here."
2) I believe most serious computer simulations operate this way. My biggest compliment to the computer simulations I've studied (briefly) is their ability to mix up decisions and not do the same thing in the same situation every time.
3) My concern is that using this notation would lead to cop outs. Say there's is a {100,0,0] answer and we just can't deduce it, so we guess {70,30,0}. That's a lot different than {70,30,0} being correct because of game theory decision-balancing concerns.
4) This feels like moving from newtonian to quantum physics.

2nd

[2ndGoat]

[ QUOTE ]
Think that's a lot of stuff to know. Hell yeah it is. It would take days or maybe weeks to go through all the math. But imagine the confidence you'd have stealing the blinds at that point.


[/ QUOTE ]

I've done this in a spot or two before, figuring something out for a specific hand/flop/opponent. It's useful, but it's not speedy. Perhaps some kind of spreadsheet is in order. hm...

2nd