Whats in a Range

[LearnedfromTV]

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The game-theoretic value is in the appearance of randomized play. A lot of times you don't have to randomize to have your play appear random.

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i think what your saying is absurd... isn't 2+2 the place where we have all decided that having a set with different variables should be played in different ways? i mean maybe having an Ace on board really should differ the type of play you make. i believe what MLG is trying to say is that for ever specific situation, there is a correct percentile way of playing the hand. the question of if it is possible for a human to do this is another matter.

to imply that your goal is just to appear random is not logical. if you just appear random, but are not accually random, a perfect player could beat you in those situations, a good player would be able to take advantage of the fact that you appear random, but are not atually random. randomness to some extent is what gives you the ability to make money when playing other good players.


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An attempted restatement of my point:

We often talk about game theoretic randomization as though it is an attempt to achieve an ideal ratio of different plays in a given situation, like "flopping a set vs. preflop raiser." There is a big difference between theory and practice, however. In theory, if we encounter a specific situation 100 times, we want to do x 60 times, y 20 times, and z 20 times. In practice, every one of those 100 situations is different, and there are often situational considerations that push you toward x, y, or z. Also, in practice, situations come up one at a time, not as part of some theoretical bundle of similar situations.

Another way to think about this is that any particular hand fits into several boxes within which you could choose to randomize your action. "Flopping a set vs. a preflop raiser" could also be "flopping a set on an ace-high board" or "flopping a set on a two-tone straight board" or "flopping bottom set with deep stacks versus a tight UTG raiser on an AQ5 board" or "flopping a set when I'm perceived as a maniac" or "flopping a strong hand when i've just checkraised two weak hands" or "flopping a strong hand versus a guy I know overplays medium strength hands when bet into."

When we say there are situational factors involved in decision-making, what we are really saying is that any given hand falls into several of these type of categories. In theory, you would want to randomize within every category. In practice, one or two of these considerations will usually dominate in a particular hand.

Even most observant players only go as far as to remember your actions with respect to the most straightforward of these categories. So you can check-raise with a set for a particular reason but the only mental note some observant players will make is "he checkraised a set."

Remember that the game theory goal when you randomize is to create a future situation in which an observant opponent will get your hand range wrong. An observant but not-too-sophisticated opponent may only remember that you checkraised a set 1 in 3 times, which is enough to confuse him when you get in a hand with him where you may or may not have a set. The better your opponents are at remembering details, the more likely it is they will properly evaluate the reasons you made certain plays in the past (that is, the less random your play will look to them). They will more accurately evaluate your hand range in a given situation b/c they understand better which pieces of other plays were related to your play in the current hand. Against the best of these, you do need 'pure' randomization to achieve the game-theoretic goal of masking your range. But bear in mind that the goal is to mask your range, not to be random for the sake of being random.

Finally, even though masking your range is a goal, it is not the only goal. You have to make decisions one at a time, and masking your range for the future by doing something other than what you expect to earn the greatest profit in a particular hand is only worthwile if you can expect to get back that profit and then some later. This is why people often focus on randomizing between options that have roughly equivalent EV.

[Foucault]

Excellent post, Learned. The bit about every hand falling into multiple situation 'boxes' is gold. Only one thing I would quibble with:

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The game theory goal when you randomize is to create a future situation in which an observant opponent will get your hand range wrong.

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I don't think it is just about future situations. If your range in the hand you are currently playing does not differ from the range on which your opponent puts you, then your play is 0 EV at best. The range he assigns you will be dependent on other hands he has seen you play and he knows you have seen him play, and you may want to do something in this hand that will help you create deception about your range in a future situation, but even if you were going to play exactly one hand at this table and against this opponent, there would still need to be a 'gap' between your actual range and the range on which you think Villain will put you.

[LearnedfromTV]

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Excellent post, Learned. The bit about every hand falling into multiple situation 'boxes' is gold. Only one thing I would quibble with:

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The game theory goal when you randomize is to create a future situation in which an observant opponent will get your hand range wrong.

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I don't think it is just about future situations. If your range in the hand you are currently playing does not differ from the range on which your opponent puts you, then your play is 0 EV at best. The range he assigns you will be dependent on other hands he has seen you play and he knows you have seen him play, and you may want to do something in this hand that will help you create deception about your range in a future situation, but even if you were going to play exactly one hand at this table and against this opponent, there would still need to be a 'gap' between your actual range and the range on which you think Villain will put you.

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I agree with this. I worded that poorly. With that line I was referring to opponents who are not in the current hand but with whom you will be involved in future hands.

Of course the other (related) goal is to create a gap in current hand between perceived and actual range, with perceived range built up from past situations in which you took into account what effect your actions might have on a potential future (now current) hand.

Or more properly, since in the current hand you have a specific hand rather than a range, the goal is to maximize your EV on that specific hand given your opponent's perception of your range and your (we hope more accurate) perception of his.

[MLG]

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so, is there any starting strategy that is more correct than any other? short of folding the nuts throught 20th nuts, and only raising hands that don't play on the board, can't any realistic starting strategy be viable assuming one is able to adjust to his/her oponent?


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very nice, and an important concept to get at. The answer is, theoretically speaking, there is a strategy which you oculd employ (if anybody could figure it out) that would be unexploitable by your opponent. That is, you would be doing things with a frequency that would make the EV of all your opponents decisions exactly the same. If you and your opponent both played perfectly then this would be the optimal strategy for you to employ. However, nobody plays perfectly and everybody is exploitable to some degree. So, the result is we all try to adjust our frequencies to take exploit our opponents. If our opponents were static, never changing, individuals then there would be a frequency mix that we could find that would exploit him to the max. However, such a person doesnt exist so we go on playing and adjusting to our opponents, and they go on playing and adjusting to us, and whoever adjusts the best wins the most money.

[MLG]

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Check-raising is not 'best'. The combination of 70% check-raises and 30% leading out is 'best'. It sounds like this is what MLG is saying. How can this be the case? Because your opponents are always playing against a range of possible hands you could have, and you gain EV every time they either incorrectly estimate your range or incorrectly play their hand against a correctly estimated range. The latter occurs quite often at lower buy-in tournaments, which is why it is less important to use mixed strategies at those levels. Your opponents aren't likely to estimate your range correctly (though they are putting you on a range, even if they don't think they are), and they often misplay their hands even when their estimation is correct (drawing with improper odds, for instance). You ought to be able to exploit these mistakes without mixing up your play too often.


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Against players who do think you are quite correct, that mixing up your play is usually pointless. Against a passive calling station, you always value bet and you never bluff and you basically never go for a CR because they rarely bet. Against a thinking player, however, one who can say to himself, my opponent may have this or may have that, then it becomes harder to exploit them. That's the point. If they think I have a draw 90% of the time I lead, and a set 10% of the time, when in fact my range is closer to 33% a hand that beats top pair, 33% a monster draw, 33% a bluff then if they raise with pretty much anything they are making a mistake. I have created a range for myself, that is very difficult for an opponent to exploit and one that.

[LearnedfromTV]

Thinking about doing some research on tendencies (mine and opponents') along the lines of the discussion in this thread. I am brand new to pokertracker (just got it two days ago). Are the filters sophisticated enough for this sort of work on postflop play?

Like, I assume I can filter down to all the hands where I raise in UTG - UTG+2. Can I then sort by # of callers (setting aside times reraised for the time being) and figure out with what range I pot the flop headsup, in three way pots, etc. Or can I search for headsup OOP turn pots where I check-called the flop? Etc.

This kind of research of course runs the risk of having too many artificial controls and ignoring key variables (like flop texture) and the risk of limited sample size the more a situation is narrowed down, but it could be somewhat interesting. One of the main things that frustrates me in thinking about this stuff in theory is that our postflop examples leave out a ton of cases (our range is never really 33/33/33 set/monster draw/bluff, it's more like 22/18/16/11/6/5/5/4/2/2/1/1 or something.)

So the question is, can pokertracker do stuff like this and has anyone has tried it?

Edit: And is there a way to sort by bet size in relation to the pot? Narrow it down to a certain flop situation and then separate the times I check from the times I bet 1/2 pot from the times I bet 3/4-full pot.

[Cactus Jack]

Thank you, all, very much for this thread. There's probably more in here to study than 90% of the books on the shelves.

Recently I ran across this. (See link below.) This is possibly a simpleton question, but does it have anything at all to do with the discussion at hand? I'm trying really hard to get an understanding of game theory and how it applies to the games I play.

http://cardsspeak.servebeer.com/arch...s_theorem.html

If you guys can bear with my dumb questions, I may be able to work this out somewhat in my mind.

Again, really appreciate the thought that went into this thread.

CJ

[Flopzilla]

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Now, in some situations in order to make a decision we must consider what range our opponents put us on

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I have found that, for the most part, the average online player does not consider the cards I may be holding, only his/her own.

I believe the abilty to put an opponent on a range of hands, the use of position, hand selection, and the calculating/use of pot odds are the keys of relatively few good online players.

[DeezNeez8]

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The Actual Point
If an opponent can figure out your specific range when you bet, he can call with perfect frequency to maximize his positive outcomes.

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I have been toying around with an idea for a while and i think this thread is a great place to present it. Instead of a typical UTG raising standard of AQ+, 99+, i have opened up my UTG raising standard to AQ+, 22+, 45s-89s.

I have done this because of the "He raised UTG!!!!" reaction most opponents have, putting you on at least AQ and probably TT+. This is not an easy tendancy for my opponents to discover, due to the fact that i play the rest of the early positions with a typical tightie range (i don't feel like people regard UTG+1 and UTG+2 in the same way they fear UTG). As soon as i show down a pair below nines or any of the sooooted connectors after an UTG raise at a particular table, i will then tighten my UTG standards back to AK, TT+ and just wait to get repopped by some donk thinking his A10o or KJs is good because he has a "read".

I don't know if this is a strategy many imploy, but i think it falls along what MLG was saying about if your opponents assume your UTG range to be AQ+ 99+, and that's what your range really is, you are playing at a disadvantage.

Thoughts?

[Cablelessray]

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Remember that the game theory goal when you randomize is to create a future situation in which an observant opponent will get your hand range wrong. An observant but not-too-sophisticated opponent may only remember that you checkraised a set 1 in 3 times, which is enough to confuse him when you get in a hand with him where you may or may not have a set. The better your opponents are at remembering details, the more likely it is they will properly evaluate the reasons you made certain plays in the past (that is, the less random your play will look to them). They will more accurately evaluate your hand range in a given situation b/c they understand better which pieces of other plays were related to your play in the current hand. Against the best of these, you do need 'pure' randomization to achieve the game-theoretic goal of masking your range. But bear in mind that the goal is to mask your range, not to be random for the sake of being random.

Finally, even though masking your range is a goal, it is not the only goal. You have to make decisions one at a time, and masking your range for the future by doing something other than what you expect to earn the greatest profit in a particular hand is only worthwile if you can expect to get back that profit and then some later. This is why people often focus on randomizing between options that have roughly equivalent EV.

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i believe MLG's logic implies that one can forget about future hands. there will be a correct decision for the situation, taking into consideration your oponents and the past hands you have played with them. setting yourself up for some type of future hand implies you can't just adjust to the way you played the last hand. the adjustments you can make give you the edge when you realize that you can maximize your oponents missread on your range by just rememebring what you have done, and counter analizing instead of premeptively mading a worse choice to gain confusion later.

the problem with the theory we are going into is that each situation is unique... we are trying to do the impossible... make decisions that only come up one in a million hands (yes sometimes you guys can be that specific), with the EV of if you had played this hand time and time again.