Whats in a Range
 

Perhaps the most fundamental thing we do on this board is put opponents on ranges. When faced with a decision we try and figure out what they might have and make a decision based on how our hand fares against that range. Now, in some situations in order to make a decision we must consider what range our opponents put us on. For example on the river with a good but not great made hand we need to decide whether or not to value bet when first to act. So, the first thing we think about is what hands can our opponent have. The next thing we think about is, well which of those hands will our opponent call us with. Well, what defines what our opponent call us with is the range of hands he puts us on. This isn't really earth shattering. However, many people will say its pointless because Joe Internet doesn't understand ranges. Thats wrong. If Joe Internet calls to much its because he always thinks, hey he might be bluffing, so the range he puts you on is quite quite wide with a high bkuffing percentage. Knowingly or not, all opponents put you on a range, just as you put all your opponents on a range.

So, how do we exploit this situation. How do we make opponents who are putting us on a range make a mistake? When we bet on the river there are 4 possible outcomes (ignoring raising for the time being).

1. We have a better hand than villain and villain folds.
2. We have a better hand than villain and villain calls.
3. We have a worse hand than villain and villain folds.
4. We have a worse hand than villain and villain calls.

2 and 3 are obviously good for us, while 1 and 4 are obviously bad.

Simple. So, lets take an extreme example. A villain who will never ever ever call a reasonable (1/2 pot) bet on the river unless he has the mortal nuts. When you bet on the river he always puts you on the nuts. Likewise, if you check he will never bet anything short of the nuts. How do we deal with this situation? Seems simple, bluff a lot, but don't value bet medium strength hands right? Wrong. Every bet you make is a bluff, and they all have a very high chance of working. You should bet every hand on the river except for the 2nd nuts (because that is the only hand that cannot get a better hand to fold). Clearly Mr. Tighty McNuts is easy to exploit, thats not the point, the point is understanding why. He is easy to exploit, because the range he puts us on is so comically tight that he allows us to have a positive outcome for us (3) a rediculously high percentage of the time. Notice that it doesnt matter that the second highest outcome is (1) which is technically a bad outcome for us because we gain so much equity the times he folds. Also notice, that just because its absolutely correct to bet all of our hands doesnt mean we win every hand when we bet (we still lose the times he has the nuts).

Still, nothing ive said is earthshattering untill we begin to generalize away from the comic extreme. Why do we make money, because our range is extremely wide, while Tighty McNuts thinks its extremely tight. On the other extreme a villain who calls with any 2 hands will also be exploitable by value betting with a wider variety of hands than normal because he will call with worse hands, but never bluffing. Even though betting hands like 3rd pair will increase the instances of outcome 4 the increase in outcome 2 more than makes up for it.

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. Tighty McNuts would be profitable if you only bet the 2nd Nuts and the Nuts. It is not his action that makes him bad, but his action in light of your range. So, if a villain think your range is tight in a spot (lets say he thinks you will never bluff) but in fact you are bluffing 5% of the time you are exploiting him even if those bluffs are never called, and you never show them because he is folding too much (or more accurately too large a % of his hands). The key is not what hands get shown down but what range of hands you will bet compared to what range of hands your opponent thinks you will bet. This gets much much much more complex as you add in more and more variables. Even this oversimplified post is pretty muddled, but its the beginnings of game theory. Use at your own peril.

Re: Whats in a Range
 

I just saw this post. Don't have time to respond right now but think a bump is appropriate.

Re: Whats in a Range
 

[ QUOTE ]
Perhaps the most fundamental thing we do on this board is put opponents on ranges. .......Even this oversimplified post is pretty muddled, but its the beginnings of game theory. Use at your own peril.

[/ QUOTE ]

I've been thinking about these very things over the last couple of days, THANK YOU for for the post!!!

What I hear the better players talk about when making decisions, has got to be applied game theory.

Put them on a range, where do we fare against that range, what price am I getting, throw in a read and make the decision....

Re: Whats in a Range
 

wow how did this get lost for a month?

nice post.

Re: Whats in a Range
 

[ QUOTE ]
wow how did this get lost for a month?

nice post.

[/ QUOTE ]
The answer . . . . noise!!!!!!!!!!!!

Thankfully Foucault included this in his digest. I'm hoping that with me looking at every post these days for inclusion in the 3-day digest we won't be missing too many good posts.

Re: Whats in a Range
 

[ QUOTE ]
The key is not what hands get shown down but what range of hands you will bet compared to what range of hands your opponent thinks you will bet.

[/ QUOTE ]

Trying to figure this out. It seems important, but my brain hurts. Little help?

Re: Whats in a Range
 

Like MLG said, this is an initial post that will need further discussion to make it worthwhile. After reading this twice I know I need to read it a couple of more times. But I think this post has the potential to be very valuable to most of the forum. Not yet, but with ample discussion perhaps.

Re: Whats in a Range
 

[ QUOTE ]
Like MLG said, this is an initial post that will need further discussion to make it worthwhile. After reading this twice I know I need to read it a couple of more times. But I think this post has the potential to be very valuable to most of the forum. Not yet, but with ample discussion perhaps.

[/ QUOTE ]

I usually pride myself on writing clearly. This post was/is fairly garbled and not particularly clear, which is why i didnt bump it. So yes, this post is gonna need some help to get its ppoint across.

Re: Whats in a Range
 

I don't think it's a clarity thing but more of an incomplete thought. Seems like you slowly move from A-L and then all of a sudden where at Z and done. But I do think a theorem can be extracted with more examples. And who should be the first to expand but you yourself!!!

Re: Whats in a Range
 

I actually had "most underappreciated post of the month" in parentheses after this one in the digest, but chose to delete it because I wanted to be the one to revive it! Oh well, at least it is back. Here's what I was going to say:

I've been thinking about how ranges relate to the Fundamental Theorem of Poker. Sklansky says that we make money any time an opponent plays his hand in a way other than he would if he could see our cards, and conversely that we lose money any time we play our hand in a way other than we would if we could see our opponent's cards.

At least where online poker is concerned, I feel like this is results oriented, in some sense. Suppose Villain raises to 150, I push for 1000, and he calls with 22. If I have AK, then by the FTP, Villain's call is +EV. But I don't really 'have' AK, I 'have' TT-AA, AK. The fact that I turned over AK doesn't change the fact that calling with 22 was bad. Moreover, if Villain were to play like this against me in this same situation 1000 times, he would be in the red at the end of the session, because I'm turning over a dominating hand more often than not.

Now if we're playing live, maybe Villain notes that I always bet with my left hand when I have AK and my right when I have a big pair, and so he confidently and correctly calls. Over 1000 games, Villain could fold when I bet with my right hand, call when I bet with my left, and finish in the black. This tell helps him to determine which hand in my range I have this time I push. But absent such a tell, which is much harder to come by online, calling with 22 in this spot is not profitable for Villain.

I guess this is all pretty elementary so far, but I think it has some interesting implications for what deception means. It's not good enough to fool Villain about which hand I am holding right now; I have to fool him about the range of hands I could be holding when I play in a certain way. If I always and only check-raise sets and flush draws, then Villain is not really making a mistake when he calls with top pair and I have a set, since I will have a flush draw much more often.

This is why changing gears and being aware of table dynamics is important against thinking players. If you had a flush draw the last time you check-raised Villain, you may need to lead out with it the next time.

Often, however, you won't have enough history with a particular Villain to set up this kind of play. So where else can you get information about what range Villain will assign to you? For one thing, you can watch how he plays his hands. If he never raises a draw, he probably won't put you on a draw when you raise. If he slow-plays his sets, he won't expect you to have a set when you push.

The chat box can be helpful, too. Table coaches, in particular, reveal a lot about how they expect you to play through their berating of others. "All in with a draw? Donkey." The semi-bluff has got to be a substantial portion of your pushing range against this guy.

Finally, you can show uncalled hands if you intend to play differently in the future and you think Villain is alert enough for this to matter.

Sorry if this is a bit rambling, it's just what re-reading MLG's post got me thinking about. The bottom line is that you profit by deceiving your opponents about the range of hands you could have at any time, not just by playing the hand you are holding as though it were something else.

Re: Whats in a Range
 

[ QUOTE ]
The bottom line is that you profit by deceiving your opponents about the range of hands you could have at any time, not just by playing the hand you are holding as though it were something else.

[/ QUOTE ]

Well. I think thats only the case when you're playing good players who will be able to correctly put you on a range if you're not being deceptive. its why game theory becomes more important when your opponents don't make as many awful mistakes.

against some players, like tightie mcnuts, and the loosie, you don't need much deception or game theory, you just need to play in a way that exploits their mistakes to their fullest. these people are putting you on some bizzare range b/c thats the way they think, not b/c they've observed your play and have a good line on you. these players are usually horrible at adjusting too, so most times you can get away with exploiting their mistakes over and over before they begin to catch on and adjust.

So, I think, the bottom line is that you need to get good at spotting which players put you on horribly innacurate ranges (either WAY to big, or WAY to small) and then exploit the mistake as much as possible. the toughest part is figuring out how long it takes them to start adjusting, and then figuring out just how much they adjust.

Re: Whats in a Range
 

[ QUOTE ]
I think thats only the case when you're playing good players who will be able to correctly put you on a range if you're not being deceptive. its why game theory becomes more important when your opponents don't make as many awful mistakes.

[/ QUOTE ]

I see what you're saying, but in a theoretical sense, bad players are still deceived about your range, it just doesn't take much work on your part. But you make money because they make a mistake against your range, not against the hand you happen to have, as the FTP would have it.

Re: Whats in a Range
 

[ QUOTE ]
So where else can you get information about what range Villain will assign to you? For one thing, you can watch how he plays his hands. If he never raises a draw, he probably won't put you on a draw when you raise. If he slow-plays his sets, he won't expect you to have a set when you push.

[/ QUOTE ]

Nice.

Very true, but not often mentioned.

Later,
Che

Re: Whats in a Range
 

it's been awhile but isn't this what the theory of poker is?

Post deleted by Mat Sklansky
 

Re: Whats in a Range
 

Thats really not true...

Sunday afternoons aren't the norm-- it just happens to be the day for tournaments.

Re: Whats in a Range
 

Great post, this is the most common mistake I see players make nowadays.

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
So where else can you get information about what range Villain will assign to you? For one thing, you can watch how he plays his hands. If he never raises a draw, he probably won't put you on a draw when you raise. If he slow-plays his sets, he won't expect you to have a set when you push.

[/ QUOTE ]

Nice.

Very true, but not often mentioned.

Later,
Che

[/ QUOTE ]

i think this is the most insightful part of the whole piece. it makes complete sense. i'm embarrassed to say that i'm guilty of this line of reasoning. any time i'm faced with a tough call, and i have no info on the player, i automatically start thinking 'well, if i were in his position what would i have rasied with?'

that's obviously the wrong way to go about it, becuase he isn't me, but it seems like the most logical starting point in the analysis. i try to avoid this 'trap', but i think the average online player doesn't even realize the 'trap' exists.

your opponent will most likely assign HIS range to your hand in any given situation. a tight player doesn't just call less because he needs to have good cards, he calls less because he projects his line of tight thinking onto his opponent.

that feels a little ground breaking to me, because i never really thought of it. very good post. maybe post of the month material.

Re: Whats in a Range
 

For me, this has the most impact when either calling late position raises in the small blind or when raising from late and getting a blind caller.

Re: Whats in a Range
 

Foucault got at a lot of what I was getting at (in terms of my problem with the FTOP) and about what deception, and hand reading means.

My other point is how you create your own ranges. When you put somebody on a range its a static proposition. You are saying at this time there is a percentage chane of A, a percentage chance of B, and a percentage chance of C. When you are creating your own ranges you need to be thinking actively, not statically. You cant only think I have a set/flush draw how should I play it, you need to think I have a set/flush draw, how frequently should I bet/CR/checkcall with it in order to create ranges that deceive my opponent. Quite frequently then the answer to these questions is not you should to A, B or C, but rather you should do A X%, B Y% and C Z%, at least when you are playing against players who think about what you are holding.

Re: Whats in a Range
 

[ QUOTE ]
You cant only think I have a set/flush draw how should I play it, you need to think I have a set/flush draw, how frequently should I bet/CR/checkcall with it in order to create ranges that deceive my opponent. Quite frequently then the answer to these questions is not you should to A, B or C, but rather you should do A X%, B Y% and C Z%, at least when you are playing against players who think about what you are holding.

[/ QUOTE ]

Good point. Harrington usually gives advice in these terms, at least when discussing pre-flop play, yet we see so many one-word responses on this board to "Push" or "Fold".

Question for you: it's generally thought that there is no need mix up your play online as you so rarely encounter the same players or sit long enough with them at the same table. But as you point out in your original post, even those who don't think about it in these terms are always putting us on ranges and playing against a range of hands we could be holding.

So suppose I wanted to combine your advice and Harrington's in a particular situation and use the second hand of my watch to check-raise 70% of the time and lead out 30% of the time. But I've just been moved to a new table, and it's going to break up soon. Since check-raising is presumably the 'better' option, should I just go ahead and check-raise? Or should I actually check the second hand of my watch and randomize my play, even though I'm unlikely to be in the same situation with the same players again?

I guess what I'm asking is, if a tree falls and no one is around to hear it, does it make a sound?

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
You cant only think I have a set/flush draw how should I play it, you need to think I have a set/flush draw, how frequently should I bet/CR/checkcall with it in order to create ranges that deceive my opponent. Quite frequently then the answer to these questions is not you should to A, B or C, but rather you should do A X%, B Y% and C Z%, at least when you are playing against players who think about what you are holding.

[/ QUOTE ]

Good point. Harrington usually gives advice in these terms, at least when discussing pre-flop play, yet we see so many one-word responses on this board to "Push" or "Fold".

Question for you: it's generally thought that there is no need mix up your play online as you so rarely encounter the same players or sit long enough with them at the same table. But as you point out in your original post, even those who don't think about it in these terms are always putting us on ranges and playing against a range of hands we could be holding.

So suppose I wanted to combine your advice and Harrington's in a particular situation and use the second hand of my watch to check-raise 70% of the time and lead out 30% of the time. But I've just been moved to a new table, and it's going to break up soon. Since check-raising is presumably the 'better' option, should I just go ahead and check-raise? Or should I actually check the second hand of my watch and randomize my play, even though I'm unlikely to be in the same situation with the same players again?

I guess what I'm asking is, if a tree falls and no one is around to hear it, does it make a sound?

[/ QUOTE ]

I'm going to say in a situation like this u should always go with the 'better' option. However, of course, if you were at a table that appeared was going to stay together for a while (i.e. a deep stack final table or something) the second hand thing would be the best approach.

I am just a journeyman and really just wanted this question back on the front page so i could get a better answer than i can give.

Re: Whats in a Range
 

[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

[/ QUOTE ]

Yes...but on a hypothetical level i believe Foucault's question remains unanswered.

Re: Whats in a Range
 

On a hypothetical level if one option is clearly "better" you take it. The point is that the majority of situations in which you start with at least a medium sized stack do not involve a specific "better" option. In those situations a mixed strategy is the "best" option.

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

[/ QUOTE ]

One thought on this. I tend to like leading into the raiser with a set but I do play it differently sometimes. I think choosing to mix it up in a particular case should be done for a combination of game-theoretic and opponent-specific reasons.

Meaning - You often are at a table long enough for opponents to notice how you play certain hands. I'd rather have someone see me c-r a set once and lead into the raiser twice, rather than do the same thing three times. But which time I choose to checkraise will often be opponent specific. Say there's an ace on board and I expect someone to threebet push me with TPTK b/c he just saw me checkraise a draw or middle pair against him. Maybe it's a threeway pot and I think that if he doesn't have the ace he'll bet if checked to but fold if bet into. So either way I get the most, this time, and someone else sees me checkraise a set and makes it easier to get the raise next time when I lead into them.

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.

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

[/ QUOTE ]

This is when stacks are deep, right? If stacks are shorter and I flop a set shouldn't I check to the raiser who is semi-short so that I commit him to the pot after he makes a play at it?

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

[/ QUOTE ]

This is when stacks are deep, right? If stacks are shorter and I flop a set shouldn't I check to the raiser who is semi-short so that I commit him to the pot after he makes a play at it?

[/ QUOTE ]

When stacks are short you're getting TPTK or an overpair's money anyway, so you might be better off checkraising to get a continuation bet when he misses, or to let him catch a turn card.

Re: Whats in a Range
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Since check-raising is presumably the 'better' option, should I just go ahead and check-raise?

[/ QUOTE ]

Thge idea that checkraising is better than check calling or check folding here, and that the other two are worse options that you should use only to randomize is wrong. Leading into a preflop raiser with a set is a great way to get there stack. CRing is frequently the worst way.

[/ QUOTE ]

One thought on this. I tend to like leading into the raiser with a set but I do play it differently sometimes. I think choosing to mix it up in a particular case should be done for a combination of game-theoretic and opponent-specific reasons.

Meaning - You often are at a table long enough for opponents to notice how you play certain hands. I'd rather have someone see me c-r a set once and lead into the raiser twice, rather than do the same thing three times. But which time I choose to checkraise will often be opponent specific. Say there's an ace on board and I expect someone to threebet push me with TPTK b/c he just saw me checkraise a draw or middle pair against him. Maybe it's a threeway pot and I think that if he doesn't have the ace he'll bet if checked to but fold if bet into. So either way I get the most, this time, and someone else sees me checkraise a set and makes it easier to get the raise next time when I lead into them.

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.

[/ QUOTE ]

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.

to another matter, i wanted to discuss, and ask you all about the ability to answer this thread. having reread it countless times, i would say the real question is if there is a strategy that can come out of this incredible poker insight. and my answer is no, although i am open to other's oppinions [img]/images/graemlins/smile.gif[/img] but here's my stab at it:

the reason this type of thread has no relevance at lower stakes is quite simple to see. at low stakes, no matter how much better you get at winning, or "maximizing your profits", as we are toaght here on 2+2, your oponents honestly really never get much better, they still call you down like donkeys, and/or allow you to out play them like donkeys. in short, if there are a losing player at some stake, they will most likely always be a losing play at that stake, or at least for a very long time. now, as we move up in stakes, we begin to encounter people who accually think! what a shocker... they start saying"what does he have?" which is what this thread is about. how there is an obvious answer to the issue of oponents saying what does he have, and that is"what does he think i have?"
these players are beat by a simple question also. so we get to a place now where everyone is thinking what does he think i have. and here is the issue. original question was the existance of a strategy that can be deduced from there insights. and here we find our answer. let's say you are playing a head's up match. hero vs. villain
you as the hero, adjust first to how villain is playing. you are able to adjust to his ranges, and his betting styles and structures. but wait! villain is not an idiot, so he imidiately adjusts to your game, figuring out your ranges and betting structures. you then do the same. and as you can see, it will never end. 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?

last, but i hope not least, i'd just like to say that this thread is the first i've accaully enjoyed reading, and i've been reading 2+2 for months. i'd say post of the month material easily... assuming i didn't just ruin it:)

Re: Whats in a Range
 

[ QUOTE ]
On a hypothetical level if one option is clearly "better" you take it. The point is that the majority of situations in which you start with at least a medium sized stack do not involve a specific "better" option. In those situations a mixed strategy is the "best" option.

[/ QUOTE ]

This is what I was getting at. I didn't mean to start a tangent about how to play a set out of position. In fact, I didn't even mention what hand Hero had in my example, because that was irrelevant. What I meant to say was, suppose there is some situation where you would advocate 70% check-raises and 30% leading out (maybe it's a set, maybe it's a combination draw, doesn't matter). There are at least three ways of interpreting this:

1. Check-raising is the 'best' way to play this hand, that's why we do it most often, but we don't want our opponents to catch on to our plan, so we have to lead out sometimes. But when I'm at a table that's going to break soon and I expect to be in this spot only once, I should check-raise every time, since it is on balance best and I need not worry about deception.

2. 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.

At higher levels, your opponents will estimate your range more correctly even when they have never played with you before. Conventional wisdom has it that an UTG raise is generally a big hand, maybe TT-AA, AQ-AK. Your opponents likely put you on a range such as this one the first time they see you raise under the gun. They don't assign you this range because they've studied your UTG raising tendencies, they assign you this range because there are mathematical reasons why you would not generally want to build a pot out of position with hands weaker than these. If you really do raise only these hands UTG, then your opponents can exploit you by folding, calling with good implied odds, calling with the intention of taking the pot away later, or re-raising their biggest hands, knowing you can pay them off.

Suppose you've just been moved to a new table deep in one of the big Sunday tournaments, and you decide to raise 87s UTG. If folds around to the BB, who mucks AJ, and you take the blinds. Has he made a mistake? Not if your range is 40% TT-AA, 58% AQ-AK, and 2% suited connectors. It doesn't matter that you had 87s this time, any more than it matters that Villain hit a two-outer after you made a great call. Although BB has never played with you, he's got a good idea what your UTG raising range is. The only way to combat this is to have a wider, less predictable range.

Similarly, if you have a draw 90% of the time you lead into the pre-flop raiser, but you have a set this time and he pushes, he still hasn't made a mistake. You need to make a guess as to what range he will put you on if you are unknown to him, and then you need to deviate from that range.

3. Some say you should mix up your play situationally, not randomly. Lead out on the 30% of flops that you think were most likely to hit a pre-flop raiser, check-raise otherwise. I don't think this is actually a separate alternative, since flopping a set on an AQ5 flop is a different situation from flopping a set on a T65 flop. Against a player who can make a reasonable estimation of your range and play correctly against it, you need to mix it up in both circumstances. If you know or have reason to think Villain will make a particular mistake, such as folding any flop he missed or jamming whenever he has top pair, then you can choose the play that best exploits that mistake.

Re: Whats in a Range
 

[ QUOTE ]
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.

[/ QUOTE ]

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.


[/ QUOTE ]

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.

Re: Whats in a Range
 

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

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

[/ QUOTE ]

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.

Re: Whats in a Range
 

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

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

[/ QUOTE ]

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.

[/ QUOTE ]

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.

Re: Whats in a Range
 

[ QUOTE ]
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?


[/ QUOTE ]

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.

Re: Whats in a Range
 

[ QUOTE ]
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.


[/ QUOTE ]

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.

Slight Hi-Jack/Pokertracker Question
 

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.

Re: Slight Hi-Jack/Pokertracker Question
 

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

Re: Whats in a Range
 

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

[/ QUOTE ]
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.

Re: Whats in a Range
 

[ QUOTE ]

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.

[/ QUOTE ]

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?

Re: Whats in a Range
 

[ QUOTE ]
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.

[/ QUOTE ]

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.