The evolution of the mid-high stakes forum

[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]

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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.

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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.

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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.

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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]

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


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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.

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


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


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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.

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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 .


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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.

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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.

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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?


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


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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.

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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?


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


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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]

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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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I've already acknowledged that I was not correct in my wording in my last post.
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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?
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.


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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.

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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.


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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]

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

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


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

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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