The evolution of the mid-high stakes forum

[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.

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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.

[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]

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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.


[/ 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.

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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