Ciaffone and Game Theory

[Mason Malmuth]

Hi Everyone:

The following appears in the latest Ciaffone article in Card Player. I thought that some of you might want to comment on it.

Best wishes,
Mason

One critic said that our strategy here is an “exploitable strategy.” He meant that such a strategy is not in accordance with game theory, and can be taken advantage of by an aware opponent. He most certainly is right, but this does not mean we are wrong. Most people do not turn loose of top pair on the turn when raised. The opponent normally does not know you may do so. The fact is, it can easily be a poker mistake to play according to game theory. To do so means you are not optimizing your play against an opponent who does not play according to game theory. As this pertains to our situation here, when you are raised on the turn, you are going to run into a big hand more often than game theory would dictate. (I note that our “exploitable strategy” critic is a player from Vegas, a place where you are more likely to run into a sophisticated opponent who has some tricky moves.) So, in most poker games, you are supposed to fold more often than game theory would dictate. Poker is not a game in which you stick to a certain strategy regardless of whom you face or the character of a particular game. Frankly, top players fold more often than they are “supposed to,” because they know when they have likely run into a big hand.

[rigoletto]

when you are raised on the turn, you are going to run into a big hand more often than game theory would dictate

I believe this is true for the average game, but the following statement is very important.

Poker is not a game in which you stick to a certain strategy regardless of whom you face or the character of a particular game.

To Bob this sentence is a defense for not sticking to game theory, but it can equally be used as an argument for using game theory when the situation calls for it.

Bob advocates laying down top pair top kicker for a turn raise, but I've played plenty of players who'll raise with any big A, or big draws, here hoping you'll lay down, and if you do, you're toast playing with guys like that on your left.

Another important point is how your opponents percieve you. If you play agressive and raise hands like 88, and AJs from middle position, they are more likely to raise you with any A on the turn.

[BB King's]

The crucial point is:

As this pertains to our situation here, when you are raised on the turn, you are going to run into a big hand more often than game theory would dictate. For some players in some games this is true - a turn-raise means two pair or better. In some other games it may not be true.

I note that our exploitable strategy critic is a player from Vegas ... I wonder who that could be ?

No, I'm not folding AK for a turn-raise w/ a xxAx-board.

[BruceZ]

Mason,

It is true that you make more money by not using game theory against a player who is also not using game theory as long as this situation remains static. Poker is not static though, and by making tough lay downs you may encourage these opponents to begin playing more correctly. So while it is true that you should play in such a way as to capitalize on your opponent's errors, you must also make sure to keep him playing incorrectly.

BTW, After an enormous amount of thought, I have added a response to our discussion about Ciafone's book in the mid-limit forum. I also responded to Sklansky's analysis of one of the hands.

-Bruce

[gilly]

"The fact is, it can easily be a poker mistake to play according to game theory. To do so means you are not optimizing your play against an opponent who does not play according to game theory."

I do not really like the way the term "game theory" is being used synonymously with full rationality. Game theory should be viewed as a setting in which to view the game. An apparatus where you have to fill in the assumptions (ie how rational your opponent is).

The comment "an opponent does not play by game theory" is in a lot of ways a poor statement. The better way to say it is you are going against an opponent that is not fully rational, or does not have full information. These are things that must be taken into consideration when making your decision. While I know it is a tautology and of very little use, everyone applys "game theory" to their decision process whether they know it or not. It is up to the person viewing the game to put in the paramters that the other player is using.

This is at the heart of a game I created where if you play assuming your opponent is rational you end up with one decision (and do poorly), however in a series of these games you should pick up that the opponent is only maximizing his total possible win, rather then playing rationally. Now given this information you can re-optimize to get an optimal outcome. This is still game theory. It is just that your opponent is playing in a different manner. Both players are playing in a game theoretic environment.

I know this is somewhat off the wall and probably makes very little sense but it is just what I thought.

[SoBeDude]

The comment "an opponent does not play by game theory" is in a lot of ways a poor statement. The better way to say it is you are going against an opponent that is not fully rational, or does not have full information. These are things that must be taken into consideration when making your decision. While I know it is a tautology and of very little use, everyone applys "game theory" to their decision process whether they know it or not. It is up to the person viewing the game to put in the paramters that the other player is using.

I'm no expert on game theory but this is not what I understood it to mean.

Not using game theory does not mean the player is not playing in a "rational" manner. It means he is playing in an exploitable manner.

There are times where proper play "by the book" becomes exploitable and hence no longer correct. I believe this is one of those sitiations. In my games, when I've raised preflop and bet the flop, then get raised on the turn means my opponent has a made hand 85% of the time, perhaps more.

Now against shrwed opponents who can take advantage of me wanting to lay down to the turn raise I have to call them down a fair percentage of the time. Here I can use game theory to provide me with a sufficiently random event to control my fold/call decision so my play is not predictable.

Mason, did I get that right?

-Scott

[bernie]

shouldnt that depend on who's raising you? and if it's a c/r and the players c/r-raising standards?

just a thought

b

[bernie]

i never thought game theory was a cookie cutter approach the way bob is implying here. i thought it was the adjustment of the percentage plays an opponent, regardless of skill, is using against you.

for instance, if an opponent always calls, it would go against game theory to try and bluff him wouldnt it? since he'd never fold. as compared to playing someone who folds alot. arent there 2 ways to play both these players based on how game theory applies to each?

"As this pertains to our situation here, when you are raised on the turn, you are going to run into a big hand more often than game theory would dictate."

doesnt this also depend on the players turn raise standard and how g theory would dictate to play against that based on the opponents tendency? i see what bob is saying, but i dont think he's saying it that well.

am i off on this? ill have to reread the game theory section again....

b

[gilly]

There is no sense in which one plays "game theory". It is a tool of analysis not a recomendation on how to play (although one can surely analyze a situation USING game theory to come up with how they should play).

To say someone is playing an "exploitable strategy" is defining them as being in the game theory setting. Game theory itself does not have anything to say about optimality.

Lets look at it like this. We are playing a game where two players cannot communicate. They show a coin head or tales. If they match player A gets $1 if the do not match Player B gets $1.

Here is what they do
Player A : T H T H T H T H T
Player B : T H T T H T H T H

Here player B has "exploited" Player A's strategy of alternating between heads and tails. Player B was able to analyze this in a game theoretic model even though player A was playing a terrible strategy. There is no sense of "not playing game theory" that just does not make sense.

[BB King's]

As i see this debate - it goes like this:

Bob C: If a player is bluffing with a lesser frequncy than Game Theory would indicate you should call less often with your marginal good hands - hands that can only beat a bluff - thereby saving you some bets.

Mason: Wrong ! If you do that - sooner or later your opponent will catch on and begin to bluff with GT - or maybe even more.

Bob C: We don't know for shure that my opponent will catch on - or how soon he will do it. If he does I have the easy choice to change my calling-strategy.

[SoBeDude]

I'm not sure we're disagreeing.

But in your example player A is playing poorly. I maintain that given a sufficiently more complex game, I can play a "proper" strategy where a very sharp individual could find a way to dominate me.

In this case, I can use game theory to help me. Going back to your example, if player B has found a pattern he can expliot in my game, I can then use a random event to dictate my head or tail decision. For example, if before I place my coin I look at my digital watch, and put up a head if the second hand is on an even number, and tail if on an odd. Now assuming we're not playing with a timed rhythm I have used game theory to eliminate my opponents advantage over me.

-Scott

[gilly]

OK. It is true. Player A is playing poorly. But that does not mean he is not playing in a game theoretical manner and that I should throw game theory out the window. Like you said you can now use game theory to devise a strategy to capatilize on his poor play.

I just do not understand what you meant in your first post when you said.

"I'm no expert on game theory but this is not what I understood it to mean."

[Mason Malmuth]

Hi Everyone:

The reason I posted this is that I'm obviously the critic that Ciaffone is referring to. But that's not the only reason. I believe it is a good example of how people who play and (sometimes) write about poker become confused when it comes to Game Theory.

Game Theory, a branch of mathematics, does has some applications when applied to poker. But for almost all of us, it should only rarely be used. It comes into play when our judgement is failing or when we are up against a superior player. In other words, if a poker situation develops where you don't know what to do, then you may be able to fall back on a Game Theory strategy. But if you play poker well, especially if your game is hold 'em where you get to see your opponent's last card, it should rarely be used.

Notice that I said you would fall back on Game Theory when you don't know what to do. But suppose you are against someone who looks to save bets. If you know this, you don't even think about Game Theory. You give that opponent extra opportunities to save bets unless you hold a very strong hand. If you're against someone who is a loose raiser before the flop, you reraise him more frequently. If you're against someone who still requires high quality hands to raise first in from late position, you don't defend your blinds as often as you would against a typical player who raises from the same position. And so on.

Finally, my experience is that many players bluff and semi-bluff more often than a game theory strategy would indicate, especially on the turn and river. That's because in games like limit hold 'em the pots become very large compared to the size of the bet, and Game Theory when applied to poker takes these two factors into account. Thus the statement:

So, in most poker games, you are supposed to fold more often than game theory would dictate.

is terrible advice in my opinion for middle limit games. This is especially true in games outside of Las Vegas which are more likely to feature a smaller number of skilled players, and which feature players who have a fair amount of disposable income meaning that they come to gamble.

best wishes,
Mason

PS:

This statement:

Frankly, top players fold more often than they are “supposed to,” because they know when they have likely run into a big hand.

is also rediculous. My suspicion is that what is happening here is that Ciaffone is confusing pot-limit strategy with what is appropriate for limit play.

[Mason Malmuth]

Hi Bernie:

I agree that who raises you is very important and should play a significant role in your decisions. Notice that this is the opposite from a Game Theory strategy.

Best wishes,
Mason

[Mason Malmuth]

Hi BB:

You wrote:

Mason: Wrong ! If you do that - sooner or later your opponent will catch on and begin to bluff with GT - or maybe even more

This isn't correct. If you're folding a lot, your opponents are going to begin to bluff you more, and they might not change their strategy against anyone else. Notice that they do this without thinking about Game Theory. But it will be disasterous for you.

Best wishes,
Mason

[Mason Malmuth]

Hi Dude:

You wrote:

There are times where proper play "by the book" becomes exploitable and hence no longer correct. I believe this is one of those sitiations. In my games, when I've raised preflop and bet the flop, then get raised on the turn means my opponent has a made hand 85% of the time, perhaps more.

Two points. If the book tells you to bet all your good hands and then to occasionally bluff, how is that exploitable.

Also, if your opponent has a good hand 85 percent of the time and you always fold, you might have a big problem. You need to consider the size of the pot.

Best wishes,
Mason

[bernie]

Mason,

im going to reread the game theory part in TOP. i was under the impression that it was based on your opponents tendency. which would change at times depending on how he's playing. it seems youre saying it's a gross generalization on how to play a faceless opponent. is that right? ill be reading

er, best wishes /forums/images/icons/wink.gif

b

[bernie]

havent reread it yet.

so it's like when you lose the count in BJ and fall back on basic strategy. is that it? maybe i wont have to reread it. heh heh...yeah right

thanks

b

[Mason Malmuth]

Hi Bernie:

That's right. When you go to a Game Theory strategy you ignore any characteristics that you believe your opponent may have. Part of the reason for this is that you may have become unsure of your judgement (against this particular player) and thus can't make poker decisions well.

Best wishes,
Mason

PS: If you've read the Poker MBA, a book I happened to like, the Game Theory chapter, while a worthwhile chapter, has nothing to do with Game Theory.

[BruceZ]

Mason,

But suppose you are against someone who looks to save bets. If you know this, you don't even think about Game Theory. You give that opponent extra opportunities to save bets unless you hold a very strong hand. If you're against someone who is a loose raiser before the flop, you reraise him more frequently. If you're against someone who still requires high quality hands to raise first in from late position, you don't defend your blinds as often as you would against a typical player who raises from the same position. And so on.

And if you are against someone who only bets or raises with a good hand, you should fold more often when he bets or raises than you would against someone who may semi-bluff or bet weaker hands. So while it is important not to make him play better by folding too often when he bets or raises, you still must fold more often than if he were playing optimally according to game theory, or else you are deriving no benefit from his incorrect play. So how do you balance these two opposing concepts? I think that is at the crux of the debate here.

Also notice that by your argument alone, it would become important to FOLD often enough against an aggressive player who bets and raises more than game theory would indicate, in order to keep him playing too aggressively. Of course we know that we must also call this player more often in order to take advangage of the fact that he is betting too many hands. Again we have two opposing forces.

It appears that your emphais here is on only one side of this balance, namely on keeping a player playing incorrectly in the future, and not on actually exploiting the fact that he is playing incorrectly right now. What is the point of keeping him playing incorrectly, if we never exploit his incorrect play?

-Bruce

[BruceZ]

Game theory has nothing to do with adjusting to your opponents. Game theory tells you how often you should bluff or call based only on the size of the pot. If the pot has 8 bets, and it costs 1 bet to bluff, game theory says you should be bluffing 1 time in 9 that you bet. It also says your opponent should call your bet 1 time in 9 when the pot is this size.

Playing according to game theory does not mean you are winning the maximum amount of money unless your opponent is also playing according to game theory. If your opponent is not playing according to game theory, you will win more money by not playing according to game theory. However, if you play according to game theory, you will win THE SAME AMOUNT OF MONEY REGARDLESS OF HOW YOUR OPPONENT PLAYS. HIS DECISIONS NO LONGER AFFECT HOW MUCH YOU WILL WIN.

[Mason Malmuth]

Hi Bruce:

No. You need to read my post again. You certainly want to exploit errors in their play right now. That's what my paragraph that you quoted is about.

My point is that you want them to be the ones making the obvious errors. You don't want to be the one who is making those errors.

Here's what I mean. Suppose you are against someone who folds too much. Well, against this particular person, you work in a few extra bluffs. But you don't change your strategy against the other players. What will happen is that your opponents in most cases won't even notice that you are playing any differently, and thus no one will adjust their play against you. Many of my hands to talk about illustrate this.

You can also easily do this yourself. When in a game decide if there is anyone at your table who plays as Ciaffone advises. Now bluff them much more than you normally would, but don't change your strategy against anyone else. There's a good chance no one will notice.

By the way, if you read my critics, they often refer to me as a very tight player who has "no imagination." Of course most of these people lay down too much against me because they are sure that if I bet I have a hand. That's the way they think the book players are suppose to play, and obviously I'm the world's premier book player.

There's also another point here. When playing a game such as pot limit, the penalty for betting is far greater if you run into a good hand because they can raise so much more than in limit. Thus you need to be much more careful with your bets and calls. An easy way to see this is you should steal less if first in from the button in pot limit than in limit. That's because you can always call that reraise in limit, but should frequently give it up in pot limit. So if your steal is successful you win the same amount, but lose more when reraised.

I believe that these ideas are incorrectly carrying over to their limit advice. Also, another far worse book than Middle Limit Hold 'em (which I don't consider a bad book, just a book with a flaw) is Championship Hold 'em by Cloutier and McEvoy. They're so timid in spots, especially if you read the first edition, that it's amazing.

Best wishes,
Mason

[BruceZ]

No. You need to read my post again. You certainly want to exploit errors in their play right now. That's what my paragraph that you quoted is about.

I know, but your examples didn't include exploiting tight predictable opponents by folding more on the flop and beyond when they bet and raise. This principle is in conflict with the idea that we shouldn't fold too much lest we might make them bluff more and play less predictably. Don't you agree these are conflicting objectives?

[BruceZ]

If the pot has 8 bets, and it costs 1 bet to bluff, game theory says you should be bluffing 1 time in 9 that you bet. It also says your opponent should call your bet 1 time in 9 when the pot is this size.

You should bluff 1 time in 10 so the odds that you are bluffing are 9-1, which are the odds you are giving your opponent on his call. Your opponent should call 1 time in 10.

[gilly]

"Game theory has nothing to do with adjusting to your opponents. Game theory tells you how often you should bluff or call based only on the size of the pot."

I do not want to argue semantics (with the use of the term "game theory") but I feel the above quote was directed to my previous post so I shall reply. As Mason said game theory is a branch of mathematics (stolen by economists).

It is about playing a game given a set of information. That is what it does. (equilibrium analysis as well but that is of very limited use in this case). To say it has nothing to do with adjusting to your opponent is not true. If you are really going to use game theory, you are going to have to make assumptions on how your opponent is playing.

You say that it tells you how often to bluff based on the size of the pot. First let me say that this is just one application of game theory. Also this statement is not true. If there is 400 or 100 or 4 or 7 bets in the pot and it is to you how often should you bluff. You cannot answer this question without assigning your opponent a probability of folding. If he is NEVER going to fold. The answer is that no matter how much money is in the pot you should not bluff.

Game theory is flexible enough to take these things into consideration.

[rigoletto]

I agree with gilly and I think a lot of the disagrement in this thread steems from Bob using the term game theory as a synonym for rational (poker)behavior. We should also remember that Bob's statements is in context of LL games, where players don't semibluff etc. as much 'as they should'.

Seems to me that Bob is in essence saying, that you should fold to a turn raise more often ag. unsophisticated players in these situations then you would in a thougher game. And I don't think anybody can really disagree with this.

But Mason is welcome to try /forums/images/icons/wink.gif

[bernie]

i reread the section....

i got it.

i think bob's statements are way too weak tight. and it doesnt take game theory to exploit the flaws. just basic player knowledge. if i knew if i raised the turn and he'd only call/raise with one of the top hands, or fold, id raise much more often. game theory doesnt exploit this the way playe knowledge and adjustment does.

his statements are also very game/player dependent. i dont think it's a good generalization.

however, you also didnt (conveniently?) provide the hand or the opponent description that he is referring to as an example. these factors can make his assumptions in 'this situation' right. especially if he's taking a specific case and using it as an example.

from another response: as an aside, ive only read a couple quotes from cloutiers book and, unless im going to play many tourneys, i wouldnt touch this book. way too weak of play for limit grinding

have a good one

b

[BruceZ]

I was explaining to bernie what is meant by "using game theory" in poker as defined by David Sklansky in The Theory of Poker. His definition on p. 166 is as follows:

Essentially game theory attempts to discover mathematically the best strategies <font color="red">against someone also using the best strategies</font color>. Against an opponent you think is weaker than you are - and it can be in any game whatsoever - you would usually rely on your judgment rather than on game theory. However, against an opponent you think is better than you or against an opponent you don't know, game theory can sometimes enable you to overcome the other's judgmental edge".

So when we say we are "using game theory" in poker, we are generally refering to using an optimal strategy assuming your opponent is also using an optimal strategy. Once you decide to use this optimal strategy, you decisions no longer take into account how your opponent plays. In fact, when you use this strategy, how much you win will not depend on how your opponent plays even if he is not using an optimal strategy. Your decisions only involve the size of the pot. In this context, all of my statements above are correct. If an opponent will call less often than this optimal strategy, then you win the most by always bluffing, assuming that this will not cause him to start calling more often. If your opponent will call more than this optimal strategy, then you win the most by never bluffing, again assuming he does not change. You are correct that this too is part of "game theory" in the broader sense, but that is not what we mean by "using game theory" in poker. You don't need game theory in these cases, you use your judgement.

[Mason Malmuth]

Hi Everyone"

Bruce just wrote:

Once you decide to use this optimal strategy, you decisions no longer take into account how your opponent plays.

This is the key to all of this. When playing you may fall back on Game Theory against a superior opponent, or if for some reason you feel your judgement is failing. On the othet hand, if you know, for instance, your opponent never bluffs and only bets strong hands, you would use that information and fold unless you also held a very strong hand.

Best wishes,
Mason

[Mason Malmuth]

Hi Rigoletto:

You wrote:

We should also remember that Bob's statements is in context of LL games, where players don't semibluff etc. as much 'as they should'

I'm not going to let Bob get off this easily, The book in question is titled Middle Limit Holdem and the article from which the quote came from is a defense of some of the hand problems in this book. He is clearly not writing about the low limit games that you reference.

Best wishes,
Mason

[gilly]

All I am saying is that it is possible for game theory to have a more important role in one's analysis of the situation.

You should be able to apply it (to your benefit) in any situation, given some, none, or a lot of information about your opponent. Saying that it does not apply in certain situations is like saying probabilty does not if we play poker with a 50 card deck short 2 hearts and Ace and a King. It still works, you just have to apply it, just like game theory can still work under different situations.

[rigoletto]

Ups my mistake. That we're talking about mid limit doesn't change my point when I said:

Seems to me that Bob is in essence saying, that you should fold to a turn raise more often ag. unsophisticated players in these situations then you would in a thougher game. And I don't think anybody can really disagree with this.

The point being that by analyzing Bob's statement, his defence on the hand problem turns out to be a limitation of the circomstances where his suggested play applies.

When I say 'I don't think anybody can disagree with this' it should be read sarcastically; you can't really learn much from the obvious.

[BruceZ]

You should be able to apply it (to your benefit) in any situation, given some, none, or a lot of information about your opponent.

Tell me how I can apply game theory to my benefit when I know that my opponent calls less or more than optimal in a given situation. The optimal decision is to always bluff or to never bluff, and I don't need game theory to tell me that.

[Piers]

I am /forums/images/icons/blush.gif to admit I find Mason’s criticism of Middle Limit Hold’em reassuring.

After reading Ciaffone and Reuben’s pot limit book /forums/images/icons/smile.gif I had a lot of respect for his opinion, and was slightly disconcerted with how I felt with some of Ciaffone’s limit hold’em ideas /forums/images/icons/confused.gif .

[Mason Malmuth]

Hi Rigoletto:

You wrote:

Seems to me that Bob is in essence saying, that you should fold to a turn raise more often ag. unsophisticated players in these situations then you would in a thougher game. And I don't think anybody can really disagree with this.

I disagree completely. Against unsophisticated players, assuming you play well, you should know what to do. That is it should be clear that they bluff too much or too little. (In fact, it's been my experience that most relatively novice players bluff too much in these spots.)

The problem occurs against the sophisticated players. Now you're not so sure what to do. But one thing is virtually certain, constantly folding against this type will cause you trouble.

Best wishes,
Mason

[Mason Malmuth]

Hi Everyone:

Again, this is exactly the flaw in the Ciaffone quote. You should virtually never be using Game Theory to make your decisions at the poker table.

Best wishes,
Mason

[BB King's]

Mason:Again, this is exactly the flaw in the Ciaffone quote. You should virtually never be using Game Theory to make your decisions at the poker table. This exactly what Bob C is not doing !!!

Bob C:The fact is, it can easily be a poker mistake to play according to game theory. To do so means you are not optimizing your play against an opponent who does not play according to game theory.

[AceHigh]

"we are generally refering to using an optimal strategy "

I prefer the term unexploitable strategy. Optimal strategy is only optimal against opponents who play very well. Most opponents call too much, at least on the river, so if you use optimal strategy you may be bluffing too often. At least in my games, YMMV.

[gilly]

OK. This is just beating a dead horse. This is basically semantics. You are using game theory as a term to define a very very narrow thing, whereas I was just suggesting that there is a much more broad use.

And in reply to your previous post where you asked:
Tell me how I can apply game theory to my benefit when I know that my opponent calls less or more than optimal in a given situation. The optimal decision is to always bluff or to never bluff, and I don't need game theory to tell me that.

My response is that game theory tells you that. If you looked at this as a problem in a game theory setting you would figure that your optimal strategy is to always bluff or to never bluff. The fact that you do not need game theory (in this case) is absolutely beside the point. The odds of getting tails on a fair coin is 1/2 and given that I just got tails the odds of getting tails again is 1/2. I do not need statistical analysis to tell me this, but if I decided to use statistical analysis I would still get the same answer.