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.