Game Theory and NLHE

[Lloyd]

I re-read the section on Game Theory in "Theory of Poker" and have been trying to figure out it's applicability in NLHE. The example of bluffing seems to only apply when your card is hidden from opponents.

Besides playing a hand that you wouldn't ordinarily play to mix things up (like 98s UTG), what other ways does Game Theory apply to NLHE?

[phixxx]

What exactly is game theory? :O

[Lloyd]

In a nutshell, game theory is a mathematical approach to figuring out the best strategy for a particular decision. I would suggest reading "Theory of Poker" by Sklansky for more info on how game theory relates to poker (albeit somewhat limited). If you saw the movie "A Beautiful Mind", game theory is what John Nash won a Nobel Prize for. It has also been cited on "Survivor" for how to win that game.

I understand the basic essence of game theory but hope that some of the more advanced 2+2ers can shed some light on its applicability to poker, specifically hold em.

[Lloyd]

Let me propose a specific question concerning game theory and NLHE:

In "Theory of Poker", Sklansky's suggests selecting specific cards that you will bluff with (for example, when drawing to a flush and you don't hit) in proportion to the odds your opponent is getting. Can this be extended to starting hands in the same fashion?

For instance, let's say that without varying your starting hand requirements for the specific table conditions, there are 12 hands you'd open with UTG. Let's also assume that you'll open for 3BB, which would mean your opponent (focusing on the first to act after you) is getting 4 1/2 to 3 odds. This would suggest that you should select 8 additional hands (like various suited connectors) to also open with UTG.

Now, this certainly makes sense to me mathematically but not practically. But there does seem to be a benefit to adding some non-traditional UTG starting hands to add some trickiness to your play. But what's the magic number and how does it apply to game theory?

[citanul]

Wow. Umm... How to explain game theory and be helpful here.

So imagine any situation where more than one person/entity interacts, and there is some structure of payouts. Whenever you look at this using math of any type, including a lot of math most people don't realize is math, like drawing a little diagram with the decisions and the results, and figuring out what path to take, that's game theory. Hell, even when you look at it using nothing anyone considers "math" you're probably doing game theory.

Asking when game theory comes to play in a specific game then, is just plain silly, since every action you take in every game is dictated by some sort of game theory. For instance, in LHE, the set of hands that we are told to play from different positions work out because they play well against the ranges of hands you are likely to have to play against from the other players. A good set should hold in some way stable, meaning that playing against all people who play exactly the same, they should break even over time.

With respect to NLHE and starting hands, and particularly relating it to "bluffing preflop" hands. Think about this common situation. It is folded to you in late position, you believe you have a good likelihood of stealing the blinds because the other players play too tight, so you raise with any two cards. You did this because you thought at that moment that your chance of stealing the blinds outright was so high that even if you lost every time they decide to play, you were making a profit over the long run. That was game theory.

Hope this helps a bit?

citanul

PS: there's a lot of real great game theory books out there that range in approachability from needs to know algebra to needs to know graduate mathematics. if you're interested, you should pick one up. if you want, i'm sure i or many others could make a recommendation.

[citanul]

[ QUOTE ]
For instance, let's say that without varying your starting hand requirements for the specific table conditions, there are 12 hands you'd open with UTG. Let's also assume that you'll open for 3BB, which would mean your opponent (focusing on the first to act after you) is getting 4 1/2 to 3 odds. This would suggest that you should select 8 additional hands (like various suited connectors) to also open with UTG.

[/ QUOTE ]

I don't know from where you have selected your number of 8, but clearly there is a huge flaw in your reasoning. If the table conditions dictate 12 hands you think you should open with, then there are 12 hands that you should open with. The possibility that you should open with 8 more hands simply means that your evaluation of your original set of UTG opening hands may be incorrect.

citanul

[lucas9000]

[ QUOTE ]
PS: there's a lot of real great game theory books out there that range in approachability from needs to know algebra to needs to know graduate mathematics. if you're interested, you should pick one up. if you want, i'm sure i or many others could make a recommendation.

[/ QUOTE ]

i know i would appreciate recommendations for books that discuss game theory and don't require graduate mathematics [img]/images/graemlins/smile.gif[/img]

[queenhigh]

I think the most common application of game theory to NLHE is as follows:

You're playing a good, tricky opponent who is representing a strong hand. He has played the hand exactly as he would if he had it, but you also know that he would bluff in this same spot. Suppose the pot is $100 and he bets $100. If you think he would bluff more than 1/3 of the time, you should call.

[Lloyd]

As for book recommendations, I would suggest doing a search for game theory book in the 2+2 forums and you'll find a bunch of recommendations.

[Matt Flynn]

yes in the sense that against thinking opponents you must occasionally play and raise hands you would not normally in early position in order to make it harder for your opponents to put you on a hand. no in the sense that no limit is much more a game of situations, so you should not choose randomly (e.g., "8h7h"). what you want is, e.g., a situation where the button raises about a third of hands when there are two or more limpers. you are UTG+1 against that player on the button and have 87s. you should fold normally, but it is reasonable to limp and then check-raise big with the hand. when the button lays down, often you want to show it. i find if i'm not getting action that showing two bluffs in rapid succession works well to keep 'em calling. alternatively, if the game is getting tight enough to blind steal from utg, you can always do that with a weak hand. don't show it if you can steal a lot; show it if you cannot. alternatively, find another table.

matt