Game Theory and its NLHE Implications

[Mercman572]

I've heard some talk about game theory, read the small section on it in TOP, and used Wikipedia but I'm still a little shaky on exactly what it is and how and when to apply it to NLHE. I was hoping a few people could clarify for me.

In my understanding game theory is the optimal strategy that can never be optimally countered regardless to an opponents decision in terms of EV. Am I right so far? My other understanding is that game theory only really need be applied against very tough opponents, is that also correct?

I believe Sklansky's demostration in TOP involved 7stud and picking a bluffing frequency and assigning it to a range of cards for the final face down card, and bluffing when one of those cards falls. I believe the way the percentages break down your opponent can't make a +EV decision in either a call raise or fold since action is predetermined and the frequency of a bet that is either a bluff or made hand leave no optimal decision. Is this correct as well?

So how does this pertain to NLHE? My current thought would be, for example, betting 1/2 pot with a QQ overpair against a tough opponent whenever a flush card hit the river (if there is any possibility it may look like you're drawing). You believe the opponent to have an overpair as well, so you wouldn't mind a showdown or fold, but can't stand a raise. He would have to assume you would do this with a flush or with a top pocket pair (one that may beat his) as well as a bluff and leave him with a difficult decision. I understand that may not be a good example, so if it's flawed please let me know. I wouldn't be surprised if my whole understanding of the concept is off either so I won't be offended if I'm totall wrong. Is this a valid example, what are other (better) ones? Thanks all for the input.

[Borno]

I am not a game theorist nor do I regularly apply game theory to poker. I am not a serious math type and I only play SS poker but I will give you a very clear illustration of what game theory is - maybe this will assist you in applying it to poker.


Consider the international security dilemma: It is unclear that countries will act in order to have a mutually beneficial outcome all the time.

The Stag-Hunt:

5 actors want to hunt a stag.
Together they will likely catch the stag and they will feed all their families.
On the hunt one actor sees a rabbit.
That actor can defect from the group and get the rabbit, in which case the rest of the group will surely not be able to trap the stag.
If the opportunity arises it is unclear if the individual will stay with the group or defect to immediately satisfy his needs.



The game theory illustration of this is (in chart form):

..........Defect........Cooperate
Defect....1,1...........5,0
Cooperate.0,5...........3,3

1,1: if several members defect from the group there may be a shortage of rabbits or they will have to share rabbits and no one's needs will be satisfactorily met

5,0: The actor that defects will get a rabbit but everyone else will have nothing

0,5: same as previous

3,3: everyone recieves a mutually beneficial outcome.

Thus, game theory is the weighing of alternatives to determine the best possible outcome for, in the case of poker, yourself. By doing this you create the least beneficial outcome for your counterpart.

Hope this helps!

[Mercman572]

nh. so in your hypo if one hunter deviates, it is in everyone elses best interest to deviate as well since, as a 4 person team, they cannot catch a stag and must accept the worse alternative of each POSSIBLY catching a rabbit. I think this is touching on the nash equilibrium.

I still don't see its application to NLHE however, besides of course on the most basic level of making the most profitable decision. I guess I'm still stuck for examples of HOW to use game theory to make a decision in holdem.

[Borno]

I do not have the post I have in mind handy and I did a search for it and couldn't find it.. it was lengthy and excellent.. but let me reiterate my thoughts on what I'm talking about.

A long while back there was a post in SSNL that compared the advantages of betting 2/3rds of the pot size instead of the full pot size. In a particular situation.

if you bet 2/3rds every time you stand to make less than betting the size of the pot every time. Even taking in to account the times your raised and have to fold or lose.

The poster weighed out each bet and proved that making a pt sized bet is indisputably the better option regarding EV.

So:

Choice a: bet pot
under a: villian can repeatedly call down, fold, raise.. under each of these actions we have our actions

Choice b: bet 2/3rds pot.
under b: villian can call, fold, raise...
under these actions we have our actions.

So.. from the x then y scenario we can determine the EV for us.

this is just one use of game theory is NLHE

(I don't remember the particular case.. maybe someone else remembers this thread, if you do please post it I would want to reread it)

another example:

If I check my opponent can bet an amount that gives me odds, some other amount, 2/3 the pot, or the size of the pot, or my opponent can check behind.

Now take each option into consideration and how you will have to react based on the opponent. Then compare the EV of each of those options to the EV of you betting out each of those amounts and how villian will react.

Clearly this can become VERY complicated. I think this is the basis upon which all poker decisions are actually made, however we interpret them alot more simplistically because someone else has done the leg-work.

[Jerrod Ankenman]

Here's a short answer about applying game theory to poker.

You have a strategy for playing poker. That strategy includes what you would do in all the various possible situations you might find yourself in, from "you're on the button with A9s" to "the action has gone r50r150c;8h 2h 7s/b300c;Js/kk;Tc/b700" and it's up to you.

Now your opponent has a strategy too. And if we had those strategies and a fair amount of computer power, we could find your expectation in the game (just assume headsup for a moment).

I divide all non-exploitive poker play (which is what game theory is about) into two ideas: aggression and balance.

Aggression is, put succinctly, the hands that you play for value. You can have different levels of aggression. For example, I've played with some people whose idea of "aggressive" was raising tens in the cutoff in limit holdem. I've played with some people whose aggression-o-meter didn't run out until I got all their money (and some who got some of mine!). But the idea is that there is a set of hands you bet, raise, check-raise, etc, for value.

The other concept is balance. To understand what balance is about, suppose you had a book with your opponent's strategy in it, and he would play that strategy and not deviate. Could you make money? You probably could, although it would be a little harder than most people think. You'd construct a strategy that maximally exploited his. We call that the nemesis strategy.

Now there's a particular strategy where you COULDN'T make money. That strategy is called optimal, because it is the strategy which does the best (EV-wise) against its own nemesis. We'd love to have the optimal strategies for no-limit, but it's computationally intractable.

But you can understand this concept of balance now - suppose you have a strategy S. Now evaluate that strategy against 1) its nemesis - call that value S#, and 2) the optimal strategy - call that value S%.

If S# is close to S%, then the strategy is balanced. If it's far away, then it's unbalanced. Balance is a measure of the exploitability of a strategy. Now some strategies lose money because they are too tight, loose, aggressive, passive, whatever. Others lose because they don't properly balance their play. If you never bluff, the exploitive response is to fold mediocre hands. Bluffing isn't a value action - it's a balance action.

Now the optimal strategy is perfectly balanced with the precisely proper level of aggression. This is what game theory tells us.

This "picking a card to bluff on" stuff isn't game theory. I mean, it's inspired by game theory and it's sorta the beginning of an idea about game theory. But why don't you do this instead. Think about your own strategy. Think about the actions you take, the bets you make. Think about how you would smash yourself if you were your own opponent. Then change the way you play so that this can't happen any more. Bluff appropriately. Semibluff appropriately, and so on.

Most of the existing literature in game theory is going to talk about the prisoner's dilemma. That doesn't help you with poker, unfortuantely. it's important in life, but it just normally isnt relevant to poker. There will be a book in the not-so-distant future that will have more information about this. Now I have to go work on it some more.

Hope this helps.

Jerrod Ankenman

[elmitchbo]

here's a page full of fun reading for you.

http://www.cs.ualberta.ca/~games/poker/

scroll down to the publications section and start opening some of the .pdf's.