Game Theory and NLHE

[Lloyd]

I came up with the number 8 by using the same method that Sklansky used in "Theory of Poker" when discussing Game Theory and Bluffing. Essentially, he said that you should bluff in the same frequency as the odds your opponent is getting. So if you're on a flush draw in a game where your oppontent doesn't see your last card, there are 9 cards that will make your flush. If you opponent is getting 5 to 1 odds if you bet, your ratio of made cards to bluff cards should be 5 to 1. So in this example, you will make your flush with any of 9 cards, and you would select two random cards with which you would bluff (it's actually a little less than two but I rounded up). If you never bluffed, then your opponenet would simply fold if you bet and bet if you checked. By introducing a bluff you have optimized your profits on this hand as sometimes they will call you when you've made the hand and sometimes they will fold when you are bluffing. This more than makes up for the times when you are called on a bluff.

The same logic can be applied to starting hands. If your opponents know that you will only open UTG with pocket 8s and higher, or AQ and higher, they should simply fold if they can't beat those hands. By introducing a bluff to your starting hand requirements, they won't know exactly what to do. If for instance you'll open UTG with 76s, get called, hit the flop and go to a showdown, you would have them off-balanced on what to do with your opening raises. Now they might be more likely to call you with inferior hands. The question, in this instance, is what is the ratio of true starting hands to bluffs that would lead to optimal results.

My limited understanding of game theory is that it is only appropriate when you're playing against people of equal calibre. If you're playing online against people who don't have a clue, you don't need to introduce bluffs to your starting hand requirements because they'll call you with inferior hands anyway. But if you're in a large buy-in tournament at the Bellagio with a bunch of great players, you might need to alter your strategy to keep people off balance. This is where game theory would be useful.

[turnipmonster]

Check out "Game Theory and Strategy" by Phillip Straffin for a great read. Paul Phillips recommended it on RGP a while ago and I picked it up and thoroughly enjoyed it. it is a textbook and somewhat technical but definitely presented in a clear and easy to understand way. it helps to have a basic familiarity with matrices, that's it.

As far as game theory as a bluffing tool, the important thing to realize is what the goal of it is in your question. The goal of it is to give your opponent a decision that is EV neutral. that is, he doesn't make or lose any sklansky bucks by calling or folding.

generally with good judgement you can do a bit better than this based on a lot of info you'll have about hand probabilities, particularly with a community card game like hold 'em. in my opinion in a game like stud it's a bit more clear cut, as you mentioned.

that said, in NLHE I think it's often important to give yourself bluffing cards as additional outs when calculating pot odds. for instance, if you are sure your opponent has a pair and you are open ended, you can often give yourself any flush card as an out as well. so if you miss your hand but the flush comes in, it is often correct to lay 2 to 1 if your opponent is capable of folding a pair on the river.

--turnipmonster

[reubenf]

[ QUOTE ]
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.

[/ QUOTE ]

Maybe I misunderstood, but any set of starting hands will break even against itself. The distinguishing feature of a good set of starting hands is that is is +EV against other sets of starting hands.

[Lawrence Ng]

Buy a good 3rd year Intermediate Micro Economics book and in should have some basic explanations with regards to Game Theory.

[Unarmed]

Go here: (one of the best posts ever IMO)
http://www.decisionproblem.com/shania.html

and this:
http://forumserver.twoplustwo.com/sh...amp;PHPSESSID=

[doubleas]

[ QUOTE ]
that said, in NLHE I think it's often important to give yourself bluffing cards as additional outs when calculating pot odds. for instance, if you are sure your opponent has a pair and you are open ended, you can often give yourself any flush card as an out as well. so if you miss your hand but the flush comes in, it is often correct to lay 2 to 1 if your opponent is capable of folding a pair on the river.

--turnipmonster

[/ QUOTE ]

I love this. My problem is figuring out if my random opponent is capable of folding. Playing the stakes I play, it is probably 50/50 whether or not somebody will fold (if I don't have a read).

Guess I'll account for the 50/50 by including half of the scare card outs. [img]/images/graemlins/smirk.gif[/img]

[turnipmonster]

is decisionproblem.com your site?

[Unarmed]

Nope.
The original Shania post vanished from 2+2, that guy just reposted it.

[turnipmonster]

the site seems interesting. I wonder who he is?

--turnipmonster

[Unarmed]

Ask him yourself:
http://forumserver.twoplustwo.com/sh...mp;o=&vc=1

I agree though, when Godel's incompleteness theorem finally hit me back in the day it was a pretty cool experience.