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 07-09-2008, 06:47 PM #2 mvdgaag veteran     Join Date: Dec 2006 Location: Delft, the Netherlands Posts: 2,336 Re: Understanding Game Theory and Hold'em Thanks a lot!
 07-09-2008, 07:26 PM #3 mvdgaag veteran     Join Date: Dec 2006 Location: Delft, the Netherlands Posts: 2,336 Re: Understanding Game Theory and Hold'em I have a game theory question about how to apply it to my real game. I put a simple headsup NL/potlimit holdem game here as an example. This game has either a nuts/nothing or 0..1 distribution. This doesn't really matter. All bets are pot sized. A can bet or give up (in which case B wins the pot) and B can call or fold. I found that if we give up directly after being called we can easily find an overall strategy for each street individually as long as we know we can make our opponent indifferent between his actions on the next street. A bets 100% of the time. He gives up a% of the time when called. B calls b% of the time and folds the rest. If A gives up B wins the pot plus the bet = 2p. If A doesn't give up, B should also be indifferent on the next street we play, so he loses this bet = -1p. For B to be indifferent on this street A can give up 33% of his hands and bet the other 66% on the next street. Since A is risking p to win p, B should call a minimum of p/2p = 50% of the time, for A's bet not to be directly profitable. Now if we get to the river, B has a much stronger range than A and for B to be indifferent here, A should be having the winning hand 66% of the time when he gets called. But A still has 16/27 of his starting hands, while B has made a tighter selection of 1/8 and will optimally only call half. So he will have far more equity than the 33% A can allow him to have and make him indifferent here. The assumption that on the next street B can be made indifferent is only true if we replicate the same trick. Not if there's an actual showdown. So to apply this to an overall strategy in real holdem, without getting too specific, we should be working back from the river. We need the best hand 66% of the time, so on the previous street we only need expect to have the best hand at the river 4/9 of the time, the street before that 8/27, etc. I solve a lot of these mini games when I'm travelling to work, since I got plenty of time in the train then, but I never figured out how to translate these ideas and concepts to practical plays in more specific situations. How do I go about and figure out where to put this agression, on what boards and with which hands?
 07-22-2008, 07:41 AM #4 Nichlemn Carpal \'Tunnel     Join Date: Oct 2007 Location: The water hemisphere Posts: 9,464 Re: Understanding Game Theory and Hold'em I'd like to note that one of the reasons GTO strategies are unnecessary (except for what you mention about understanding how much your opponents deviate from it) is the employment of table selection. If you and your opponent play perfectly, the GTO strategy is best, yes, but you'll both lose to the rake. Only if your opponent was able to play some parts of the game perfectly but had significant leaks in others would you ever want to play a Nash equilibrium.
07-22-2008, 12:07 PM   #5
mvdgaag
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Join Date: Dec 2006
Location: Delft, the Netherlands
Posts: 2,336
Re: Understanding Game Theory and Hold'em

Quote:
 Originally Posted by Nichlemn I'd like to note that one of the reasons GTO strategies are unnecessary (except for what you mention about understanding how much your opponents deviate from it) is the employment of table selection. If you and your opponent play perfectly, the GTO strategy is best, yes, but you'll both lose to the rake. Only if your opponent was able to play some parts of the game perfectly but had significant leaks in others would you ever want to play a Nash equilibrium.
Sometimes you don't know how your opponent plays in certain spots. It's never wrong to choose near optimal plays in those spots while you can always make a big mistake if you choose your standard exploititive play.

 07-22-2008, 02:01 PM #6 The Bryce Stoxpoker Sponsored Forum     Join Date: Oct 2005 Location: Edmonton Posts: 4,245 Re: Understanding Game Theory and Hold'em Nice breakdown mv, at a glance it looks solid. That sort of analysis can tell you a lot about 3 barrel bluffing. You would know that if your opponent makes it to the river with a hand he intends to call with less than 50% of the time HU you could exploit him/her by bluffing more, for example.
 07-24-2008, 07:51 AM #7 BetaPro adept   Join Date: Apr 2008 Location: Montreal Posts: 1,031 Re: Understanding Game Theory and Hold'em Thanks so much. I asked you for this article.
 07-25-2008, 12:41 AM #8 JarnoV adept   Join Date: Nov 2007 Location: generating rake Posts: 960 Re: Understanding Game Theory and Hold'em I just wanted to make a couple of minor remarks. First is that GTO doesn't always make the opponent completely indifferent for the actions, but rather it makes indifferent at the thresholds of the regions. Therefore, it's not only dominated strategies that lose value against unexploitive strategy, but those deviations too that aren't at the indifference thresholds. Second, while this is just a short article and cannot go into depths discussing GTO, I think it's still important enough idea that it should be mentioned that the bluffing frequency is always proportional to the value-betting/raising frequency. If you would throw a X-sided dice at river to decide whether to bluff or not with a hand that has little chance of winning the showdown otherwise, it would not guarantee a suitable frequency for bluffing. It would be pretty difficult to exploit, but it wouldn't be completely balanced.

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