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BGonline.org Forums
Poker Question - How to play Heads Up NL Hold'em
Posted By: pfeifrot In Response To: Poker Question - How to play Heads Up NL Hold'em (Stick)
Date: Monday, 25 August 2008, at 1:06 p.m.
Thank you Stick. I think I havn't put enough emphasis on what the main point is.
My question is about how the perfect randomized strategy looks like.
Randomized means, that you assign probabilities on all the actions you can make. So, for every possible situation you can be in (hole cards, bet history of current hand, stack size), a probability is assigned to all possible actions for that situations. For some actions - like raising by an amount far too much - you will have a probability of 0 most of the time. Sometimes you will have a single action with probability 1 - e.g. for calling an all in with a nut hand.
Perfect means, that you will not loose on average - even if you disclose your strategy and exactly abide by it. You might not win, even if your opponent is a beginner, but you will not lose, even if your opponent is a pro. Such a strategy exists. Due to the randomized nature of the strategy, the opponent cannot put you on a hand reliably enough.
The idea is somewhat like expressed in this scientific paper: www.cs.cmu.edu/~sandholm/tartanian.AAMAS08.pdf ; The difference is, that I do not want to compute a strategy, I do not want to make any abstractions and I am not interested in how to get there (that is what they describe in the paper). I do want to know what the perfect strategy looks like (that is what they do not reveal), or at least make an educated guess what it might look like.
So, to answer your question, my winning chances, playing with such deep stacks would be exactly 50% or in other words, I will lose just as much as I will win, at least if I will be just as often the SB as the BB.
My question is rather about a cash game, not a tournament. The strategy you presented might work in a tournament only, where you will have to play until you lost all your chips. In a ring game, it would be far better to always fold your SB, at least if you look at it on a per hand basis. Fold your SB and stand, you will lose your SB only. Always go all in without looking at your cards - this is just as good as disclosing that you will always go in -, and you will be called whenever the pro has a better than average hand: You will lose something between 5% and 25% of your stack - which is considerably more than a SB.
The idea of varying the size of your raise - dependent on your hand - is not to conceal the hand. The idea is to max the profit for different hands. Still, I propose to use a randomized strategy to at least somewhat conceal the hand.
I think that the size of the stack might not matter, after it reaches a certain point, since you will never should bet more than a certain fixed factor of the pot. So, you will never ever go all in. Of course, the stacksize would matter, if my opponent would makes a mistake by going all in with a not nut hand. The bigger the stack, the bigger the error. It would be an error, to go all in with a nut hand, too, the size of the error would just not depend on the stack size. But errors of the opponent are out of my scope.
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