Below is an essay I’ve written for my Carpal Tunnel post. It’s long (> 2500 words for a 2500th post, I guess). I’m posting it in MTT, where I spent most of my time since joining 2p2, and in MSNL, where I have spent more time lately.
Introduction
Recently I have put some thought into strategies for studying poker, in particular NLHE. It is frequently said that there are too many variables involved in the play of a hand for anything resembling a formulaic, component-by-component analysis to be practical. I agree with this, and agree that in even the simplest cases (short-stack push/fold calculations, for example), there is a significant margin for error in the final result which is due to necessarily imprecise assumptions about an opponent’s ranges.
So even if a poker hand is one giant math problem, complete with game theoretic opponents who do a, b, and c x%, y%, and z% of the time, it’s an unsolvable problem. That said, I think a lot can be learned from thinking about poker hands in terms of their component variables, from thinking about the structure of that giant math problem and how it could be solved if it were solvable. This essay is my attempt to categorize and analyze those components. I call it a framework for poker study, because I think that one good approach to getting better is to spend time away from the table focused on these component variables one at a time, in order to be better prepared to think through all of the relevant information when faced with decisions at the table.
Core Ideas
There are three core ideas with which I assume everyone is familiar – the concepts of pot equity and Expected Value (EV), Sklansky’s Fundamental Theorem of Poker, and what I will call “hand range calculus.”
Pot equity and EV are functions of basic probability and govern every action in a poker game. Your hand has some % chance of winning the pot, the pot contains some amount of money, so you have a claim of some part of the pot. Every bet you make is an investment; you should bet when your expected return from the bet is larger than the cost of the bet. The FTOP formalizes how to maximize your return in the special case of complete information; every time you make a bet that maximizes expectation versus your opponent’s actual hand, you win, every time your opponent fails to maximize his expectation given your actual hand, you win. “Hand range calculus”, which is the form most analyses take on these forums, acknowledges that poker is actually a game of incomplete information, and attempts to define best actions in terms of maximizing expectation versus the range of possible hands your opponent could have, in light of the range of hands it is likely he thinks you have.
Because in every case, both you and your opponent have a specific hand, the FTOP is still the final theoretical measure of what is profitable or unprofitable action. In practice, however, we work with incomplete information; thus poker skill is a combination of the ability to make best decisions within the context of “hand range calculus” and the ability to read your opponents’ ranges better than they read yours. Read the rest of this entry »