Tuesday, February 10, 2009

Theories of poker

This is a reprint of Chapter 10 in The Complete Book Of Hold 'Em Poker: A Comprehensive Guide to Playing and Winning
Chapter 10

Theories of Poker

Poker theory is a topic that takes much more than a chapter in a book to cover completely. At least two books devoted almost entirely to poker theory have been written, and neither of those books even attempts to fully cover the topic. The point of this chapter isn't to give a complete review of poker theory, but to provide a summary of how poker theory provides direction to strategic and tactical thinking in poker.

One problem in poker theory is that many poker analysts who write books or magazine articles about poker don't seem to really understand how theory influences thinking about the strategy and tactics of the game. Most analysts have a favorite theory about the game, and whenever they are confronted with a situation for analysis, they immediately view the situation through their favorite perspective. There are many alternative theories of poker, and a complete analysis of the game requires a frequent shifting of theoretical perspective.

In most fields it's not unusual for researchers or analysts to blur the distinction between the theory of some phenomena and a model based on the theory. That's particularly true in the poker literature. A theory of poker and a model of poker, however, are really distinct things, and I think it's important to understand that distinction when you're thinking and learning about poker.

What is a theory?
A theory has three characteristics: descriptive, explanatory, and predictive. None of these characteristics are necessarily explicit or even complete in any particular theory. A good theory is usually one that can be simply stated in one or more straightforward declarative sentences that has desirable implications for describing, explaining, or predicting observed behavior of the phenomena under study. A good theory doesn't need to do all three of these things. A good theory, however, does need to have some strong explanatory power. A theory that doesn't help us understand the game doesn't really help all that much.

An example is a simply stated theory of poker is: Poker is a struggle among the players for the rights to the ante. This theory doesn't lend much towards describing poker. It doesn't tell us how the betting is structured to facilitate the struggle among the players. It doesn't tell us how to determine which player ends up with the pot.

The theory does have some explanatory power for the first round of betting. It explains why it's usually best to limit your opening hands to those hands with self contained power rather than those that have value through drawing power. Since it does not address the pot growth that comes from multiple betting rounds, it adds nothing to an explanation of the value of hands like Jack, 10 suited in Hold 'Em.

The theory has some predictive power, but not much. A theoretical prediction for poker should provide us with a prescription for play - it should tell us something about the best way to play the game. For poker variants with multiple betting rounds, like Hold 'Em, it just doesn't do that. It does help us predict things like a tight range of likely hands that a knowledgeable player who opened from early position might have.

An example of a theory with a different kind of predictive power is: Money flows from bad players to good players. This theory doesn't have much descriptive power; it doesn't tell us who the good and bad players are. Assuming we have some other method to identify good and bad players, it does help us predict the outcome of a poker session. In fact, I used a simple mathematical model of that theory to develop the recommendations in Chapter 8 for when a single really bad player in a game can make an otherwise unprofitable game profitable.

What is a Model?
A model is a structured representation of a theory. It's descriptive of the theory, not necessarily descriptive of the phenomena. Often we can use a model to derive the predictive elements of a theory. A model might be in the form of an explicit mathematical statement, or it might just be a conceptual structuring.
An example is a game theory model of the Poker-is-a-struggle-for-the-ante-theory. You can use a game theory model to derive a list of opening hands by position. In relatively tight games, where it's typically heads-up after the first round of betting we can use that same game theory model to determine the hands with which we should be willing to call an opening bet. We can extend the use of the same model to determine when to bet, call, or bluff on the river.

For a game like draw poker, where in most games the players tend to be relatively tight and you only have two rounds of betting, you can use a game theory model to almost completely specify a winning playing strategy. That approach, however, just doesn't extend for a game with more than two betting rounds. It doesn't help all that much for a game like Hold 'Em.

Although a game theory model does help us analyze some situations, a game like Hold 'Em requires a different approach to the game. Hold 'Em is very complex and it's doubtful that we could formulate a complete model of the game - even if we could do so, the mathematics of solving it would very likely be intractable. We can, however, develop theories related to particular aspects of the game, and use the models that those theories suggest to analyze tightly defined situations.

The game theory model suggested by the ante theory is one such use. As I've already mentioned, that model can be used productively to analyze opening hand requirements in tight game conditions.

Another model is suggested by the theory that Poker is a struggle between made hands and drawing hands. This theory suggests the use of a multinomial probability model to analyze the play of drawing hands. By multinomial I mean a model that assumes multiple discrete outcomes, such as win large pot, win small pot, lose small pot, or lose large pot. Multinomial is like flipping a coin with more than two sides. A dice game is an example of a multinomial game.

The theory that Money flows from bad players to good players suggests a conceptual model of the game that implies that table selection involves looking for a table with large pots. This step from theory to model is not always an obvious one. But, it's an important one in an analysis of the game.

Variables in theory
Implicit in a theory of poker is the concept of a variable. This is something that might change value or might even be a constant with an indeterminate value. By indeterminate I mean we won't know its value until the hand is over. For example, the hand we are dealt is a variable. It's a special kind of variable in that it's random, but it's not indeterminate -- we know our hand as soon as we look at it.
The hand our opponent is dealt is also a variable, in the same way our hand is, but it's indeterminate, we won't know his hand until the showdown. By the way, my description of the hand you've been dealt as a random variable is something of an example of what I talked about earlier in the blur in the distinction between a theory and a model. In the extreme it's not really correct to call the deal random - once you've specified the initial order of the cards, tracked the exact shuffle and cut the deck it is perfectly deterministic and predictable. Of course, we don't keep track of things like the exact shuffle so it makes sense to just think of them as occurring as the result of randomness. Randomness is a model of the shuffling process, not a theory of shuffling.

Strategy and tactics
Although it's not directly relevant to theories and models, I think here is a good place to differentiate between strategy and tactics. Strategy is about the metagame. An optimal strategy is one that maximized your expected playing result over some period of time, maybe a playing session of a few hours, maybe a longer period such as months or years. Tactics are about the individual decisions that make up the play of the hand. An optimal tactic is one that maximizes the expected result of the particular situation.

The topics we've already discussed, game and seat selection, are strategic issues. There is no expectation of an immediate payoff from picking a good game or a good seat. In fact, there is no possibility of an immediate payoff. No one is going to toss you a few chips as soon as you sit down.

Playing poker as a string of tactically optimal plays does not generally lead to an optimal strategy. However, an optimal playing strategy will lead to optimal playing tactics. The reason for this is that a focus on strategic issues will tend to maximize the opportunity for profit. Without maximizing opportunity, you can't maximize profit. For example, if you consistently play in a game where the other players just aren't going to lose much money, then no amount of tactical superiority will win as much money as you would win by playing in a game where the other players will always just play until they go broke. Strategic issues, such as game selection, come first. Only then can you rationally deal with tactical issues such as a choice of what hands to play. In poker, it's usually the case that strategy focuses on the other players, and tactics focuses on the cards. The distinction isn't really that sharp, but you won't go far wrong by thinking of strategy and tactics in these terms.

Uses of Poker Theory
Poker theories help us gain a deeper understanding of inherent elements of the game. They help us develop a perspective of the game. Some of the current poker theories are given in the table below.

Table 10-1

Theoretical perspectives and game conditions

Perspective Game Conditions

Poker is a struggle among the players for the rights to the ante Very tight, tight

Money flows from bad players to good players all game types

Poker is a game of money and odds loose and very loose games

Poker is a game of partial information Very tight, tight, typical, loose, aggressive
Poker is a game of strategy and deception Very tight, tight, typical, aggressive

Poker is a contest between a made hand and a drawing hand Tight or typical

Poker is a game of kickers and hand domination Tight or very tight

Poker is a game of manipulation and pressure Typical, loose, very loose

As you can see, each of these different theoretical perspectives essentially focuses on the key variable of some particular facet of the game. No one of these theoretical perspectives provides a complete theory of poker, but each of them has its uses in developing a complete understanding of the game.
Uses of Poker Models
A poker model helps us explore the implications of a particular theory. It's through the analysis of either a formal mathematical model or a conceptual model of a theory that we can uncover the strengths and weaknesses of a particular theoretical perspective. A good poker model isn't going to try to reflect every nuance and quirk of a poker game. We can use explicit poker models, inspired by the appropriate theoretical perspective, to analyze the effects of a wide range of decisions; from deciding whether to play in a particular game or deciding whether to raise with an A A.
An example of a model is an Equity Model. PokerStove (downloadable from www.pokerstove.com) is an example of an implementation of an Equity Model.
Equity is the percentage of wins of a hand in a given situation. It’s not just the percentage of time that a hand will win, equity computation includes split pot situations as a half a win.
Some poker TV shows give hand equities of situations, some just give expected win probabilties, ignoring split pots. Some of the TV equity calculations include what’s known about discarded cards, some don’t.
A General Theory of Poker
We don't have a general theory of poker. By a general theory I mean a unified theoretical view that encompasses most, if not all, of the commonly accepted theoretical perspectives of the game. Some of these perspectives are:
Poker is a struggle among the players for the rights to the ante
Money flows from bad players to good players
Poker is a contest between a made hand and a drawing hand
Poker is a game of strategy and deception
Poker is a game of partial information
Poker is a game of money and odds
Poker is a game of manipulation and pressure
Poker is a game of kickers and hand domination
Poker is a game of implied odds

All of these theoretical perspectives are useful. No one of them is better than the others. Each is useful in a different aspect of the game. At different parts of this book, we look at poker through different perspectives. You've already seen two examples of this.
In Chapter 8, on game selection, we looked at poker through the perspective that money flows from bad players to good players. We used that perspective to identify games that involve many players putting a lot of money into the pot as profitable games.
Some poker players argue that the best games are those when the players are passive, preferably loose/passive, but also tight/passive. The reason they come to that conclusion is that they are looking at poker through a perspective of strategy and deception. A weak game of passive players does afford you more opportunity at using advanced strategies and deceptive plays, but that's not the most important source of profit in poker.
It's not a question of which perspective is superior to the other. It's a question of which perspective is more useful in helping to answer the question at hand. In the case of game selection, the key variable is the amount of money available. The money-flow perspective focuses on this key variable, and is the preferable perspective to use when considering selection of a game.
In Chapter 9, on seat selection, we looked at the game with a different perspective. There the focus was on the point of view suggested by a strategy and deception perspective. Most poker writers seem to look at seat selection through a prism of a partial information perspective.
One major difference in seat selection strategy that results from these different perspectives is in the case of maniacs. A common recommendation is to sit with the maniac to your immediate right. I suggest the opposite, sit with either him on your immediate left or half-way across the table from you. What is the reason for the difference? It's because of the difference in focus from the two different theoretical perspectives.
If you use a partial information perspective you'll want him on your right to ensure you have as much information as you can get before you have to act. There is nothing wrong with that except: We are talking about a maniac, someone who plays almost every hand and raises at every opportunity. How much more information can you have? You get very little extra information from having a maniac on your right. But having him on your left expands your tactical playing options tremendously.
Poker is a struggle among the players for the right to the ante
This perspective has relevance in the early parts of the first betting round. In Hold 'Em we use blinds rather than antes, but the point of the perspective is that the game begins as a struggle for the initial money in the pot. It's a useful perspective in determining opening hand requirements, particularly in somewhat tight games and from early position.
Money flows from bad players to good players
The premise of the ante-theory is that without some initial seed money in the pot, you have no game. The point of view of the bad-player perspective refutes that, however, with the observation that some players play so badly that they'd be willing to play even if the pot had no money to start with at all.
Poker is a contest between a made hand and a drawing hand
This is a perspective of a simple two-player confrontation where one of them has the best hand and the other has a possibility of becoming the best hand. It's a useful perspective to use when analyzing situations where you're fairly certain that you either have the best hand or are fairly certain what the best hand is. This perspective is not useful, and in fact can lead you far astray, once you have more than two or three players competing for the pot.
Poker is a game of strategy and deception.
This perspective has a focus on making advertising plays to establish a false image, outwitting your opponents by bluffs and semi-bluffs, and using position to steal pots.
Poker is a game of partial information
This perspective views poker as a mathematical game. The focus is on evaluation of information about your hand and the probable hands of your opponents. The idea of partial information games is derived from game theory.
Poker is a game of money and odds
This perspective is a view of poker where pot size and drawing odds are the important variables. It's a particularly valuable perspective for play in loose games and some aggressive games.
Poker is a game of manipulation and pressure
This perspective is similar to the strategy and deception perspective. The difference is primarily more of an emphasis on false image than on tactical uses of position. Players who view the game primarily through this perspective tend to use a lot of table talk to manipulate and confuse opponents. Amarillo Slim was a master of this. Other's who view the game through this perspective tend to apply pressure by playing in a fast, aggressive style. The current master of the techniques suggested by this perspective is probably Mike Caro.
Poker is a game of kickers and hand domination
This is an important perspective in tight games or in any games where tight players have entered the pot. The emphasis is on the added value of having two high cards rather than one. Of course, two high cards have value because of the increased probability of flopping the top pair, but the domination perspective focuses on the card that does not have a match on the board -- the kicker.

Poker is a game of implied odds
In deep stack no-limit games it’s often more important to think in terms of the possibility of winning future bets than it is to be concerned with current hand value.

What it all means
Which theoretical perspective you use to analyze a situation just depends on the situation and the game-condition context of the situation. Before you finish this book, you'll see examples of using all the theoretical perspectives to analyze the game. That's the key to developing a dynamic approach to the game. Developing the ability to quickly shift your point of view is the first step in being able to adjust to changes in game conditions - the key to winning poker.