Game Theory and Poker (Part II)

See also Game Theory and Poker (Part I)

Efficiency and Diminishing Returns.
The concept of efficiency and the notion of diminishing returns relate to the conservation and the most effective use of power/momentum and resources. In poker this is about a player's chips, cards and table image. These two concepts are particularly helpful to the no-limit player when it comes to "pricing" bets and raises.

In any game, and most especially in no-limit poker tournaments, a player's "Mo" (power) comes from an amalgamation of

1. His image at the table.
2. The size of his stack.
3. The strength of his hand.

If a player is rich in one, he can lean on the other two. If a player has a very strong hand, not only will he win chips, he will add to his image at the table. If he is possessed of a strong image, he can steal with smaller bets. If his stack is huge, players with smaller stacks will often avoid conflict and he will be able to play weaker hands.

In tournament poker, a player's stack goes down in value with the passage of time. At any point, a player's stack size is finite and, therefore, he must carefully consider pricing when he makes his bet. He must consider

1. At what price will his opponent be "priced out" of the hand.
2. At what price will his opponent be "priced into" calling.
3. Given a careful study of the opposition, what is the best price to achieve the best result without risking more chips than absolutely necessary.

Conventional poker wisdom has long held that a primary obligation of the big stack is to knock out the small stacks. A game theorist would say that the primary obligation of the big stack is to not pump up the small stacks. The increasing stakes and other, more desperate players will eliminate most of the short stacks — which will leave the big stacks to carefully pick their spots and eliminate anyone left.

Strategy.
The value of applying Game Theory principles in any arena is primarily to help a player develop an efficient strategy that dominates the competition.

From a practical perspective, Game Theory is about strategic development. As no effective strategy is likely to be developed in a vacuum, its formation must be the result of a close study of not only the opposition but also past interactions.

As more players play more poker, many of them increase their skills, and the result is that the game becomes ever tougher to beat.
The players who have dominated the game in the past and the players who will do so in the future are the few who can convert the common knowledge available to every player at the table into more complete knowledge.

Assuming that all greatly successful players are possessed of advanced knowledge of or instinct for odds and strategy, the primary property of their game that differentiates them from the rest of the field is an uncanny ability to discern an opponent's strength and likely action or reaction.

Today the bulk of poker is about one game — No-Limit Texas Hold'em. In a game where you can either greatly in-crease or lose all your chips in a single move, knowledge of opponents and their tendencies in certain situations becomes much more important than either stack size or the power of a hand.

With complete information on odds and strategy available to a growing and increasingly more able and competitive pool, the one area of opportunity open to aspiring poker kings is the study and application of Game Theory in poker.

The most difficult calculation in all of poker, especially in No-Limit Texas Hold'em, is that of a player's Total Odds of winning the pot. This calculation includes far more than the odds of making a certain hand — it includes the odds of making the hand, the likelihood that your opponent's hand is stronger or weaker, and (most difficult of all) the probability of an opponent's action or reaction to your action or reaction.

The only hope of coming to a reasonably accurate calculation of this matrix of probabilities is via the very essence of Game Theory. You must make a detailed and almost instantaneous analysis of your opponent and his strengths, weaknesses and other propensities.