## Optimal vs. non-optimal strategy in poker

Let me start this article with some basic concepts on game theory: what is game theory? and, first, what is a game?

A game describes situations in which different agents interact “strategically” choosing rationally actions that maximize their individual targets up to a set of specified constraints.

The game theory proposes criteria to resolve and define the results of “strategic” interaction.

The term “strategic” is used to mean the fact that every agent’s choice of actions depends on his knowledge or expectations about the behavior of other interacting agents.

In 1921, Emile Borel, a French mathematician, published several papers on the theory of games. He used poker as an example and addressed the problem of bluffing and second-guessing the opponent in a game of imperfect information. Borel’s ultimate goal was to determine whether a “best” strategy for a given game exists and to find that strategy. While Borel could be arguably called as the first mathematician to envision an organized system for playing games, his ideas remained rough and vague.

Just a few years later, in the 1928 article, “Theory of Parlor Games”, John Von Neumann initiated the discussion of “game theory”. Also for him the inspiration for game theory was poker, a game he played occasionally and with poor results. Von Neumann realized that poker was not guided by probability theory alone and formalized the idea of “bluffing,” a strategy that is meant to deceive the other players and hide information from them.

In The Theory of Poker, David Sklansky utilizes game theory to discuss whether or not to call a possible bluff. He writes:

“Usually when your hand can beat only a bluff, you use your experience and judgment to determine the chances your opponent is bluffing . . . However, against an opponent whose judgment is as good as yours or better than yours, or one who is capable of using game theory to bluff, you in your turn can use game theory to thwart that player or at least minimize his profits.”

But what game theory really teaches you is to play “well”, in the sense of optimally.

In game theory, an optimal solution is also called an “equilibrium”.

But while this might be desirable in certain situations (e.g. in politics or economics), it is certainly not so desirable in poker.

In poker if you use the optimal strategy, your opponent cannot profit through superior play, but he also cannot suffer through inferior play. By playing “optimally” you have created a situation in which your opponent’s choices, good or bad, will have no effect, exactly an equilibrium situation, you don’t lose and you don’t win. What a waste of time!

Remember that the heart of poker is struggle!

So what you should do is to choose a non-optimal strategy which takes advantage of the mistakes of your opponents. You must play non-optimally in order to win. But, on the other hand, to capitalize on your opponent’s mistakes, you must play in a way that leaves you more exposed to the chance of being attacked.

Let’s consider for example the situation in which your opponent is bluffing too much. To take advantage of this, you should raise your calling frequency above the optimal frequency. Once you do this, however, your opponent could stop bluffing and take advantage of your calls. As soon as you realize he has done that, you will reduce your calling frequency, and so on. In this way, you and your opponent’s bluffing and calling frequencies oscillate, sometimes above, sometimes below the optimal frequency.

That being said, there is still value in understanding the theoretical aspects of optimal play. In order to profit, as seen for example, from your opponents’ bluffing, you should know when bluffing is too much, that means, of course, bluffing more times than the optimal value. So you should know what the optimal strategy is in order to decide, at any moment, on the proper counter-strategy against your opponent.

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