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Game theory and poker

Game theory was developed by John Nash in 1950 as distinct branch of mathematics.  We know that poker also has a strong mathematical element to it so we wondered if we could understand poker better by applying game theory to it.

Game Theory Helps Players Win by Defining All Actions as Logical

First of all, game theory has two different names depending on who is talking about it.  Mathematicians call it game theory whilst social scientists usually use the term “the theory of social situations”.  In both cases, we are talking about a unique interaction between two groups or two individuals.

As competitive as poker is, it is also clearly a social situation.  One of the things we like about watching poker on YouTube is the banter between and amongst the players.  The banter is often calculated to misdirect an opponent.  This is a major aspect of game theory.  it emphasizes the fact that the eventual outcome of a hand is always the result of the decisions each player makes.  So, if one player confuses the other and wins the pot as a result, it is perfectly in line with game theory.

As such, we might say that the talking players do, may have strategic value as they seek to maximize their advantage in subsequent hands.

Game Theory and Online Poker

One of the facts of life about online poker is that we can’t see our opponents or hear them talk.  The interactions between individuals are different if they are playing poker online rather than in a land-based casino.  There is much more visual data that players can process when they can see their opponents.  Game theory may actually have more important applications to poker online than to land-based poker.

For poker players and enthusiasts, we are also talking about the “non-cooperative” side of game theory.  It is clear that the cooperative aspect of game theory works better in the political arena but it doesn’t reflect reality in zero-sum games such as poker.

Exploitative Play in Poker

So, the outcome of every hand depends on each player’s decisions and there is little to no cooperation between players.  In fact, cooperation is often against the rules.   Therefore, we often say that poker is a game in which every player tries to exploit both an opponent’s weaknesses—which is obvious— but also the strengths of their opponents—which is dramatically counter-intuitive.

He Knows that I Know

Game theory as it applies to poker tries to simplify the strategic needs of each player.  Without a coordinated theory, most hands would boil down to a series of circular analyses.  Instead, we can use the theory that John Nash developed to focus more closely on what an opponent is thinking about.

In order to take poker out of the circular nature of hand analysis, we need to understand that game theory as it is applied to poker means that there is an inherent logic to every step we take in poker.  It may be that we fold with the best hand but there is still intrinsic logic behind even that decision.  Game theory here means that one player’s decisions—even ultimately wrong ones—are rooted logically in the prior actions of our opponents.

Expected Value

This is the value of winning a pot before the pot has been built.  Game theory posits that in order to confuse one’s opponents, every player should at some point in a match make a bet that is quite out of character and defies logic.  The very fact that these types of bets defy logic is what makes them so strong.

When an opponent is trying to simplify the betting sequences in a hand and is trying to ascertain if the opponent is bluffing or not, he will reach a point where his analysis cannot continue because the opponent has made a bet that he can’t explain.

Adjusting to Conditions

Game theory provides the best basis for adjusting to situations over the table.  There are so many changes in a single poker hand that you need to apply the notion that your opponents are following perfect strategy in order to properly evaluate how you will proceed.

Game theory considers every action by a poker player to be in accord with perfect strategy even when it isn’t.

Using game theory helps you avoid getting all twisted up mentally when you’re trying to analyze a hand either how to proceed yourself or how to react to an opponent’s action.

Getting twisted up is the colloquial way of saying getting lost in circular thinking.  Circular thinking is a fallacy in logic but in complex analyses it’s often hard to avoid it.  The same happens in poker as we have to balance so many elements into trying to determine what the hidden cards are.

Level Analysis

If you can bet for value or bluff in the same hand range, you should bluff from time to time to throw opponents off the best analysis of your actions.

Level-based thinking from the 90’s had players going through permutations like he knows that I know that he knows that I know.  This is the circular analysis we spoke about earlier.   Very few people can hold so many twists in their heads on any issue from political theory to game theory or game play.

Game theory states that in the long run it’s impossible to outsmart a game but it is possible to play any game in such a way as to enhance your chances of winning.

Level analysis takes away the complicated twists in analysis and simplifies all analyses into “levels”.  In theory, you determine your opponent’s level and play in accordance with your decision.  You also assume that he or she is using the best strategy at their level. 

At one time, the flighty play of inexperienced and weak opponents confused better players.  Now, we can see that the weak and inexperienced players are using perfect strategy at their level.  Level analysis takes what was once very unreliable analysis against weak or inexperienced players and turns it to your advantage.   

Weak players don’t know or understand the minutiae of poker but in game theory it doesn’t matter.   When they make a bet that makes no sense, game theory says to see it as logical within their framework.   Then you can exploit the inferiority of their framework and win at poker.