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Poker Digest I
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The Inside Scoop

This month’s The Inside Scoop and The Poker Digest cover aspects of Game Theory as it relates to Poker. Game theory was first conceptualized by John von Neumann, who along with Oskar Morgenstern published their 1944 treatise “Theory of Games and Economic Behavior.” Even back then, poker was well known enough to the general public that von Neumann used poker hands to diagram certain game-theory problems.

   The Zero-Sum Dichotomy

By Daniel L. Cox

Editor, Poker Insider Magazine

February 1, 2011

Poker Professional Max Shapiro once quipped, "They say Poker is a zero-sum game. It must be, because every time I play my sum ends up zero?"

Mathematicians and serious students of Hold'em strategy have long looked into the concepts of game theory as they relate to poker. Game theory is the branch of mathematics dealing with the decision-making process in situations where two or more players have competing interests, which describes poker extremely well. 2000 WSOP Main Event World Champion Chris 'Jesus' Ferguson did not get his poker background in back room games, instead he studied optimal poker strategies from an academic viewpoint, leaning heavily on his understanding of game theory garnered while obtaining his doctorate at UCLA.

Due to the influence of game theory, many poker experts consider poker to be a zero-sum game. The concept may be true when considering the pure form of poker. Unfortunately, this is incorrect when it comes to casinos, poker rooms or most home games. The reason is simple, when mathematicians discuss the zero-sum aspect of poker; they fail to consider the affect the rake has on the game.

In game theory, the zero-sum game is a special case of a constant-sum game in which the gains or losses of one player exactly balance the gains or losses of the other players. When you add the total gains of the participants and then subtract the total losses, the sum is zero. In poker terms, as one player's chip stack increases, other player or player's stacks shrink. Therefore, zero-sum games are also known as strictly competitive games. This is one of the features that makes poker the most popular game in the world.

As previously mentioned, in its purest form, poker is a zero sum game. For example, place ten equally skilled players in a $2-$4 Limit Hold'em ring game with a $100 buy-in. The deal rotates around the table, with the players dealing the cards themselves. Without allowing the players to replenish their stacks and none of the players getting involved in an All-in situation, there is $1,000 in play on the table. For this scenario, the players complete 30 hands an hour. If, on average, each player wins one $50 pot each circuit of the table, each player will end their six-hour game with the same $100 they started with. Since the players are dealing in this scenario, tipping the dealer is not a factor, either. This is the basis for the erroneous belief that poker is a zero-sum game.

Unfortunately, when money is involved, people rarely play poker in this pure form since the rake is such a huge part of the game. The rake is how poker rooms profit from poker players. The casinos charge a percentage of each pot as 'rent.' In essence, the rake is the amount of money the casino or card room charges for the use of its cards, chips, dealers and floor personnel. One of the most important items casinos provide is security. As little as thirty years ago, robberies and worse were common occupational hazards of the back room poker games in Texas, New York and California. Doyle Brunson, commenting on his days as a Texas road gambler, "People today who play in all the big fancy card rooms don't understand what it was like back in those days to be a poker player with all the problems we had."

The rake is not the only way the house charges rent. In high-limit cash games, where a percentage of each hand would be prohibitively high, they charge an hourly table rent to each player. Even most organized home games ask for some form of remuneration from the players in home games are routinely asked to 'donate' to the host an amount equal to their portion of the evenings costs.

In a normal $2-$4 game, the house rake is typically 10%, capped at $5. For every $50 pot a player wins, the house takes $5 off the top. For this example, we will not consider the option of the poker room taking something off the top of each hand for Jackpots or other promotions. Most of the time in a casino environment the dealer also gets a tip from one to five percent of the pot.

Using our previous example, with each player starting with $100, they will all go broke before the end of a six-hour session. Though the statement seems unbelievable, it is easy to figure. On average, for each $50 pot, the house collects a $5 rake and the dealer receives a $2 tip. Each player wins once every ten hands, which equates to three hands an hour. Therefore, your net loss is $21 an hour, which means that three-fourths of the way through the fifth hour, each player will have no chips left in their stack, the house will have made approximately $720 and the dealers will have collected $280.

Though it is true that many commonly perceived aspects of game theory are useful when studying poker, even the most casual player easily can see the dichotomy of poker as a zero-sum game. When placing the precepts of game theory onto Texas Hold'em, insure you look deeper into them, not trusting the basic concepts to be the complete answer.