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The World Of Information and Game Theory

Jul 7, 2014

game-theory-070714Game theory

Information theory created the framework around which both the modern digital world, and card counting in casinos, are based.

Turning decision making into a science rather than an art form was process that developed from around the 1940s onward in response to a problem all telephone companies had with long distance communications. Build a long telephone wire and the quality degrades over distance, stick an amp half way and the signal will still be strong, but you’ll be amplifying the distortion too.

Shannon and his cohorts developed a system whereby all information was turned into a positive or negative state that could be used to transmit the symbology of all communication. It didn’t matter if it were words, numbers, music, imagery, whatever, it could all be encoded down into a series of bits. These bits (single pieces of yes/no information) became the common denominator of information.

Bits revolutionized communications… then the world. The microprocessor you’re using to read this, the internet you got it from, the drive you might store it on and indeed any compression you care to use to make it smaller, they all still work on binary information, they still work on bits. At the time this was a paradigm shift in thinking that some have compared to the work of Einstein.

Rational betting through Game Theory

• A system for winning at blackjack

• Modern world based on information theory

• Bits connecting the pieces

Shannon’s pursuit of digital logic in the late 1940s is directly responsible for most of the modern technology we now take entirely for granted. It is even responsible for the manner in which a great many people spend their time winning at blackjack. Counting cards is merely information theory used in a very specific way.

Game Theory

John Larry Kelly Jnr worked for Claude Shannon at the Bell Telephone Lab and felt “Information theory can be thought of as a way of quantifying information so as to make the best decision in the face of imperfect information” and one of the situations in which there was imperfect information was at the blackjack table.

The history of Blackjack is full of people with “a system” but perhaps for the first time a mathematical basis was applied not to winning a single bet or hand, but to win over the long term growing the bankroll of the player. This fractional betting of payroll based on the maximization of opportunity as against risk is still the basis of card counting strategies.

The mathematical formulas of information theory are now being applied to the relatively simple construct of a card game, and the pursuit of the best possible response to each circumstance. This is regardless of decisions made by the opposition, the dealer, because there’s no control over that side of the situation.

The Kelly Criterion is an established and proven theory of not just gambling per se but of any speculative action. The application of these theories and formulas has been as successful on wall street as they have in Las Vegas or, indeed, the laboratory. Game theory is merely the part of information theory that explores how we use information for our own advantage.

Prisoner’s Dilemma

The idea that there is a logical basis for decision making despite imperfect information was best summed up in the prisoners dilemma, an example of game theory. Two prisoners held apart and incommunicado must choose to either betray their fellow prisoner or stay silent. Each possible permutation of their actions has a different outcome.

If they both betray each other they’ll get both get 2 years in the chokey. If either one betrays the other they’ll be set free but the other will serve 5 years inside. And if they both stay schtum they’ll only get 1 year each in prison on a lesser charge. So now what is the best course of action for each one?

Well if both are purely rational the logical thing to do is for both to betray each other, because that is the promotion of self-interest. The betrayal of the other is the best course of action regardless of the other prisoner’s action. Either you get 2 years each for betraying each other, or if the other prisoner didn’t you’re going to go free. This is better than the possible 5 year stretch you’ll be doing if you don’t.

This example of game theory is quite esoteric as it denies the possibility of cooperation (something humans tend towards most of the time) and also demonstrates that you should never commit a crime with a scientist or mathematician because they’ll grass on you. In the real world game theory of this nature is applied to business in Wall Street just as much as it is to blackjack in Asia. Rational choice made from known data.

Read more about Claude Shannon, blackjack and information theory.

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