# Zero-sum games

## Zero-sum games

In the famous prisoner's dilemma, of which we spoke last week, a "balance of fear" occurs when both accomplices confess. Note that it is not the most advantageous option, because in this way they will fall five years in prison to each, whereas if both silenced only one year would fall; But the option of not confessing is very risky, because if the other confesses it falls ten years to silence. The "Equilibrium of value" (neither confesses) requires great mutual trust, and that is why the prisoner's dilemma is sometimes mentioned as an argument for collaboration and trust that are more profitable than selfishness and distrust. But do not be deceived: although, in general, collaborating and trusting may be better than competing and leering, in the concrete case of the prisoner's dilemma it would be foolish not to confess whether the accomplice was a unscrupulous type (a common thing among criminals). Most games are "zero-sum", that is, what some players win is exactly what others lose (especially clear when playing with money); Hence the name, because if we give positive value to the gains and negative to the losses, the total sum is zero. The prisoner's dilemma, however, is a non-zero-sum game, as there are "moves" that benefit or harm both at the same time. Equitable Games The fact that a game is zero sum does not mean that it is equitable. In roulette, for example, what the bank earns is what the players lose; But the 0 (and sometimes the 00) gives a slight advantage to the bank, which eventually becomes decisive. It is not always easy to know whether a game is fair or not. In fact, the probability calculation began with a study on the supposed fairness of a game of dice. In the mid-17th century, Antoine Gombaud, an expert gambler, had the feeling that a friend was cheating him with a falsely equitable game and asked Blaise Pascal to mathematically determine whether it was advantageous or not to bet, throwing 24 times a couple of Dice, it'll be two sixes at least once. This seemingly simple problem provoked a substantial correspondence between Pascal and Pierre de Fermat, in which the bases of the probability calculation were laid. What would my shrewd readers do to find themselves in the place of the perplexed Gombaud? Would you bet in favor of getting at least a double six by launching two dice 24 times? A clue that has some enigma: the game is so close to balance (that is, to be equitable), that it is hard to believe that Gombaud's friend did not know the probability calculation ... before his official discovery.

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