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Economists’ Untold Secrets 133: Gambling I

This video explains why people bet unfair games, offers stochastic explanation, and explains the St. Petersburg Paradox. This is my theory of betting. AB is the wager money, AC is the winning amount. The -1 line represents fair game. You will bet, if your EP lies higher than the fair game line. But, that is not usually the case. In most games, the EP is lower, so they
are unfair games. But, why do people still bet? Attached to the EP is a distribution. This distribution means that some people may still win, even if the game is not fair. However, when the distribution becomes concentrated at the EP, it makes no sense to bet any more, for it is a definite loss. When people bet too many times, their distribution becomes concentrated. This is called the central limited theorem. In the extreme, when the betting number is infinity, the distribution becomes a single line with zero variation. This is called the law of large numbers. So, you may bet once or twice, you should not bet continuously. This also explains the St. Petersburg Paradox: that people may wager $2 for the first bet, but not $4 for the second.

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