What is paradoxical about the St. Petersburg Paradox

Petersburg paradox

The Petersburg paradox is intended to make it clear that the general application of the Bernoulli criterion as a decision rule can lead to nonsensical consequences. In the Petersburg game, a player tosses a coin until the number falls. The game is over when a number is dropped for the first time on the nth throw. If number falls on the nth roll, then the player is paid 2 "monetary units. If tails already come on the first throw, he receives 2 monetary units, on the second throw he receives 22 monetary units, and so on. The probability that on the first throw The number falls is 1/2. The mathematical expectation of the payoff for the game is infinite. If the Bernoulli criterion were to be applied, participation in this game would have to be preferred to any other alternative course of action with a finite expectation, which is generally not considered to be a sensible behavior.

Constructed game of chance, which is pointed out as an argument against the usefulness of the g, principle as a decision rule for risky situations: An ideal coin is tossed until "number" appears for the first time. If this is the case with the first throw, the player receives 2 DM; If "number" falls in the second throw, he receives double the amount, i.e. 4 DM; If "number" only appears on the third throw, the profit is twice that again, ie 8 DM, etc. The mathematical expected value for the profit that can be achieved in this game is infinitely high. If the —1.1 principle is applied, everyone else would have to take part in this game. Alternative action with finite expected value, e.g. B. a gift of 1000 DM or 1 million DM, which would generally hardly be regarded as sensible behavior.

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