24. The St.-Petersburg paradox

This paradox has the direct relation to global catastrophes as shows that infinitely big damage from the extremely rare events has bigger weight, than all other events, however psychologically people are not ready to apprehend it. G.G. Malinetsky so describes this paradox in the book ăRisk. Sustainable development. Synergetrics": "We will consider the following game. The coin is thrown until the heads for the first time will not drop out. If it was required n throws the prize will make 2n units. That is prizes 2,4,8, ╔ 2n will occur to probability 1/2,1/4,1/8, ╔ 1/2n. The expected prize in this game is infinite:

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It is asked, how much a man is ready to pay for the right to enter into such game. The paradox consists that the majority of people is ready to pay for this right no more than 100, and sometimes only 20 units╚.