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| Nicolás Bernoulli |
In 1713, Nicolás Bernoulli formulated the St. Petersburg paradox, which can be
summarized as follows:
Let us consider the
following game: a coin is tossed. If it comes up heads, you receive $2. If it comes up
tails, it is tossed again. If it comes up heads, you receive $4. If it comes up
tails, it is tossed again. And so on. With each toss, the prize is multiplied
by 2. How much would you be willing to pay to participate in the game?
The probability of winning $2 is 0.5; the probability of winning $4 is 0.25; the probability of winning $2k is 2-k. The expected value is obtained by multiplying each value by its probability and adding them all together. So the expected value of the profit that could be obtained by playing that game is:
