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Lobnek Newsletter, February 2021

The St. Petersburg Paradox

Lobnek Wealth Management,  February 2021

“Everything that happens once can never happen again. But everything that happens twice will surely happen a third time.”

Paulo Coelho (1947 - ), Brazilian novelist


Daniel Bernoulli, the famed 18th century Swiss mathematician known for his pioneering work on probability theory, was living in St. Petersburg around 1738 when he stumbled upon a curious anomaly in game theory1. Whereas the “expected value” of a random variable with a finite number of outcomes is the probability weighted average of those outcomes2, he noticed that when the expected value approached “infinity”, people began to behave somewhat “irrationally”. This is best illustrated with an example where the participant in a game of chance is offered to toss a coin in which an initial payoff of $2 is doubled if the outcome is heads and the game terminates if the result is tails. The mathematically derived expected value in this instance happens to be infinite, because there is a chance, even if it is slim, that the payoff ends up being infinitely large3. This would happen if heads were to turn up at every single flip of the coin which, of course, would also mean that the game never ends.

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Lobnek Wealth Management

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