Game Theory & Decision
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St. Petersburg Expected Value

A game with infinite expected value yet little real worth.

Formula

EV=∑k=1∞12k2k−1EV = \sum_{k=1}^{\infty} \tfrac{1}{2^k} 2^{k-1}

Variables

EVExpected value
kRound number

Example

The sum diverges to infinity, yet nobody would pay much to play.

Did You Know?

The St. Petersburg paradox (1738) forced mathematicians to invent utility — value isn't just expected cash.

game theoryparadoxexpected value

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