The Infinite Money Paradox

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Deciding whether to play a game is usually very easy… you crunch the numbers and if they work in your favor, you play. If they don’t, you shouldn’t. Mathematical case closed.

But what happens when the math of a game tells you that you have access to infinite wealth and unlimited expected value and real life tells you not to play? Enter: The St. Petersburg Paradox.

The Bernoulli family first started corresponding about the paradox in the early 1700s with a series of letters examining the puzzling math behind the simple game. But it wasn’t until 1738 when Daniel Bernoulli realized that he could factor real life utility — how much something actually means to you — into the calculations.

The St. Petersburg Paradox opens up doors to how we think about what math really means to us, including modern research into Prospect Theory and everyday issues like whether we decide to buy life insurance. And in the end, one thing we know for sure: we’re all much, much more than numbers.

*** SOURCES ***

Original Bernoulli family correspondence: http://cerebro.xu.edu/math/Sources/NBernoulli/correspondence_petersburg_game.pdf

Play the St. Petersburg Paradox game: http://www.mathematik.com/Petersburg/Petersburg.html

“Ending the Myth of the St. Petersburg Paradox,” by Vivian Robert William: https://mpra.ub.uni-muenchen.de/50515/1/MPRA_paper_50515.pdf

“St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described,” by Paul Samuelson: https://www.jstor.org/stable/pdf/2722712.pdf

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