A Guide to the Risk-Averse Gambler and Resolving the St. Petersburg Paradox Once and For All

By Lucy Martinez and Doron Zeilberger

.tex

[Published in The College Mathematics Journal, v. 55 (2024), 226-234]

We use three kinds of computations: Simulation, Numeric, and Symbolic, to guide risk-averse gamblers in general, and offer particular advice how to resolve the famous St. Petersburg paradox.

Written: July 2023

# Maple package

• StPete.txt, a Maple package to advise the risk-averse gambler with particular applications for the St. Petersburg paradox.

You also need to put in the same directory in your computer the following file:
StPeteData.txt,

# Sample Input and Output for StPete.txt

• If you want to see advise for the risk-averse gambler on how many times to insist on playing the gamble : You lose one dollar with probability (i-1)/i and win i dollars with probability 1/i (or equivalently: You lose i dollar with probability (i-1)/i and win i2 dollars with probability 1/i for i from 2 to 15 (without the very complicated recurrences, that are distracting)
the input file yields the output file

• If you want to see the above information with the very complicated recurrences,
the input file yields the output file

• If you want to see advise for the risk-averse gambler how many times to insist on playing various finite forms of the St. Petersburg gamble:
the input file yields the output file

• If you want to see more succinctly, advise for playing "You lose one dollar with probability (i-1)/i and win i dollars with probability 1/i" for risk-averseness, for i from 2 to 15 1/10,1/100, 1/1000, 1/10000,
the input file yields the output file

• If you want to see advise for playing "You lose one dollar with probability (i-1)/i and win i dollars with probability 1/i" , for i from 2 to 20, for risk-averseness, but using the Central Limit Theorem Approximation (so you get cutoffs slightly bigger than necessary) for risk averseness 1/10,1/100, 1/1000, 1/10000,
the input file yields the output file

• If you want to see advise risk-averseness cutoffs for the finite versions of the St. Petersburg game, with i rounds, for i from 3 to 20, using the Central Limit Theorem approximation (so you get cutoffs slightly bigger than necessary) for risk averseness 1/10,1/100, 1/1000, 1/10000,
the input file yields the output file

# Pictures

Articles of Doron Zeilberger