A Guide to the RiskAverse Gambler and Resolving the St. Petersburg Paradox Once and For All
By Lucy Martinez and Doron Zeilberger
.tex
.pdf
Journal version .pdf
[Published online before print in the College Mathematics Journal, volume and page number tbd]
We use three kinds of computations: Simulation, Numeric, and Symbolic, to guide riskaverse gamblers in general, and offer
particular advice how to resolve the famous St. Petersburg paradox.
Written: July 2023
Maple package
Sample Input and Output for StPete.txt

If you want to see advise for the riskaverse gambler on how many times to insist on playing the gamble :
You lose one dollar with probability (i1)/i and win i dollars with probability 1/i
(or equivalently: You lose i dollar with probability (i1)/i and win i^{2} 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 riskaverse 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 (i1)/i and win i dollars with probability 1/i" for riskaverseness, 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 (i1)/i and win i dollars with probability 1/i" , for i from 2 to 20,
for riskaverseness, 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 riskaverseness 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
 Here is the
riskaverseness graph for the gamble [[1,1/2],[2,1/2]]
 Here is the
riskaverseness graph for the gamble [[1,2/3],[3,1/3]]
 Here is the
riskaverseness graph for the gamble [[1,3/4],[4,1/4]]
 Here is the
riskaverseness graph for the gamble [[1,4/5],[5,1/5]]
 Here is the
riskaverseness graph for the gamble [[1,5/6],[6,1/6]]
 Here is the
riskaverseness graph for the gamble [[1,6/7],[7,1/7]]
 Here is the
riskaverseness graph for the gamble [[1,7/8],[8,1/8]]
 Here is the
riskaverseness graph for the gamble [[1,8/9],[9,1/9]]
 Here is the
averseness graph for the gamble [[1,9/10],[10,1/10]]
 Here is the
EXACT averseness graph for the 7round St. Petersburg Gamble with Entrance Fee 7,
for n from 1 to 300.
 Here is the
Approximate averseness graph for the 7round St. Petersburg Gamble with Entrance Fee 7,
for n from 1 to 2000, using the Central Limit Theorem approximation.
 Here is the
Approximate averseness graph for the 11round St. Petersburg Gamble with Entrance Fee 11,
for n from 1 to 10000, using the Central Limit Theorem approximation.
Articles of Doron Zeilberger
Doron Zeilberger's Home Page
Lucy Martinez's Home Page