A Return-Probability Perspective on the St. Petersburg Paradox
Year: 2025
Type: article
Abstract: The classical St. Petersburg paradox is based on the infinite expected value of a simple coin-toss game. Mathematically, this suggests that a rational player should be willing to pay any amount to participate. In practice, however, no one would pay a fortune for such a game. This paper presents a simple alternative approach: instead of relying on expectation, we examine the probability that the payout exceeds the entry fee. This criterion yields an intuitive threshold: once the entry fee surpasses 4, the probability of breaking even drops below 50%. For higher fees, the probability declines rapidly (e.g., only 0.39% for X = 500). This perspective reconciles mathematical theory with everyday intuition and decision-making. It also highlights how different, yet equally correct, mathematical approaches (expected value vs. return-probability) can lead to opposite conclusions.
Author: Bubenicek, Milan
Language: English
Subfield: General Decision Sciences
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7082292013
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