# The St. Petersburg Paradox: A Subjective Probability Solution

- Hongbin Wang,
*Texas A&M University*
- Yanlong Sun,
*Texas A&M University*
- Jack Smith,
*Texas A&M University*

## Abstract

The St. Petersburg Paradox (SPP), where people are willing to pay
only a modest amount for a lottery with infinite expected gain, has been a famous
showcase of human (ir)rationality. Since inception multiple solutions have been
proposed, including the influential expected utility theory. Criticisms remain
due to the lack of a priori justification for the utility function. Here we
report a new solution to the long-standing paradox, which focuses on the
probability weighting component (rather than the value/utility component) in
calculating the expected value of the game. We show that a new Additional
Transition Time (AT) based measure, motivated by both physics and psychology, can
naturally lead to a converging expected value and therefore solve the
paradox.

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