An analysis of two modifications of the Petersburg game

TL;DR

This paper examines two variants of the Petersburg game—truncation with finite capital and borrowing costs—and derives limit theorems to assess their profitability.

Contribution

It introduces and analyzes two modifications of the Petersburg game, providing limit theorems to evaluate their outcomes.

Findings

Limit theorems for truncated game with finite capital.

Limit theorems for game with borrowing costs.

Framework to judge game favorability.

Abstract

Two modifications of the Petersburg game are considered: 1. Truncation, so that the player has a finite capital at his disposal. 2. A cost of borrowing capital, so that the player has to pay interest on the capital needed. In both cases limit theorems for the total net gain are derived, so that it is easy to judge if the game is favourable or not.