On the Chances of Completing the Game of "Perpetual Motion"

Abstract

This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated games. The key result is that 54.55% +/- 0.89% of games can be completed (by a patient player!) but that the remaining 45.45% result in non-terminating cycles. The lengths of these non-terminating cycles leave some outstanding questions.