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

TL;DR

This paper analyzes the game 'Perpetual Motion' using Monte Carlo simulations, revealing that about 54.55% of games can be completed while the rest cycle indefinitely, raising questions about cycle lengths.

Contribution

It provides the first computational analysis of 'Perpetual Motion,' quantifying the probability of game completion and identifying the prevalence of non-terminating cycles.

Findings

Approximately 54.55% of games are completable.

45.45% of games result in non-terminating cycles.

Cycle lengths in non-terminating games remain an open question.

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.