On Zermelo's theorem

TL;DR

This paper extends Zermelo's theorem to all finite-stage two-player games of complete information with alternating moves, establishing that one player always has a winning or unbeatable strategy.

Contribution

It generalizes Zermelo's theorem beyond chess to a broader class of finite, complete information, alternating move games.

Findings

Either the first or second player has a winning strategy.

Both players can have unbeatable strategies.

The result applies to all finite-stage two-player games of complete information.

Abstract

A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all finite-stage two-player games of complete information with alternating moves. It is shown that in any such game either the first player has a winning strategy, or the second player has a winning strategy, or both have unbeatable strategies.