Sneaky Angel and Devil Game

TL;DR

This paper introduces an imperfect information variant of the Angel and Devil game, proving that the Devil still has a winning strategy, thus extending previous results to a more complex game setting.

Contribution

It proves that the Devil wins in the imperfect information variant, generalizing the original game's known outcome to a new, more complex version.

Findings

Devil has a winning strategy in the imperfect information game

Generalizes previous results from the original game

Extends understanding of game strategies under imperfect information

Abstract

In this paper we introduce an imperfect information variant of the Angel and Devil game, which was first introduced in 1982 by Berlekamp, Conway, and Guy. The Devil player has a winning strategy in this game, but the main problem they pose is whether this changes if the Angel player is allowed two moves for every one of the Devil. This and many other variants of the game have been considered, and the original question was only solved in 2007, when it was shown that the so-called power 2 Angel could win. Our main theorem, Theorem 4, is that the Devil player wins the imperfect information variant of the game. This generalizes the result that the Devil player has a winning strategy in the original Angel and Devil game.