Angel, Devil, and King

Abstract

The Angel-Devil game is played on an infinite chess board. In each turn the Angel jumps from his current position to a square at distance at most k. He tries to escape his opponent, the Devil, who blocks one square in each move. It is an open question whether an Angel of some power k can escape forever. We consider Kings, who are Angels that can only walk, not jump. Introducing a general notion of speed for such modified pieces, we obtain an improvement on the current best Devil strategy. Our result, based on a recursive construction of dynamic fractal barriers, allows the Devil to encircle Kings of any speed below 2. © Springer-Verlag Berlin Heidelberg 2005.