MATE WITH THE TWO BISHOPS IN KRIEGSPIEL

Thomas S. Ferguson

Abstract:

In kriegspiel, it is known that in general position with no immediate loss of a piece, mate with the rook can be accomplished surely, and mate with the bishop and knight can be accomplished almost surely. In this paper the problem of mate with the two bishops is considered. It is shown that this is a win for the player with the two bishops. Interestingly, there does not exist a strategy that wins with probability one if the king and two bishops are in the center of the board, say King at d4, Bishop at d5 and Bishop at e5. However, if the king and two bishops are along an edge, say King at b4, Bishop at b3, and Bishop at c3, then mate may be accomplished surely, and in the suggested position, mate may be accomplished in at most 32 moves. Some consideration is also given to larger sized boards and to an infinite quadrant.