1. Introduction

The game of Quadraphage, invented by R. Epstein (see [3] and [4]), pits two players against each other on a (generalized) m x n chess board. The Chess player possesses a single chess piece such as a King or a Knight, which starts the game on the center square of the board (or as near as possible if mn is even); his object is to move his piece to any square on the edge of the board. The Go player possesses a large number of black stones, which she can play one per turn on any empty square to prevent the chess piece from moving there; her object is to block the chess piece so that it cannot move at all. (Thus the phrase “a large number” of black stones can be interpreted concretely as mn - 1 stones, enough to cover every square on the board other than the one occupied by the chess piece.) These games can also be called Chessgo, or indeed Kinggo, Knight go, etc. when referring to the game played with a specific chess piece.

Quadraphage can be played with non-conventional chess pieces as well; in fact, if we choose the chess piece to be an “angel” with the ability to fly to any square within a radius of 1000, we encounter J. Conway's infamous angel-vs.-devil game [2]. In this paper we consider the case where the chess piece is S. Golomb's Duke, a Fairy Chess piece that is more limited than a king, in that it moves one square per turn but only in a vertical or horizontal direction. In this game of Dukego, we will call the Chess player D and the Go player G.

Berlekamp, Conway, and Guy analyzed the game of Dukego in [1], drawing upon strategies developed by Golomb.