What is Hare and Hounds?
Hare and Hounds is played on a small board of 11 points: a square of three by three points, with one more point beyond the middle of its top edge and one beyond the middle of its bottom edge. Lines join the points of each row and column of the square, both diagonals cross at its centre, and each end point is joined to all three points of the row next to it.
One player has the hare, the other three hounds. The hare starts on the top end point. The hounds start on the bottom end point and the two bottom corners of the square. The hounds move first, and the players take turns, moving one piece one step along a line to an empty point. Nothing is ever captured.
The hare may move in any direction. A hound moves forward, toward the hare's end of the board, diagonally forward along a line, or sideways, never back. The hounds win by trapping the hare so that it cannot move. The hare wins by getting past all three hounds, to a point nearer the hounds' end than every one of them. It also wins if the hounds stall: when the hounds make ten moves in a row without moving forward, the hare wins on the tenth.
Rule changes
| Rule | Standard Fox & Geese | Hare and Hounds |
|---|---|---|
| Board | Standard Fox & Geese33 points on a cross, with a diagonal between every two neighbouring points. | Hare and Hounds11 points: a 3×3 square with both diagonals through its centre, and one point beyond each end. |
| Pieces | Standard Fox & GeeseOne fox and 13 geese (15 or 17 with the option in the table setup). | Hare and HoundsOne hare and three hounds. The geese count option is not used. |
| Starting position | Standard Fox & GeeseThe fox on the centre point; the geese on the row across the middle below it and on the bottom arm. | Hare and HoundsThe hare on the top end point; the hounds on the bottom end point and the two bottom corners of the square. |
| First move | Standard Fox & GeeseThe fox. | Hare and HoundsThe hounds. |
| How geese or hounds move | Standard Fox & GeeseForward or diagonally forward along a line; sideways only with the option in the table setup. | Hare and HoundsForward, diagonally forward or sideways along a line, never back. |
| Captures | Standard Fox & GeeseThe fox captures a goose by jumping over it. | Hare and HoundsNone. The hare cannot jump or capture. |
| How the hare wins | Standard Fox & GeeseThe fox wins by capturing geese until fewer than four remain, or by leaving the geese with no move. | Hare and HoundsGet past all three hounds, or wait out ten hound moves in a row that do not move forward. |
| How the hounds win | Standard Fox & GeeseThe geese win by trapping the fox. | Hare and HoundsTrap the hare so that it cannot move. |
History
Hunt games in which a single hare tries to escape several hounds were played in northern Europe for centuries. In 19th-century France a version on this small 11-point board was popular with the military and became known as le jeu militaire, the French military game. It has also been called Hare and Hounds, the game of dwarfs and the devil among tailors.
Martin Gardner brought the game to a wide audience in his Mathematical Games magazine column in October 1963, where he wrote that it combines extreme simplicity with extraordinary strategic subtlety. The rules played here are the usual ones: the hounds move first and never move back, and a hound player who makes ten moves in a row without advancing is judged to be stalling and loses.
The game has been analysed completely. Frederik Schuh, who called the board the Soldiers' Game in The Master Book of Mathematical Recreations (1968), found that the hounds win with perfect play wherever the hare starts, and Berlekamp, Conway and Guy reach the same verdict in Winning Ways for Your Mathematical Plays.