On a board of size n×m, each player begins with m pawns, one for each square in the row closest to them.
Hexapawn on the 3×3 board is a solved game; with perfect play, White will always lose in 3 moves (1.b2 axb2 2.cxb2 c2 3.a2 c1#).
Indeed, Gardner specifically constructed it as a game with a small game tree in order to demonstrate how it could be played by a heuristic AI implemented by a mechanical computer based on Donald Michie's Matchbox Educable Noughts and Crosses Engine (MENACE).
If one restricts 3×N hexapawn with the additional rule that capturing is always compulsory, the result is the game Dawson's chess.
[1] Dawson's chess reduces to the impartial game denoted .137 in Conway's notation.