This is a very simple game played with chess pawns. The machine will learn from its mistakes and win more and more often.
As in chess, a pawn may move forward one space into an empty square, or capture an enemy pawn by moving diagonally forward one space. If you get a pawn to the last row, you win. You also win if you capture all the enemy's pawns, or if the enemy cannot move.
You always play white, and you always go first. Click on a pawn to select it, then click on the square where you want it to move to.
Hexapawn was introduced in Martin Gardner's Mathematical Games column in the March, 1962 issue of Scientific American magazine. He gave instructions for how to construct a machine out of matchboxes that will learn to play a perfect game. The article was reprinted in his book, The Unexpected Hanging.
The way my machine learns is based on my earlier project, Mimi learns from you: http://scratch.mit.edu/projects/16714501/
It would learn more quickly if it recognized mirror-image positions, so I'll probably add that before too long.