The perfect card sharp

NOUGHTS and crosses (known as tic-tac-toe in America) is one of the first games children learn. The more inquisitive among them soon realise there are strategies that always win if your opponent makes a mistake, and guarantee a draw even if he does not. (The best is to start out in one of the grid’s corners.) When a provably ideal strategy such as this is discovered for any given game, mathematicians describe that game as being “solved”.

Using computers, quite a few games have now been solved in this formal mathematical sense. These include Connect Four, nine-men’s morris and draughts. One thing those examples have in common is that they are “perfect information” games, meaning each player knows, at all times, everything that is going on. Not all perfect information games have been so solved. Chess has not. Neither has Go. But no non-trivial “imperfect information” game, such as one involving playing cards, has ever been solved formally.