Enigma 1284: Os and Xs offside
22 October 2014
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From New Scientist #2442, 10th April 2004 [link]
We are playing ordinary noughts and crosses but with two extra rules:
(i) A player may not go in the centre square if going in the centre square puts that player in a position which is better for them than every other position they could have gone to instead.
(ii) If after eight turns no one has won and the centre square is empty then the game ends and is declared a draw.
For the purpose of rule (i), position P is better for a player than position Q if either (a) the player can force a win from P but not from Q, or (b) the player can force a draw or better from P but not from Q.
If, in a game, O goes first and each player plays as well as possible, is the result a win for O, a win for X or a draw?
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.