Quote:
Originally Posted by antialias
Well, as you note this only works if the opponent makes an error - so this is not solution but rather the usual "give the opponent opportunities to make a mistake"-play.
A solved game means you win even if the opponent makes the best possible move every time (e.g. the one who makes the first move in connect four can win if he makes no mistakes - and there is nothing the opponent can do about it).
Are you seriously claiming that
tic-tac-toe is not a solved game?
A 'solved game' is just one where the optimal moves for every possible outcome have been computed. IIRC, tic-tac-toe only has about 138 terminal board positions. A 12 year-old could solve it, and computers in the early 1950s played it perfectly.
A game being "solved" doesn't mean you always win. The solution is the one that is a Nash Equilibrium, wherein all rational players minimize their losses (or maximize their winnings) by making the optimal move, even if it merely delays the opponent's victory, or minimizes their score.
In many games (such as some chess endings, and tic tac toe) the solution, from a particular decision point - if both players act optimally - is a draw.
In a prisoner's dilemma with simple payouts, and where both prisoners act rationally in their best interest, and in the knowledge that their co-conspirator will do likewise, no one 'wins'. Both prisoners still go to jail.