a perfect logician playing Chess will make the most logical move that will make them mostly likely to win, but determining the best move always involves some degree of predicting the other player's behaviour. if I move the knight here, they will logically have to take it with the bishop. but that sort of planning assumes the opponent to also be a perfect logician. a less logical opponent will be more unpredictable to a logician. being unpredictable has potential to beat logic. being very illogical will make it harder for the logical player to predict your moves
Sometimes crazy people arnt really as crazy after all but that is one way. An awesome way as well. Who was that chess player that showed up super late to a match and keep everyone waiting???
Test your driving skills through busy streets full of obstacles to avoid police pursuit in smashy road. Have fun.
Actually, if you're doing it right, then the illogical player doesn't really have an advantage Just because their moves may be surprising doesn't mean they are better moves than the logical players, and it certainly doesn't mean they should win the game.