How opponent's information affects combinatorial game

Bounded rationality is a typical characteristic of decision making process. Our previous work shows that in combinatorial games bounded rational players with more opponent information may lead to worse outcomes - this surprising phenomenon is called “knowing more is less”. This phenomenon happens in special situations when the accuracy rate of the player's evaluation function is below a critical value 0.5. This paper studies this phenomenon in a more general framework: (1) player X predicts player Y's next move correctly with a probability, which is called preciseness rate; (2) With a probability (called completeness ratio) player X knows player Y's next move, otherwise player X makes decisions based on the ordinary Minmax process. Our results shows that when the accuracy rate of player X is below 0.5, higher preciseness rate and completeness ratio lead to lower winning probability of player X; while the accuracy rate of player X is above 0.5, higher preciseness rate or completeness ratio increases the winning probability of player X. So the critical value of player X's accuracy rate is remained 0.5.