“knowing more is less” in combinatorial games

In Complex Adaptive Systems, agents co-adapt to each other through interaction. A typical example is game: players learn and adapt to the opponent through game playing. This paper studies the adaptive characteristic of co-adaptation through a combinatorial game “Five-in-a-row” focusing on the evaluation function and game tree. The computer simulations show that a high-level player (with a good evaluation function) will win more if she knows the opponent\´s next move, but a low-level player (with a relatively worse evaluation function) will lose more if she knows the opponent\´s next move. We call this phenomenon "knowing more is less". To explore the reason and the generality of this phenomenon, an abstract theoretical model is built on a full k-ary game tree. Analysis and numerical simulations based on this model prove that “knowing more is less” will happen for a player if her evaluation function accuracy rate is below 0.5. This result indicates that during combinatorial game playing, identification of the opponent only is not enough; the player also need to improve her evaluation function for the board in the sense of mini-max solution as well.