“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.