Mobility

Piece mobility is an important concept in the strategy of Othello. The position below may appear to be clearly winning for black, since the score is so much in its favor. Yet, the position is in fact winning for white. This is because black has little options as to where to play. In this case, black doesn't even have a move and must pass. Therefore white has the ability to control black's moves and as a result the direction of the game:

Mobility is irrelevant at the beginning of the game, since it is difficult to predict the outcome of the game so far in the future. The closer we get to the middle game, however, mobility becomes increasingly important for maximal control. Altough this must not be carried too far: by the end game, having maximal control with a high losing score does not leave much room for recovery:

Here, no matter what, white has very little chance of a come back. Thus mobility can be relinquished in favor of other criteria by the end game. A parabolic function normalized to the game's progress provided the gradient by which mobility was emphasized:

In the above graph, maximal score is emphasized when the board is nearly empty or full, and minimized during the middle game when the board is about half full. This has the indirect effect of determining piece mobility.

Although the normalization parameter and increasing width of the middle game portion parameter could have been made available to the genetic program as terminals, it was decided to keep these within program control mainly for speed of execution. Likewise, a quadratic function, rather than exponential function was used for speed.

Two terminals were therefore added: white_mobility and black_mobility. Using a white player as an example, a high value is returned if white has a high score at the beginning or at the end of the game, but a low value if white has a high score during the middle game. The converse is true: a low score is given for low score at the beginning and end of the game, and high value for a low score during the middle of the game.

Once again, the genetic program could have determined these terminals from the other terminals; it would have just taken more time to evolve.

Performance

Surprisingly, the number of evolved trees which used this feature were small. This may be because these terminals were overshadowed in terms of performance by the finer-grained symmetrical terminals. It is suspected that longer runs would introduce such 'advanced' tactical features in the evaluation trees. (It was noticed that when global features, such as white, black, empty, white_mobility, or black_mobility, were used, these were generally deeper in the trees. This reveals a finer exhibition of control than if these tactical terminals were used exclusively or on a high level.) On the other hand, when trees did make use of these two terminals, they were very small, often only one or two levels deep.