Unite 2010GDC ChinaAsia Game Show 2010GDC 2011
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Mobility and Board ControlOne of the characteristics of checkmate is that the victim has no legal moves left. Intuitively, it also seems better to have a lot of options available: a player is more likely to be able to find a good line of play if he has 30 legal moves to choose from than if he is limited to 3. In chess, mobility is easily assessed: count the number of legal moves for each side given the position, and you are done. However, this statistic has proven to be of little value. Why? For one thing, many chess moves are pointless. It may be legal to make your rook patrol the back rank one square at a time, but it is rarely productive. For another, trying to limit the opponent's mobility at all costs may lead the program to destroy its own defensive position in search of "pointless checks": since there are rarely more than 3-4 legal ways to evade check in any given position, a mobility-oriented program would be likely to make incautious moves to put the opponent in check, and after a while, it may discover that it has accomplished nothing and has dispersed its forces all over the board. Still, a few sophisticated mobility evaluation features are always a good thing. My program penalizes "bad bishops", i.e., bishops whose movement is hampered by a large number of pawns on squares of the same color, as well as knights sitting too close to the edges of the board. As another example, rooks are more valuable on open and semi-open files, i.e., files where there are no pawns (or at least no friendly ones). A close relative of mobility is board control. In chess, a side controls a square if it has more pieces attacking it than the opponent. It is usually safe to move to a controlled square, and hazardous to move to one controlled by the opponent. (There are exceptions: moving your queen to a square attacked by an enemy pawn is rarely a good idea, no matter how many ways you can capture that pawn once it has done its damage. You may also voluntarily put a piece in harm's way to lead a defender away from an even more valuable spot.) In chess, control of the center is a fundamental goal of the opening. However, control is somewhat difficult to compute: it requires maintaining a database of all squares attacked by all pieces on the board at any given time. Many programs do it; mine doesn't. While mobility is less important than it seems to the chess programmer, it is extremely important in Othello (where the side with the fewest legal moves in the endgame is usually in deep trouble). As for board control, it is the victory condition of Go.
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