Mobility and Spatial Advantages

Mobility is a measure of the number of choices (legal moves) a player has in a given position. It is often used as a term in the evaluation function of chess programs. It is based on the idea that the more choices you have at your disposal, the stronger your position. A study of tournament games in which the material balance was still even after the 20th move showed a definite correlation between a player's mobility and the number of games won. In computer programs, mobility is sometimes calculated differently than simply by summing up the number of legal or pseudo-legal moves. Often, it is done piece-by-piece, and the mobility bonus per possible move is not always the same for each type of piece (e.g. in the opening, the mobility of the bishops and knights is more important than that of the rooks). Sometimes forward mobility is scored higher than backward mobility, sometimes (in case of rooks) vertical mobility gets priority over horizontal mobility. Also, if a piece can move to the square of another friendly piece, sometimes that move is also counted - although it would not be a legal move, it is protecting the friendly piece, and therefore still serves a useful role.

Said the physician and chess master Siegbert Tarrasch, "Cramped positions bear the germs of defeat." Mobility and spatial advantages are key to a positional understanding of chess. A spatial advantage in a game will allow you to move your pieces from one edge of the board to the other faster than the opponent. In general, the side with a weak pawn or weak square to defend has a spatial disadvantage, as he would have by reason, needing to huddle up all of his pieces together to defend that weak point. A spatial advantage allows you more territory to maneuver through. If your opponent has a spatial disadvantage, this is a long-term plus for you. The spatial advantage allows you to build up slowly, letting your opponent stew in his own juices for as long as you want him to. The advantage in space will not go away. The principal idea of a spatial advantage is to not make too many exchanges. Think of a bottle of water. If you have a spatial disadvantage and your pieces are the water, the air is the remaining maneuvering space you have. But as the water is drunk (pieces get exchanged), there is more space for you, and material is still level.

In the following puzzle, White (Keres) has his pieces at their optimal posts. Every piece is pressuring a weak point in Black (Capablanca)'s position. The queen is especially well-posted; she is attacking both weak pawns at a6 and c6. Black's chances of surviving this game are pretty bad, but he can still struggle on. Therefore, White creates a third weakness and Black's position collapsed: 22.Ne6! Qb8 23.Ng5! Rb7 24.Qg4 Bf4 25.Rc4 Rb5 26. Nxf7!! White sacrifices his knight to create a kingside weakness, for after 26....Kxf7 27.Rd7+ and White wins due to the weakness of the g7-pawn. Black declined the sacrifice with 26....Re8! 27.g3 Qc8, hoping to alleviate the pressure by making the transition into an ending. However, Black's game is still lost due to the organic weaknesses on a6 and c6. 28.Rxf4 Qxg4 29.Rxg4 Kxf7 30.Rd7+ Re7 31.Rxe7+ Kxe7 32. Bxg7. White is up two pawns and won on move 38.