MATHEMATICS 177 CHESS
FREEDOM and SPACE in chess

 Definition 1. The FREEDOM NUMBER of a piece is the number of squares to which the piece can legally move (excluding the square it currently occupies). Definition 2. The FREEDOM NUMBER OF YOUR POSITION (at some moment during a game) is the sum of the freedom numbers of all pieces in that position, including king and pawns. Definition 3. The SPACE of a piece is the number of squares in your opponent's half of the board to which the piece can legally move, excluding the square it currently occupies. Opponent's half of the board is encircled in the figure at the right. Definition 4. The SPACE of a position is the sum of the spaces of all pieces in the position, including king and pawns.
 Opponent sits here You sit here

Classroom exercize: fill in the empty boxes of the table below.

 piece Bishop queen king knight rook pawn Maximum freedom number on an otherwise empty board. Locations of piece at which maximum freedom number is attained

 Note 5. Chess positions with larger FREEDOM NUMBERS are more flexible and more easily changed to take advantage of new ideas and/or new problems.
 Note 6. Chess positions with larger SPACE are better suited to supporting an attack on your opponent's king, which usually sits at the opposite side of the board (encircled in the figure above).
 Note 7. Both FREEDOM and SPACE are more useful tools in the middle game and opening, and less useful in the endgame, when pieces are fewer and can move more easily across the board (even the king).

In class, students must pause 3 times during an actual game to calculate the FREEDOM NUMBER and SPACE for both themselves and their opponents.

 move number My total freedom number My opponent's total freedom number My total space My opponent's total space