KnightFighter: so with your current rules, each player will be able to land on or move through exactly 40 of the 64 spaces on the board. (if you don't understand why, get out a board and try it.) so depending on the placement of each players pieces, it might be possible for 24 spaces to be 'untouchable'.

What if each player had 2 pieces that start in opposite corners. so one player's pieces would start in the upper left and lower right corners, and the other player's pieces in the upper right and lower left.