11. (16 points) A and B are playing a game on a $20 \times 15$ chessboard. At the beginning, a queen is placed on a square of the chessboard except for the top-right corner; starting with A, the two players take turns moving the queen. Each move can be along a straight line or a diagonal, but only to the right, up, or up-right; the player who moves the queen to the top-right corner wins. There are 287 starting squares on this chessboard that give A a winning strategy.
【Solution】
The shaded squares total 13.
The chessboard has a total of $20 \times 15=300$ squares,
$$
300-13=287
$$

Therefore, the answer is 287.
11. (16 points) A and B are playing a game on a $20 \times 15$ chessboard. At the beginning, a queen is placed on a square of the chessboard except the top-right corner; starting with A, the two players take turns to move the queen. Each move can be a straight or diagonal move of several squares, but only to the right, up, or up-right; the player who moves the queen to the top-right corner square wins. How many starting squares on this chessboard allow A to have a winning strategy?