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black squares'' and the more complex ''fewer moves for the fox'' bites them, so we
will fix it.
This last evolutionary step is to change how the black squares were counted. If the
fox cannot get to an open black square, that square should not count in
the computation. Otherwise, the hounds could be distracted into making a move
that reduces the number of black squares but does not reduce the moves available
for the fox. Late in the game, most moves for the hounds reduce the total number
of black squares by one. All such moves are equally good, and if the line is intact,
the hounds do not look ahead. Look back at the sequence of boards shown in
Figure 6.6. After the fox has taken move 41, there are two moves for the hounds
that do not break their line. The first is to move the hound near the center of the
board down and to the left, directly toward the fox. The second is the one shown
as move 42 in Figure 6.6: The right-most hound moves down and to the right,
placing it on the last row. Using the na¨ve method of counting black squares, each
of these hounds' moves reduces the number of black squares by one, giving them
identical evaluation scores. The hounds do not have any moves that reduce the
number of black squares more than one; in fact all of their other moves break the
line. The two moves we are considering do not give identical results! The first
move we considered will bring victory to the hounds on their next move when
the fox retreats to one of three squares, each of which allows the hounds to trap it.
The second move, shown as move 42 in Figure 6.6, leads the fox to make move
43 as shown, which dooms the hounds.
A more sophisticated way of counting black squares prevents this from hap-
pening. We count a black square in the board evaluation score only if it has a
hound on it or if the fox can get to it. In Figure 6.6, there is a black square after
move 41 in the bottom row that becomes a white square with the number 2 after
move 42. In the na¨ve counting method, this square counted as a black square for
the evaluation score. It is the square that lead the hounds to make the ill-fated
move shown. Under the better method for counting black squares, this black
square does not count in the evaluation score because the fox cannot get to it.
The coloring algorithm colors it black after move 41, but it no longer counts in
the score. The two moves that do not break the line no longer have identical
scores; the hounds will now prefer the winning move of pushing the center
hound directly at the fox.
We will implement both ways of counting the number of black squares. The code
for this will be described in the next section when we deal with game state. The
ColorMe routine will call either NaiveBlackCount or BetterBlackCount to get
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