Some words from the author: Note that on the first move, only one piece is flipped, due to the
checkerboard setup of the board. Note also that a winning row is one that
contains one "group" of color--either all white or all black. If, at the beginning of a turn, a player has a row that contains two "groups", they
have a winning move, as one group can always be flipped to match the second (unless this would simultaneously create a winning row for the
opposite side). A row with three groups is also a winning row, because the middle group can always be flipped to match the outer groups. So the
strategy boils down to reducing the number of groups in one's own rows, and increasing the number in one's opponent's. Also, it is not necessary
to have a row containing only two or three groups to win in one move. For
instance, if a row consists of three white groups and two single black pieces, it is possible to flip the two black pieces to white, if they are
on converging diagonals. Of course, when making a move, the diagonals work against one at least as often as they do in one's favor, and one
finds oneself saying, "I would move here, except...." But that's what makes walking through a minefield difficult.
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