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we will leave them separate so that we can control how smart our AI appears. We
also leave them separate because one version is easier for humans to see than the
other. Both of these points are game-design issues. We want our AI to play like a
human and we want to easily control how well it plays.
So how will the rule work? It takes a revealed square and attempts to use a nearby
square as a helper. In the simpler version of the rule, the nearby helper is adjacent
to the original revealed square. The two squares need to share some blank
squares, and the original square also needs to be adjacent to some blank squares
that are not shared. The helper square computes the minimum number of mines
and the minimum number of clear squares that are in the shared squares. These
numbers can be zero but not negative. If either number is greater than zero, the
helper has provided the original square with potentially new information. The
original square already has information about all of its squares, but the helper
gives information about a subset of them. If the minimum number of mines in
the shared squares is equal to the number of mines the original square has not yet
placed, the original square can safely click all the squares that are not shared
because it knows that all of its mines are somewhere in the shared squares. If the
minimum number of clear squares in the shared squares is equal to the number
of unknown clear squares around the original square, then all the non-shared blank
squares around the original square must be mines. This rule does not act on the
shared squares; it acts on the original square's private squares. If your brain is in
danger of exploding, perhaps a picture will make the situation clear (see Figure 4.6).
The upper 1, with the dark border, is the helper square. The lower 1 is the original
square. The rule will not work the other way around because the upper 1 has no
private blanks. The lower 1, the original square, has three private blanks, in
addition to four shared blanks. The helper can compute that at least one mine
must be in the shared squares; it sees one mine, and the only thing around it is
shared squares. The original square needs to place one mine, and the helper just
told it that at least one mine is in the shared squares. That was all the mines
the original square had left to place, so the private squares must all be clear. If
there are any flags nearby, they adjust the various numbers, but the method is the
same. Note that the move is in the original square's private blank squares. The
two squares do not yield enough information to safely determine anything about
the shared squares. Note that the move consumes all the private blank squares.
The same method also places mines. If the original square had been a 4 and
the helper square remained a 1, the helper would report that there are at least
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