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computer-go: Mathematic Go
Mathematic Go theory has achieved some quite interesting results regarding
the end games. It demonstrated that in many end game situations, the best
score can be calculated from the topological properties of the position alone
and the look forward search is not needed. This success raise the hope of a
'magic formular' for winning Go games.
However, the extension of these theories to the other parts of the game (such
as the middle game) is met with difficulties. The reason is that there are
just too many possible positions to be enumerated as required by existing
mathematic Go thoery. I think there maybe one way to avoid this problem.
Instead of studying the game positions, one may study the mathematical
properties of the empty Go board. Since all possible game positions are
completely pre-determined by the mathematical properties of the Go board and
the set of Go rules. This becomes interesting that one may find the 'magic
formular' by not studying the game, but ,instead, the empty Go board. It
would be very interesting if someone can prove or disprove that such an
approach is possible. One possible justification of this appraoch is that the
Go boards can cost much more than the Go stones. A clear demonstration of the
importance of the Go board.
Dan Liu