In order to translate the importance of board locations to a computer
algorithm, an 8X8 matrix of integer values could be used. This gives
us 64 board locations with each of them needing a value. If we allow each
board location to have a possible value range of -20 to 20, this gives
us approximately 3.4 E102 potential board configurations. That is a few
too many board configurations to investigate. However, careful inspection
of the symmetry of an 8X8 othello board gives 10 unique board location
values:
This reduces the solution set to 1.0 E16 possible board configurations.
This is still quite a large number but, believe it or not, the size of
the solution set has been reduced by more than 99.9%. A genetic approach
to finding the best 10 values for the board is probably the best. However,
without taking an organized approach, but more hit and miss trials, I believe
the best initial board values to be very close to
Looking at these board values, you can see that, as you probably
expected, the corners are given a very high value. Yet the locations immediately surrounding
the corners are given a negative value. This is because these surrounding
locations, if occupied before the corner is taken, typically create an
opportunity for the opponent to take that corner.
[7] The location on the diagonal and next to the corner is the most
dangerous place on the board. If your piece occupies this location, then
your opponent has the ability take that corner within 2 moves over 90%
of the time. Hence, I have given that location the nickname of "corner
give" and a value of -10.
[3] The locations next to the corner but not on the diagonal are dangerous
as well. However, there are several occasions when it is a smart move
to occupy those locations. So it earns a negative value but not nearly as
extreme.
[10] The locations at the center of the board earns a value of 0
because it is anticipated that it will change hands so often that there
is no inherent value in owning it.
[2] There is yet another, not so obvious, set of key locations about
a quarter way down each side of the board. These locations have a high
value of 5 because they are meant to create a bias for gaining control of
a side. Consider that on a given side, both of these key locations are owned
by a given player.
One can now see that if the opponent was to place a piece in any
of the locations marked by the X's, then it could be immediately regained
by black. Furthermore, in all 4 possible cases, black would retain a position
of undiminished strength along the side. However, it is worth noting that
this is only really an effective strategy if no other board locations on
that side are previously owned by either player.
In fact, most of these board values discussed above would change
depending on the state of the game. For example, the "corner give" [7]
would no longer be a "corner give" if the corner was already owned. Thus
if the corner is already owned, the value of the "corner give" should change
accordingly.
Note: In order to properly calculate the value of a move, you must not
only consider the value of the location you moved to, but all locations
gained as a result of that move [a.k.a. impact flips].
