This is an archived copy of the original site of Marc Mandt
Initial Board Location Values
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].
