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:

board5

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

board6


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.

board7

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].

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Copyrightę Marc Mandt, 2001
mmandt@mindspring.com