Reversi (Othello) — Strategy
VOG — Vinco Online Games
Frontiers
Each move is played to an empty square adjacent to an opponent's disc. This is the principal which will guide us in the choice of a good move.
At each move you must flip at least one of your opponent's discs. It is therefore clear that the more opponent's discs there are neighbouring empty squares, the more possible moves you will have, and hence the better your mobility will be. Conversely, if very few of your discs are adjacent to an empty square, your opponent will have very few possible moves. A disc adjacent to an empty square is called a frontier disc; the others are called internal discs. The set of frontier discs is called the frontier. From what we just said, it seems natural to try and minimize your number of frontier discs.
In Diag.s 12, 13 and 14, we show three positions which appear similar. What can we say about a black move to a6 in each of these three positions?
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In Diag. 12, a move to a6 seems disasterous: after white responds with g1, blck will be forced to give up a corner to white (since his only remaining legal moves are b1, g2 and h2). Playing a6 is very poor since it flips a large number of frontier discs (those on row 6) and establishes on this row a large black frontier adjacent to which black may no longer play. Playing a6 in Diag. 13 is much more reasonable since, among the flipped discs, only b6 and c6 are frontier discs. However, this move still deprives black of access to some squares which may become important later on, for example a7. Perhaps it would be better to play e7 which flips fewer frontier discs. By contrast, the best move in Diag. 14 is a6. If white responds with b2 or g2, black can immediately take a corner, and if he responds with g1 (the only other legal move), black may respond with a7 and white is now forced to give up a corner to blck (he can only play b2 or b7). In this Diag., the move to a6 is called a perfectly quiet move, since it flips no frontier discs (after playing a6, b5 is no longer a frontier disc). Now we can see the limits of an evaluation of moves based simply on a positional strategy: what's important isn't just where you play but especially what discs which you flip. We can now better understand the weakness of white in Diag. 8. All the frontier being white and black having many moves at his disposal (7 moves in addition to those to an X-square or C-square). He has a perfectly quiet move to e8 which adds no discs to his frontier. White now sees the consequences of his enormous frontier: he is obliged to play b2 or g2. Similarly, in Diag. 10, a large part of the frontier is white (largely because of the white wall on the east), and by playing g6 black offers no new moves to white. One of the methods of reducing your opponent's mobility (and especially of not reducing yours by much) will be to avoid flipping too many frontier discs. It's better to have internal discs (that is, discs which are not adjacent to an empty square) than frontier discs. This is what we call the strategy of control of the center. Of course, it is not an accident that all the black discs in Diag. 8 are internal discs. |
