Reversi Strategy: Corners and Mobility

The rules

• The board is 8 × 8 with four discs in the centre, two of each colour on the diagonals. Black moves first.
• A move places a disc so that one or more straight lines of enemy discs (across, down or diagonally) lie between it and another of your discs. Every trapped disc flips to your colour.
• If you have no legal move you pass. When neither player can move, the game ends and the most discs wins.

Corners are forever

A disc in a corner can never be flipped, because no line can run past it. From a corner you can build stable discs along the two edges, and stable discs are the only discs that are truly yours. So: take a corner whenever you can, and never give one away cheaply.

Giving a corner away usually happens through the three squares next to it: the two edge squares beside the corner (the C-squares) and the diagonal square (the X-square). A disc on the X-square lets your opponent flip along the diagonal into the corner; a disc on a C-square often lets them flip along the edge. Avoid these squares, especially the X-square, unless the corner is already taken or you have calculated that the opponent cannot reach it.

Mobility: fewer discs, more moves

Early and in the middle game, the player with more legal moves is winning. A player with few moves is eventually forced to play a bad square (an X-square, say), and the game turns. Mobility comes from having few frontier discs, discs that border empty squares, because every frontier disc is a disc the opponent can flip and a square the opponent can play next to.

Practical consequences:

• Flip fewer discs. A move that flips one disc deep inside your own group keeps your frontier small; a move that flips a long line creates frontier everywhere.
• Play quiet moves that give the opponent no new squares to play.
• Keep your discs in the middle of the board, surrounded by the opponent's, rather than spreading to the edges early.

Edges

Edges are better than the interior but not as good as corners, and a careless edge disc can hand over a corner. An edge move is good when it cannot be flipped soon (anchored to a corner or balanced so the opponent cannot approach from either side) and bad when it creates an unbalanced edge the opponent can attack. Learn the simple rule: do not be the first to play onto an empty edge next to an empty corner.

Parity: having the last move

In the endgame, empty squares come in regions. The player who makes the last move in a region usually gains the most discs there, because nothing flips back afterwards. With an even number of empty squares in a region and you to move, you will get the last move if you both play only in that region; so count the empties in each region and steer the game so that you move last in the big ones. Passing (having no move) breaks parity, which is another reason to keep mobility.

The Hard robot calculates the last dozen moves exactly, so against it the parity fight must be won before the endgame starts.

Counting discs: only at the end

Ignore the disc count until the last ten moves. Then it is everything. Before each late move, count what each candidate flips and what it allows the opponent to flip back. A late corner is worth many discs because of the stable edges that follow it.

Common mistakes

1. Grabbing discs early. A big early lead in discs is usually a mobility disaster.
2. Playing the X-square. It gives away the corner.
3. Playing onto an empty edge beside an empty corner. It invites an attack along the edge.
4. Ignoring passes. If you can force your opponent to pass, you gain parity.
5. Leaving corners for later. A corner now is worth more than a corner later, because its edges fill in earlier.

Glossary

• Corner: a square that can never be flipped.
• X-square: the square diagonally next to a corner.
• C-square: an edge square next to a corner.
• Stable disc: a disc that can no longer be flipped.
• Frontier disc: a disc next to an empty square.
• Mobility: the number of legal moves a player has.
• Parity: who gets the last move in a region of empty squares.