Reversi

Rules of the Game

Reversi (also known as Othello) is a classic board game which is played by two players on an 8x8 grid with pieces that have two distinct sides (typically a dark side and a light side, or black and white).

Each player places a piece on the board in turn, with their colour facing upwards, which designates it as their piece. Opponent pieces that are situated contiguously between the played piece and another of the player's pieces, orthogonally or diagonally, are flipped over (so they become the player's pieces).

Every move must result in at least one of the opponent's pieces being flipped. If a player has no valid moves, the other player plays again. The game ends when the board is full or when neither player can make a valid move. The winner is the player with the most pieces on the board. A game can be drawn if each player has an equal number of pieces on the board.

The game starts with two of each player's pieces in the centre four squares of the board, as shown below. Black always plays first.

Conventions

Squares on the board are referenced by a letter from a to h, and a number from 1 to 8 as shown in the board below. The starting state of the board is shown, with white pieces at d4 and e5, and black pieces at e4 and d5. Some squares are given special names: the squares diagonally in from each corner are known as X-squares (b2, g2, b7 and g7); the edge squares adjacent to the corners are known as C-squares (b1, a2, g1, h2, a7, b8, h7 and g8); the two edge squares in the middle of each edge are known as B-squares (d1, e1, a4, a5, h4, h5, d8, e8) and the edge squares between the B-squares and C-squares are known as A-squares (c1, f1, a3, a6, h3, h6, c8, f8).

Game Complexity

Reversi has a state-space complexity (the number of nodes in the game tree for a fully evaluated game) in the order of 10²⁸.

Strategy

Some of the common strategies used when playing reversi are discussed here. The rules of the game page published by the French Othello Federation is a good reference more detailed descriptions of the common strategies and for more advanced strategies.

Piece Differential

Although the aim of the game is to end up with more pieces on the board than the opponent, it is generally not advantageous to gain a majority too early in the game as this limits mobility.

Mobility

Mobility is a measure of the number of possible moves that a player has. When a player's mobility becomes low, they may be forced into making undesirable moves. It is therefore advantageous to play moves that improve mobility and/or decrease the opponent's mobility. Mobility is often the key factor in winning a game.

Frontier Pieces

Frontier pieces are those that are next to empty squares on the board. The fewer frontier pieces a player has, the lower the opponent's mobility becomes. A quiet move is a move that flips no frontier pieces and is often a good move. A corollary measure of frontier pieces is potential mobility, which is the number of squares that are potentially moves (open squares next to opponent frontier pieces). Improving potential mobility increases the chances of improving mobility.

Corners

Once a piece is placed in a corner it can never be flipped, so corners can be used to anchor other stable pieces on the edges.

Stable Pieces

Pieces that cannot be flanked by an opponent's piece cannot be flipped and are referred to as stable. Corners are always stable, as well as neighbouring pieces of the same colour. Establishing several stable pieces during the game guarantees an end score for the player of at least the number of stable pieces.

Edges

Playing pieces on edges can have mixed results. Playing edges too early in a game should be avoided. Generally, A-squares are stronger positions that B-squares.

C-Squares

Playing pieces on C-squares are often weak moves that open the player up to tactical traps which result in the opponent winning the corner. C-squares should thus be played with care.

X-Squares

Playing pieces on X-squares adjacent to open corners often result in the opponent winning the corner. X-squares should thus be played with caution.

Parity

As there are an even number of squares on the board and black always plays first, white always plays last, which gives white a slight advantage. More generally, the player making the last move in a particular closed-off region of the board has a slight advantage. Establishing parity involves leaving an even number of empty squares in each region in which the opponent can play.

Stages of the Game

As the game progresses, a player's strategy needs to change in response to the opponent's moves and to the state of the board. A player's strategy through the early and middle stages of the game should lay the foundation for gaining a majority of pieces on the board in the endgame.

Opening Moves

There are numerous documented opening moves to a game of reversi - some covering as many as the first sixteen moves. The three possibilities for the first two moves are shown here. All of them are illustrated with d3 as the first move; however the same openings apply for the other three possible first moves, c4, f5 and e6, just transposed on the board.

Parallel Opening

The parallel opening is d3 e3 or c4 c5 or f5 f4 or e6 d6. It is generally considered to be the weakest opening by white.

Diagonal Opening

The diagonal opening is d3 c3 or c4 c3 or f5 f6 or e6 f6.

Perpendicular Opening

The perpendicular opening is d3 c5 or c4 e3 or f5 d6 or e6 f4.