Reversi

Screen dump of WZebra 4.1, a Reversi program by Gunnar Andersson and Lars Ivansson

Reversi and Othello are names for a strategic boardgame which involves play by two parties on an eight-by-eight square grid with pieces that have two distinct sides. Pieces typically appear coin-like, with a light and a dark face.

Mattel produces Reversi equipment under the name "Othello". Anjar Co licenses the registered trademark "Othello" from Tsukuda Original.

The best Othello computer programs can easily defeat the best humans. As early as 1980, the program The Moor beat the reigning world champion, and in 1997, Logistello defeated the human champion Takeshi Murakami 6:0. This dominance is not seen in games like chess, where the best computers are about equal to the best humans (although the Hydra machine may soon change that), or Go, where even average human players trounce the best computers.

Human beings cannot generally win against computer intelligence in Othello because computers can look ahead much further than humans can. Analysts have estimated the number of legal positions in Othello as at most 10²⁸, and it has a game-tree complexity of approximately 10⁵⁸.

Mathematically, Reversi still remains unsolved– that is we don't know the result of the game with perfect play on both sides. However, there is growing evidence that on the standard 8-by-8 board a reasonable play on both sides results in a draw.

When generalizing the game to play on an n-by-n board, the problem of determining if the first player has a winning move in a given position is PSPACE-complete. On 4-by-4 and 6-by-6 boards under the perfect play the second player wins.

Origins

The game derives from two different sources.

In the 19th century unknown authors in Europe invented "Reversi", which the well-known German games publisher Ravensburger started producing in 1898 as one of its first titles.

The modern rule set, now universally accepted (except by those who know only the still-produced Ravensburger edition) originated in Japan as "Othello" in the 1970s.

Goro Hasegawa, who wrote How to win at Othello, popularised the game in Japan in 1975. It took its name from the Shakespearean play Othello, the Moor of Venice.

Play

Each of the two sides corresponds to one player; we will call them light and dark after the sides of Othello pieces, but "heads" and "tails" would identify them equally as well, so long as each marker has sufficiently distinctive sides.

Originally, Reversi did not have a defined starting position. Later it adopted Othello's rules, which state that the game begins with four markers placed in a square in the middle of the grid, two facing light-up, two pieces with the dark side up. The dark player makes the first move.

Reversi Starting position

Dark must place a piece with the dark side up on the board, in such a position that there exists at least one straight (horizontal, vertical, or diagonal) line between the new piece and another dark piece, with one or more contiguous light pieces between them. In the above situation, dark has the following options indicated by "ghost" pieces:

Reversi Where dark may play

After placing the piece, dark turns over (flips, captures) all light pieces lying on a straight line between the new piece and any anchoring dark pieces. All reversed pieces now show the dark side, and dark can use them in later moves -- unless light has reversed them back in the meantime.

If dark decided to put a piece in the topmost location (all choices are strategically equivalent at this time), one piece gets turned over, so that the board appears thus:

Reversi After dark play

Now light plays. This player operates under the same rules, with the roles reversed: light lays down a light piece, causing one or more dark pieces to flip. Possiblities at this time appear thus (indicated by "ghosts"):

Reversi Where light may play

Light takes the bottom left option and reverses one piece:

Reversi After light play

Players take alternate turns. If one player cannot make a valid move, play passes back to the other player. When neither player can move, the game ends. This occurs when the grid has filled up, or when one player has no more pieces on the board. The player with more pieces in the board at the end wins.

One difference between Reversi and Othello involves the supply of pieces. In Reversi each player owns 32 pieces at the start of the game. Once a player has placed 32 pieces (including the initial 2 pieces placed on the centre squares) that player may not make any further moves. He/she may not use any of the opponent's pieces. In Othello all the pieces belong to both players equally; they come from a pool, from which both may draw in order to make a move.

Strategy

The game pieces flip very quickly, easily and (often) repeatedly, so it offers little advantage -- and in fact typically becomes disadvantageous -- to try to gain a majority of pieces early in the game. Corners, mobility, edge play, parity, endgame play and look-ahead form the key elements of successful Othello strategy.

Corners

Corner positions, once played, remain immune to flipping for the rest of the game: thus a player can use a piece in a corner of the board to anchor groups of pieces (starting with the adjacent edges) permanently. So capturing a corner often proves an effective strategy when the opportunity arises. More generally, a piece is stable when, in all four directions, it is on a boundary, in a filled row, or next to a stable piece of the same color.

Mobility

An opponent playing with reasonable strategy will not so easily relinquish the corner or any other good moves. So to achieve these good moves, you must force your opponent to play moves which relinquish those good moves. The best way to achieve that involves reducing the number of moves available to your opponent. If you consistently restrict the number of legal moves your opponent can make, then sooner or later they will have to make an undesirable move. An ideal position involves having all your pieces in the center surrounded by your opponent's pieces. In such situations you can dictate what moves your opponent can make.

When moves seem equal with respect to what moves you will leave yourself and your opponent, playing a minimum piece strategy will tend to advantage you, because minimizing your discs will tend to leave fewer discs for your opponent to flip in subsequent moves of the game. One should not play the minimum disc strategy to an extreme, however, as this also can quickly lead a lack of mobility.

Edges

While playing pieces to edges of the board may seem sound (because they cannot be flipped easily), this can often prove detrimental. Edge-pieces can anchor flips that influence moves to all regions of the board. Because of that, this can, sooner or later, poison later moves that you make by causing you to flip too many pieces and open up many moves for your opponent. However sometimes playing to an edge where your opponent cannot easily respond to will leave that opponent with significantly fewer available moves.

The square immediately diagonally adjacent to the corner (called the X-square), when played in the early or middle game, typically guarantees the loss of that corner. Playing to the edge squares adjacent to the corner can typically lead to tactical traps involving sacrificing one corner, or simply playing out the edge in a specific sequence.

In general you should avoid edge play in the early and middle game if possible, unless you can gain larger concessions in terms of mobility or a mass of unflippable pieces.

A good rule of thumb is to keep your pieces grouped together in the middle of the board, and minimize tangents formed by your own pieces. This strategy leads to the greatest mobility.

Parity

As play progresses, regions of the board will typically section themselves off where neither side can prevent the other from playing arbitrarily into those regions. By simply counting out the number of squares in a region, one can ascertain whether an odd or an even number of squares exist. In the case of an odd number of squares, by playing there first you can force your opponent to play first outside of that region. You achieved this by simply playing into that region at any time it has an odd number of squares available, and by not playing into it when it features an even number of squares. If you take into consideration certain squares in a region that seem very dangerous (like an X-square or an edge square that leads to an obvious trap) then you can either force your opponent to play elsewhere or to occupy one of these dangerous squares.

Look-ahead

As in any good strategy for chess or for checkers, a player should not consider only the current situation on the board. For each move you consider, you must consider possible responses from your opponent, then the subsequent responses you will make to those moves and so on. The aspects of the current position may not remain relevant a few moves hence. So when optimizing your mobility, gaining corners or anything else, you should consider how best to do this for the long term rather than just for the next move.

Endgame

For the endgame (the last 20 or so moves of the game) the strategies will typically change. Special techniques such as sweeping, gaining access, and the details of move-order can have a large impact on the outcome of the game. At these late stages of the game no hard-set rules exist. The experienced player will try to look ahead and get a feel for what will lead to the best final outcome.

Game trivia

1. Since at least 1977 an annual Othello World Championship has taken place. Each country can send a maximum of 3 players.
2. Othello has its greatest following in Japan.
3. Good computer players far out-perform any human player.

Othello World Championship

Literature

• Othello: Brief and Basic, An introduction to strategy and tactics for the game of Othello, Ted Landau, 1987
• Broken link (likely to stay broken) - Othello: From Beginner to Master, Randy Fang, 2003
• Othello: A Minute to Learn - A Lifetime to Master, Brian Rose, 2005
• Reversi WikiBook

External links