Reversi

Reversi is a strategic board game played by two parties on an eight-by-eight square grid with pieces that have two distinct sides. Coin-like markers with a light and a dark face are typical.

The origin of the game is rather controversial. Japanese believe it was invented in Japan [1] in the 1970s but some resources say the game was in existence before that.[1] In Japan, the game was introduced in 1975 by Goro Hasegawa, who wrote How to win at Othello. It was named after the Shakespeare play Othello.

Mattel produces reversi equipment under the name Othello. Othello is a registered trademark of Tsukuda Original, licensed by Anjar Co.

The number of legal positions in Reversi is estimated to be at most 1028, and it has a game-tree complexity of approximately 1058. In 1980 the program The Moor beat the reigning the world champion, and since that time the world champion has always been a computer program. One of the worlds strongest Othello AI is Logistello.

Human beings cannot generally win against computer intelligence in Reversi because computers can look ahead much further than humans can. Reversi has not yet been solved, however - we don't know the result of the game with perfect play on both sides.

Table of contents
1 Rule
2 Strategy
3 Game example
4 Game facts
5 Othello World Championship
6 External Links
7 Literature

Rule

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" is equally feasible so long as each marker has sufficiently distinctive sides.

Originally, Reversi didn't have a starting position to begin from. However, the rules for Othello state that the game begins with four markers placed in a square in the middle of the grid, two facing light-up (indicated by o in our diagrams), two pieces with the dark side up (indicated by *). The light player makes the first move.

  *o
  o*  (one of the possible starting positions)

Light must place a piece with the light side up on the grid, so that there is a straight (horizontal, vertical, or diagonal) line between the new piece and another light piece, with at least one dark piece between them. In the above situation, light has the following options indicated by dots:

  .
 .*o
  o*.
   .

After placing the piece, light is entitled to turn around all dark pieces between the new piece and the next light piece on a straight line, should one exist. All reversed pieces now show the light side, and light can use them in later moves -- unless dark was able to turn them back in the mean time.

If light decided to put a piece in the topmost location (all choices are equivalent at this time), one piece will be turned around:

  o
  oo
  o*

Now it is dark's turn. This player operates under the same rules, with the roles reversed: A dark piece is laid down so that one or more straight lines of light pieces can be turned around. Possiblities at this time:

 .o.
  oo
 .o*

Dark takes the left alternative and is able to turn around one piece:

  o
  oo
 ***

Players take alternating turns. Should one player be unable to make a valid move it is the other player's turn again. When both players are unable to move, the game ends. This is the case when the grid has filled up, or when one player has no more pieces on the board. The player with more pieces available at the end wins.

Strategy

Pieces are flipped very quickly and easily, so its not very important, and in fact typically detrimental to try to gain a majority of pieces early in the game. Corners, mobility, edge play, parity, endgame play and look ahead are the key elements of good Othello strategy.

Corners

Corners, once played, cannot be flipped, and can be used to anchor groups of pieces (starting with the adjacent edges) that also cannot be flipped. So capturing a corner is often an effective strategy when the opportunity arises.

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 is to reduce the number of available moves of your opponent. If you reduce the number of legal moves your opponent can make, then sooner or later she will be forced to make a move undesirable to her. An ideal position to be in is to have all your pieces in the center surrounded by your opponents 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 your yourself and will be open to your opponent, playing a minimum piece strategy will tend to be more beneficial. This is 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 may seem sound (because they are not so easily flipped) they can often be detrimental. Edge pieces can anchor flips that affect moves to all regions of the board. Because of that, this can, sooner or later, poison later moves that you make by causeing you to flip too many pieces and open up many moves for your opponent. However sometimes playing to an edge which cannot easily be responded to will leave your opponent with significantly fewer moves than any other moves.

The square immediately diagonally adjacent to the corner (called the X-square) played in the early and middle game is typically a guarantee of losing 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 you can avoid it, unless you can gain larger concessions in terms of mobility or a mass of unflippable pieces.

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 notice if it is odd or even. If it is odd, then by playing there first, you can force your opponent to be the first to play outside of that region. This is achieved by simply playing into that region any time there is an odd number of squares available, and not playing into it when there is an even number of squares. If you take into consideration certain squares in a region that seem to be very bad (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 concede to playing one of these bad squares.

Look ahead and Endgame

Like any good strategy for chess, or checkers, it is not sufficient to only consider 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 be relevant a few moves down the road. 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.

For the endgame (the last 20 or so moves of the game) the rules for the game 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. Unfortunately at these late stages of the game, there are no hard set rules. The best you can do is try to look ahead and get a feel for what will lead to the best final outcome.

Game example

Screen dump of WZebra 4.1. WZebra is a program by Gunnar Andersson and Lars Ivansson

Game facts

1. Since about 1980 there has been a yearly world Othello championship. Each country is allowed to send a maximum of 3 players.

2. Reversi has its greatest following in Japan.

3. Good computer players are far stronger than any human player.

Othello World Championship

Year Location World Champion Country Team Runner Up Country
1977 Tokyo Hiroshi Inoue Japan N/A Thomas Heiberg Norway
1978 New York Hideshi Maruoka Japan N/A Carol Jacobs USA
1979 Rome Hiroshi Inoue Japan N/A Jonathan Cerf USA
1980 London Jonathan Cerf USA N/A Takuya Mimura Japan
1981 Brussels Hideshi Maruoka Japan N/A Brian Rose USA
1982 Stockholm Kunihiko Tanida Japan N/A David Shaman USA
1983 Paris Ken'Ichi Ishii Japan N/A Imre Leader Great Britain
1984 Melbourne Paul Ralle France N/A Ryoichi Taniguchi Japan
1985 Athens Masaki Takizawa Japan N/A Paolo Ghirardato Italy
1986 Tokyo Hideshi Tamenori Japan N/A Paul Ralle France
1987 Milan Ken'Ichi Ishii Japan USA Paul Ralle France
1988 Paris Hideshi Tamenori Japan Great Britain Graham Brightwell Great Britain
1989 Warsaw Hideshi Tamenori Japan Great Britain Graham Brightwell Great Britain
1990 Stockholm Hideshi Tamenori Japan France Didier Piau France
1991 New York Shigeru Kaneda Japan USA Paul Ralle France
1992 Barcelona Marc Tastet France Great Britain David Shaman Great Britain
1993 London David Shaman USA USA Emmanuel Caspard France
1994 Paris Masaki Takizawa Japan France Karsten Feldborg Denmark
1995 Melbourne Hideshi Tamenori Japan USA David Shaman USA
1996 Tokyo Takeshi Murakami Japan Great Britain Stephane Nicolet France
1997 Athens Makoto Suekuni Japan Great Britain Graham Brightwell Great Britain
1998 Barcelona Takeshi Murakami Japan France Emmual Caspard France
1999 Milan David Shaman Netherlands Japan Tetsuya Nakajima Japan
2000 Copenhagen Takeshi Murakami Japan USA Brian Rose USA
2001 New York Brian Rose USA USA Raphael Schreiber USA
2002 Amsterdam David Shaman Netherlands USA Ben Seeley USA
2003 Stockholm Ben Seeley USA Japan Makoto Suekuni Japan

External Links

Literature

  • Othello: Brief and Basic, An introduction to strategy and tactics for the game of Othello, Ted Landau, 1987



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