Reversi

Reversi is a strategy board game for two players, played on an 8×8 uncheckered board. There are sixty-four identical game pieces called disks (often spelled "discs"), which are light on one side and dark on the other. Players take turns placing disks on the board with their assigned color facing up. During a play, any disks of the opponent's color that are in a straight line and bounded by the disk just placed and another disk of the current player's color are turned over to the current player's color.

The object of the game is to have the majority of disks turned to display your color when the last playable empty square is filled.

Reversi is marketed by Pressman under the trade name Othello.

Origins
The modern version is based on the game Reversi that was invented in 1883 by either of two English men (each claiming the other a fraud), Lewis Waterman or John W. Mollett (or perhaps earlier by someone else entirely), and gained considerable popularity in England at the end of the nineteenth century. The game's first reliable mention is in the August twenty-first 1886 edition of The Saturday Review. Later mention includes an 1895 article in The New York Times: "Reversi is something like Go Bang, and is played with 64 pieces." In 1893, the well-known German games publisher Ravensburger started producing the game as one of its first titles. Two 18th-century continental European books dealing with a game that may or may not be Reversi are mentioned on page fourteen of the Spring 1989 Othello Quarterly, and there has been speculation, so far without documentation, that the game has even more ancient origins.

The current most regularly used rule-set—the one used on the international tournament stage—originated in Mito, Ibaraki, Japan in the 1970s. The Japanese game company Tsukuda Original registered the game under the trademark name Othello. The name was selected as a reference to the Shakespearean play Othello, the Moor of Venice, referring to the conflict between the Moor Othello and Iago, and more controversially, to the unfolding drama between Othello, who is black, and Desdemona, who is white. The green color of the board is inspired by the image of the general Othello, valiantly leading his battle in a green field. It can also be likened to a jealousy competition (jealousy being the central theme in Shakespeare's play), since players engulf the pieces of the opponent, thereby turning them to their possession.

A 2002 press release about faked origins of the modern game makes no mention of the original version: "Othello was invented by Japanese game enthusiast, Goro Hasegawa in 1971. He chose James R. Becker, to help him develop and market the game. Inspired by the ancient Chinese strategy game 'Go', Hasegawa sought to create a game that was rich in strategy, but still approachable by the casual player. Becker simplified the game play, coined the tagline, 'A Minute to Learn...A Lifetime to Master' and named this new game after Shakespeare's classic play, because of the black and white disks. Othello was first introduced in Japan in 1973, by Tsukuda Original Co., who at Becker's suggestion organized the Japanese Othello Association."

In 1973, Othello became a commercial success in Japan and had its first national championship. Goro Hasegawa, who wrote How to Win at Othello, popularized the game in Japan in 1975.

Rules
Each of the disks' two sides corresponds to one player; they are referred to here as light and dark after the sides of Othello pieces, but any counters with distinctive faces are suitable. The game may for example be played with a chessboard and Scrabble pieces, with one player letters and the other backs.

True Reversi starts with an empty board, and the first two moves by each player are in the four central squares of the board. The players place their disks alternately with their color facing up and no captures are made. If either the second player chooses to move to the square diagonal to the first player or the first player's second move is not to this square given the choice, then a starting position before flipping moves commence that differs from the standard Othello position arises. It is also possible to play variants of Reversi and Othello wherein the second player's second move may or must flip one of the opposite-colored disks (as variants closest to the normal games).

For the specific game of Othello (as technically differing from Reversi), the rules state that the game begins with four disks placed in a square in the middle of the grid, two facing white side up, two pieces with the dark side up, with same-colored disks on a diagonal with each other. Convention has initial board position such that the disks with dark side up are to the north-east and south-west (from both players' perspectives), though this is only marginally meaningful to play (where opening memorization is an issue, some players may benefit from consistency on this). The dark player moves first.

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) occupied line between the new piece and another dark piece, with one or more contiguous light pieces between them. In the below situation, dark has the following options indicated by translucent pieces:

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. In other words, a valid move is one where at least one piece is reversed.

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:

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

Light takes the bottom left option and reverses one piece:

Players take alternate turns. If one player can not 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 neither player can legally place a piece in any of the remaining squares. This means the game may end before the grid is completely filled. This possibility may occur because one player has no pieces remaining on the board in that player's color. In over-the-board play this is generally scored as if the board were full (64–0).

Example where the game ends before the grid is completely filled:

The player with the most pieces on the board at the end of the game wins. An exception to this is that if a clock is employed then if one player defaults on time that player's opponent wins regardless of the board configuration, with varying methods to determine the official score where one is required.

In common practice over the internet, opponents agree upon a time-control of, typically, from one to thirty minutes per game per player. Standard time control in the World Championship is thirty minutes, and this or something close to it is common in over-the-board (as opposed to internet) tournament play generally. In time-defaulted games, where disk differential is used for tie-breaks in tournaments or for rating purposes, one common over-the-board procedure for the winner of defaulted contests to complete both sides' moves with the greater of the result thereby or one disk difference in the winner's favor being the recorded score. Games in which both players have the same number of disks their color at the end (almost always with a full-board 32–32 score) are not very common, but also not rare, and these are designated as 'ties' and scored as half of a win for each player in tournaments. The term 'draw' for such may also be heard, but is somewhat frowned upon.

What are generally referred to as transcript sheets are generally in use in tournament over-the-board play, with both players obligated to record their game's moves by placing the number of each move in an 8×8 grid. This both enables players to look up past games of note and tournament directors and players to resolve disputes (according to whatever specific rules are in place) where claims that an illegal move, flip or other anomaly are voiced. An alternative recording method not requiring a grid is also in use, where positions on a board are labeled left to right by letters a through h and top to bottom (far-to-near) by digits 1 through 8 (Note that this is the opposite of the chess standard, with numerals running upward away from the side (White) that has a through h left to right, and also that the perspective may be that of either player (with no fixed standard)), so that the very first move of a game may be (based upon standard starting setup) d3, c4, f5 or e6. This alternate notational scheme is used primarily in verbal discussions or where a linear representation is desirable in print, but may also be permissible as during-game transcription by either or both players.

Tournament play using ordinary sets rather than a computer interface—where this can not be an issue—have various ways of handling illegal moves and over- or underflipping (flips that should not be made but are or should be but are not). For example, permitting either player (perpetrator or its opponent) to make a correction going back some fixed number of moves (after which no remedy is available) is one procedure that has been used.

Significant variants of the game, such as where the starting position differs from standard or the objective is to have the fewest pieces one's color at the end, are sometimes—but rarely—played.

Strategic elements
Strategic concepts in Reversi include openings (and home preparation), corners, mobility, edge play, parity, end-game play and looking ahead.

Openings
For relatively inexperienced players the opening (early) part of a game of Reversi is generally not very easy to make sense of. A general rule of thumb on the opening is that a good opening is one that leads to a good middle-game. By and large, good moves in the very earliest stages are determined by whether there is a refutation to a move only and few other truly general considerations aside from what exactly constitutes a refutation. The first move (by dark) is no choice at all other than for the purpose of the player's possible sense of ideal visualization. The first move by light gives three choices, and, in fact, it is generally accepted at the highest level that one of these actually may be successfully refuted, that being what is known as the Parallel opening. The other two choices by light are called the Diagonal opening and the Perpendicular opening, and these three in the order mentioned with f5 as dark's first move (See discussion on notation above) are f4, f6 and d6. As this subtopic is generally broad and complex—at high levels of play it is routine for ten or more moves to be rattled off from rote memorization by both players, travelling down well-worn paths, and there is a common naming system for diverse early-game move choices—it is probably best to leave expansion of this topic to a separate article specifically dedicated to the issue or to say no more.

Corners
Corner positions, once played, remain immune to flipping for the rest of the game, being termini of horizontal, vertical and diagonal lines. More generally, a piece is stable when, along all four axes (horizontal, vertical, and each diagonal), it is in terminal position or if from it along the axis one reaches a terminal disk passing only through disks the same color. These are not the only kinds of stable disk, however, and occupying a corner may often be a grave error if one allows ones opponent to create a wedge that results in him or her gathering more stable disks. This can render occupying the corner largely useless, and often much worse than that because of loss of tempo (Where it is an issue of running out of desirable moves and being forced to make undesirable ones, the grabbing of a corner may give the opponent not only the wedging response but also a following move which one can not respond to practically).

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, a player must force its opponent to play moves that relinquish those good moves. One of the ways to achieve this involves reducing the number of moves available to the player's opponent. Ideally, this will eventually force the opponent to make an undesirable move.

Edges
Edge pieces can anchor flips that influence moves to all regions of the board. If played poorly, this can poison later moves by causing players to flip too many pieces and open up many moves for the opponent. However, playing on edges where an opponent can not easily respond drastically reduces possible moves for that opponent.

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. Nevertheless, such a corner sacrifice is sometimes played for some strategic purpose (like retaining mobility). Playing to the edge squares adjacent to the corner (called the C-squares) can also be dangerous if it gives the opponent powerful forcing moves.

Parity
Parity is one of the most important parts of the strategy. In short, the concept of parity is about getting the last move in every empty region in the end-game, and thereby increasing the number of stable disks.

The concept of parity led to a change in the perception of the game, as it led to distinct strategies for playing Black and White. It forced Black to play more aggressive moves and gave White the opportunity to stay calm and focus on keeping the parity. As a result the opening books and midgame were focused on Black being the "attacker" and White being the "defender".

The concept of parity also controls how edge positions are played and how edges interact.

End-game
For the end-game (the last twenty 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. Actual counting of disks in the very final stages is often critical, but sometimes in human play an inaccurate choice, for disk differential can be better than an accurate one in terms of the expected outcome (and can be essential in lost positions).

Brightwell Quotient
Invented by the British Mathematician and three times runner-up at the World Championship and five times British Champion Graham Brightwell, this is the tie-breaker that is now used in many tournaments including the W.O.C. If two players have the same number of points in the thirteen rounds W.O.C. Swiss, the tie is resolved in favour of the player with the higher Brightwell Quotient.

Computer opponents and research
Because of difficulties in human look-ahead—peculiar to Othello because of the apparent strategic meaninglessness of internal disks (making blindfold games—if not virtually impossible without enormous dedication—more difficult than is the case in, say, chess)—and the attractiveness of the game to programmers, the best Othello computer programs have easily defeated the best humans since 1980, when the program The Moor beat the reigning world champion. In 1997, Logistello defeated the human champion Takeshi Murakami with a score of 6–0.

Analysts have estimated the number of legal positions in Othello is at most 1028, and it has a game-tree complexity of approximately 1058. Mathematically, Othello still remains unsolved. Experts have not absolutely resolved what the outcome of a game will be where both sides use perfect play. However, analysis of thousands of high quality games (most of them computer-generated) appears to lead to a reliable conclusion (pending actual proof if true) that, on the standard 8×8 board, perfect play on both sides results in a draw. When generalizing the game to play on an n×n board, the problem of determining if the first player has a winning move in a given position is PSPACE-complete. On 4×4 and 6×6 boards under perfect play, the second player wins. The first of these results is relatively trivial, and the second dates to around 1990.

World Othello Championship
*This rivalling Monte Carlo world championship is not considered to be an official world championship.