------------------------------------------------------------------------- THE RULES OF OTHELLO "Othello - A minute to learn, a lifetime to master!" - The game of Othello is derived from an ancient game called Reversi, which started on the same 8x8 board as Othello, but with none of the center squares occupied. The rules of Reversi stated that the first four moves had to take place in the four center squares, thereby giving rise to one of two starting formations, a parallel formation and a checkered center formation. The checkered center formation as a starting point was copyrighted into the game of Othello which after various ownerships under Gabriel and Milton Bradley, currently rests with Pressman Toy Company. The Othello rules are simple. Black moves first and the moves alternate between players. A player must move as long as he has at least one legal move, else he passes. A legal move consists of any move that "flips" at least one of the opposing pieces. An opposing piece is flipped if it stands between (either alone or with a line of other opposing pieces and either vertically, horizontally, or diagonally) the piece just played and another piece of the same color as that just played. When a piece is flipped, it becomes the opposite color to what it was prior to flipping. The game ends when neither player has a legal move. The winner of the game is the player with the most pieces of his color at the end of the game. ------------------------------------------------------------------------- REVERSI 4.0 - PROGRAM OPTIONS Novice Level - This level consists of a random factor which plays a different game every time. The Novice Level will generally make more good moves than bad moves, but will occassionally make some really bad moves. This level is good practice for true beginners. The level plays a perfect endgame only 3 moves from the end. Advanced - This level also consists of a random factor but it is somewhat limited so that good moves are played much more often than bad moves. Still, an occasional truly bad move is not unusual. This level plays a perfect endgame 6 moves from the end (with 6 empty squares left). Master - The toughest of all levels, there is no random play here. The Master Level always makes the best play, consistent with the number of half-moves ("ply") of look ahead which has been assigned. Based on play against other top players and programs, it is my belief that the Master Level at a 3 ply search would be ranked among the top 30 U.S. players. Perfect endgame play occurs 9 moves from the end at the 3 ply level, 10 moves at the 4 ply level, etc.. In addition to the above features, the Master level employs an opening book which has been developed from world class games. This opening book is available ONLY at the Master Level. Setup Mode - The Setup Mode allows you to set up any position and have the computer start to play from that position. Once in Setup Mode, position the cursor. Type "B" for a Black piece on the cursored square, "W" for a White piece on the cursored square, or hit the space bar for a blank square. When preparing the position, remember that you will move first prior to the computer. Your piece color is established by the color selection menu. After setting up the correct position, hit the key. You will then be asked to enter your move, and the game is underway. New Game - To start the game with the original Othello position, select this mode option. White Pieces - Select this option to play the White pieces, moving second from the original Othello position. Black Pieces - Select this option to play the Black pieces, moving first from the original Othello position. Let's Play! - Select this option to start the game. ------------------------------------------------------------------------- MASTER LEVEL OPTIONS Master Level Options are available only when the Master Level is selected. 2 Ply - A "ply" is the number of half-moves 3 Ply (one move by one player is considered a half-move) 4 Ply of look-ahead for which the program will search. 5 Ply Approximate times of play are given for 6 Ply the IBM XT (8086 with 8 Mhz speed) and for the IBM AT (80286 with 12 Mhz speed) Display Option - The computer's thoughts will be displayed as it considers moves. Only the best move found will be displayed. The display consists of the value of the position (positive numbers mean the computer feels it is winning, negative numbers mean that it thinks it is losing), and the row and column numbers of the best variation. Rows and columns are numbered as follows: 1 2 3 4 5 6 7 8 1 - - - - - - - - 2 - - - - - - - - 3 - - - - - - - - 4 - - - O x - - - 5 - - - x x x - - 6 - - - - - - - - 7 - - - - - - - - 8 - - - - - - - - The above shows the position after a first move by Black (x) of row 5, column 6. No Display - Choose this option if you don't want to see the computer's thoughts. ------------------------------------------------------------------------ AN INTRODUCTION TO OTHELLO STRATEGY Welcome to the World of Othello! Reversi 4.0 is the result of alot of hard work, spent not only in the actual programming but also in learning the mathematics of gaming theory (from an article on alpha-beta pruning by D.E. Knuth and R.W. Moore) and, most importantly, in learning the correct strategies in the game of Othello. When I first considered writing the program in March of 1989, I had spent about a year playing serious tournament Othello on the USA Today Sports Center online telecommunications network and was concerned about the lack of correct strategy in most of the Othello programs on the market. While Othello is simple to learn it is indeed complex to master, especially without good opponents to play. Thus, my intention was to create a good opponent for interested Othello players. In addition to a lack of good strategical programs, there is also a lack of good instructional text written in English. The only book I had ever read on Othello, written by the Japanese inventor of the game, contained incorrect and often very bad strategical advice. The best instructional text (and in fact the ONLY good text written in English of which I am currently aware) is contained in the quarterly magazine of the United States Othello Association (USOA) and in the magazine of the British Othello organization. Through these magazines and through the wonderful data base program, OTHCGA, written by Brian Rose (one of America's top two players) I was able to open the doors to the truly correct Othello strategy. Through these last few years I've met new Othello friends, learned the basics of Othello strategy, and had enough success in national Othello tournaments to achieve a United States ranking among the top ten Othello players. In July of 1989 I distributed my first program, Reversi 2.0, through the shareware concept. The purpose of such a distribution was not to make money (and indeed, I received only about 10 contributions totalling $150) but rather to publicize the game of Othello in the hopes of attracting new players to the game. The original version of this game is nowhere near as strong as the current version, Reversi 4.0, and it occurred to me that rather than attract players to the game, the new version might scare people away from it. In fact, the current version of the game, set on the master level at 3 ply of thought, is probably good enough to routinely beat all but the top 30 or 40 players in the country. To give the beginning player some help with the fundamentals of Othello, I've decided to include here an elaboration of all of the concepts which have been employed in the Reversi 4.0 program. Unlike chess, Othello is in its infancy and the concepts are continuing to be refined and developed. Also unlike chess, it is possible to be a top Othello player in a short period of time. Indeed, a few years ago a French player by the name of Ralle won the world Othello championship just a few years after learning the game. It should be stated here that Othello is not a "solved" game. The best players in the world are not computers, despite some very extensive programming efforts by some very fine programmers. It should also be stated here that, while the second player to move has a slight advantage (because of the parity concept described later), this advantage is not overwhelming. Indeed, as in chess, the very best players of Othello are overwhelming favorites against very good players. The top two players in the United States (at this time) are expected to win 19 out of 20 games against the third ranked U.S. player. Herein, then, lie the concepts I've learned and employed in my program. THE FUNDAMENTAL STRATEGIES OF OTHELLO I. Specific Square Values - In the only English speaking book on Othello that I've ever seen, the inventor of the game put forth the theory that certain squares were more attractive to control than other squares. While this theory is completely ill-founded the names that he gave to certain squares stuck in the Othello world. The following diagram indicates the squares he named (a "-" represents an unnamed square): - C A B B A C - C X - - - - X C A - - - - - - A B - - - - - - B B - - - - - - B A - - - - - - A C X - - - - X C - C A B B A C - Of the squares listed in the above diagram, only three types merit specific attention and these are the corner squares, the "X" squares, and the "C" squares. One strategy that the beginner learns very early is that it is very important to occupy the corner square and to keep your opponent from occupying the corner square. The reason for this is that the corner square is absolutely stable, i.e. it can not be flipped regardless of the board position. Once a corner square is occupied it never changes color until the end of the game. Because the corner square is such an important square to occupy, the "X" square is important NOT to occupy, because it gives the opponent opportunities to enter the corner square. There are some instances where an "X" square occupation is correct, but these generally involve the sacrifice of one corner to the opponent for the opportunity to occupy a different corner. The "C" square would at first seem as dangerous as the "X" square to occupy, since it is one square away from the corner and therefore provides a means of the opponent's occupation of the corner. However, the entrance to the corner by means of the "C" square can only occur from the sides. It is true that the "C" square is not a good square to occupy, but it may not be entirely bad either. The correctness or incorrectness of playing into the "C" square depends entirely on the types of formations occuring along the edge containing the "C" square. We will discuss these formations later. In my program, I give a marginally bad value to a move to the "C" square. The value is much worse to an "X" square play. Finally, I give a highly positive value to the occupation of a corner square. II. Side Formations The occupation of the edges appeals to many starting players, primarily because the sides have more stability than the middle squares. Indeed, sides can only be flipped by opponents pieces occupying squares on the same side. However, in master class play occupation of the sides tends to be avoided. A statistical analysis of world class games shows, in fact, that the first player to occupy an edge tends to lose more games than the player who is not first. Occupation of the sides has one advantage, that of stability, yet has the disadvantage of allowing a number of tactical combinations which have as a result the forced occupation of a corner by the opponent's piece. It is important to recognize the tactical moves which cause certain side formations to be dangerous. Most of these tactical dangers are available only when the "C" square is occupied. The first type of danger involves the outright win of a corner without a compensating gain of another corner. The following positions show only the bottom row of an Othello board. In each case the "O"s can force the win of a corner from the "x"s, regardless of which side is on move: A) - - - O - O x - B) - - O O - O x - C) - - O - O x x - D) - - O x - O x - E) - - - - x O x - F) - - - x O x x - G) - - x O x x x - H) - - x O O x x - Note that each position involves the dangerous x occupation of the "C" square. It is important to recognize edge formations which give rise to some of the above positions: A) - - - O - - x - B) - - O O - - x - C) - - O - - x x - D) - - O x - - x - E) - - - - x - x - F) - - - x - x x - G) - - x - x x x - G2) - - x - - - x - Each of the above positions give rise to the associated edge positions previously described, provided that it is "O"s turn to play and that "O" has the opportunity to move to the crucial edge squares. Note especially that edge formations with an odd number of gaps are very dangerous. The second type of danger in edge formations comes from the opponent's sacrifice of one corner for the opponent's occupation of another corner and of most of the edge extending from that corner. Once a corner is occupied, and therefore totally stable, all pieces extending directly along the edge of the board from the stable corner are also totally stable. The second type of danger occurs in the following edge formations: 1) - x x x x x O x 2) - x x x x O O x Again, the danger occurs in the following formations when "O" is on the move and has access to the crucial empty edge squares: 3) - x x x x x - x 4) - x x x - - - x 5) - x x x O - - x 6) - x O - - - - x 7) - x x - O - - x 8) - x - x O - - x When looking at side formations, it is often important to look at the parallel row formations adjoining the edge. Consider for example the following examples of two rows on the south edge of the board: i) - O x - - - - - ii) - - x - - - - - - - x x x x x - - - x x x x x - iii) - O O - - - - - iv) - - O - - - - - - - x x x x x - - - x x x x x - Position (i) is always bad for the x's regardless of who is on move. If the southwest corner is taken by the x's, the position in (3) occurs which is favorable for the O's. Because position (ii) tends to lead to position (i), it is also usually bad. Position (iii) may be bad only if an x move to the south "C" square flips the O piece on the southwest "X" square. Finally, position (iv) is usually not bad since it gives the x's a means of occupying the important south "C" square. A very important concept in Othello play was discovered by a U.S. player named John Stoner. The edge formation trap described below is named the "Stoner Trap" after him. Consider the following southern edge positions: a) - x O - O - - - b) x - O O x O - - - O x x - - - - - O x x x - - - - - - x x x x - - x - - x x x - In each of the above cases, assume that it is x's move and that x cannot occupy the southwest corner square ON THIS MOVE. In both cases, after the x move, the O's have a very favorable play which forces either the win of the southwest corner or the win of the southeast corner and the south edge majority in exchange for the sacrifice of the southwest corner to the x's. The threat of springing these "Stoner Traps" is a common consideration in world class play, and in the Reversi 4.0 program. III. Disk Stability and Maximization of Options One of the classic truths of the game of Othello involves an instructive position: - O O O O O O - O O O O O O O O O O O O O O O O O O O O O O O O O O O O x O O O O O O O O O O O O O O O O O O O - O O O O O O - While the O's appear to be winning the game, in fact the last four moves are all x moves which allow x to flip enough disks to win the game 38-26. Why did the x's win? If you look at the above position you will note that the x island in the midst of the O's has two advantages which can be extended to correct Othello strategy. The first of these advantages is called Disk Stability, which occurs when disks cannot be flipped by any opponent move or future opponent move. Certainly the lone x disk in the above diagram qualifies as a stable disk. The second of the advantages involves the maximization of your options when compared to your opponent's options. In the above diagram, the O's have no move options at all. It is worthy to note here that it is just as important in Othello to minimize your opponents move possibilities as it is to maximize your move options. The combination of these two concepts gives rise to the correct analysis that stable cluster formations in the center of the board are most advantageous (the aforementioned position is an illustration of this). A further observation about the combination of these two concepts is that it is important to keep your disks connected to each other in the opening. Disks which are in the center of two separate opponent formations tend to be both stable and also tend to limit the opponent's options. The Reversi 4.0 program evaluates the stability and option potential of various disk formations. In addition, a value is employed of the internal cluster and disk connectivity concepts by the invention of an "Average Foreign Neighbor" statistic. This statistic in the program looks at every disk and assigns a weight of 1 for every direct neighboring square which contains an opponent's disk and a weight of 2 for every direct neighboring square which is empty. The program then tries to minimize this statistic. The Average Foreign Neighbor statistic has a few important effects. First, it is better for a disk to be near other disks its own color. Second, it is better to be in the center of opponent's disks than on the perimeter of any formation (where your disk has many surrounding empty squares). Third, a disk along the edge has the advantage of having less neighboring squares and there is a natural affinity for the edges through this statistic. IV. Evaporation Strategy Many a beginner has started the game of Othello by striving in the opening for what his goal is at the end, trying to maximize the number of disks he has on the board. Yet, there is not an opening strategy that could be worse than this. Let us take a look at why. With respect to the rule of Option Maximization, it is true that the side with more disks tends to have less possible legal moves. This is because a legal move requires the flipping of your opponent's pieces. If your opponent has more pieces to flip, you probably have more legal moves. If you have more pieces, your opponent probably has more legal moves. In fact, a correct Othello opening strategy is that of minimizing your pieces, also called "Evaporation Strategy." While this strategy is somewhat less important than the other strategies mentioned above it is nevertheless very important not to let the number of your pieces overwhelm the number of your opponent's pieces. A term coined by one of the top ten U.S. players, Arnold Kling, in an issue of the USOA newletter, the Othello Quarterly, illustrates the combined strategies of evaporation and the Average Foreign Neighbor statistic. The term, the "Perfectly Quiet Move" is a rule that any move (in the opening or middlegame) that flips exactly one disk and as a result places only one additional disk on the perimeter of the formations is in fact a very favorable move to make. Arnold explains that much of opening play surrounds the creation of Perfectly Quiet Move opportunities and the elimination of PQM opportunities for the opponent. While the Reversi 4.0 program doesn't explicitly evaluate PQM opportunities, the employment of both the Average Foreign Neighbor statistics and of Evaporation Strategy implicitly recognizes PQM. V. Parity The most important concept in endgame play (and thus middlegame play as a precursor to the endgame) is the establishment of move parity. Consider the following position: - - O O O O O O - - O O O O x O x x x O O O x O x x x O O O x O x x x x x O x O x x x x x O x O x O O O O O x O x x x x x x x O This position shows an empty region in the northwest corner of the board which has an EVEN number of empty squares. The rule of parity states that a move into an enclosed region containing an even number of empty squares is a bad move and, conversely, a move into an enclosed region containing an odd number of empty squares is a good move. This rule develops from the fact that the last person to play into a given enclosed region flips disks which subsequently become totally stable because there are no more regional flips available. In the above position, whoever moves first loses the game. If the region had one more empty square, making five empty squares, the player to move first would win. The program, Reversi 4.0, deals with parity in terms of two evaluation rules. First, the number of empty squares within a given quarter of the board (quadrant) is counted. Parity becomes more important to the evaluation routine as the number of empty squares in the quadrant decreases. Second, the program determines parity advantages by counting the move opportunies within the empty squares of a quadrant region. If the region is even, the player with the most opportunities to play within that region has an disadvantage. If the region is odd the player with the most opportunities to play within the region has an advantage. An opportunity is defined in this regard as a count of the number of squares within the empty region to which a player has access (to which he has a legal move). Parity in the endgame is in many instances far more important than the gaining of corner squares. The rules and concepts presented here are by no means complete, but they represent the total of all concepts incorporated in my program. A studious review of these concepts will be amply rewarded. While these concepts are all correct, the game of Othello is made original by the player's judgement as to which of conflicting objectives is the most important. The program is crudely consistent in the relative weights of the objectives. Perhaps this is a drawback of all computer gaming programs, for humans have the flexibility to tailor the importance of objectives to the position at hand. ABOUT THE AUTHOR David W. Parsons resides in New York City with his wife, Marie, and his three year old son, Christopher. Mr. Parsons is a Vice President for Metropolitan Life Insurance Company and is a Fellow of the Society of Actuaries. Besides his ranking as one of the top ten Othello players in the United States, Mr. Parsons has attained a Master rank in Duplicate Contract Bridge and a National Master rank in chess, among the top 300 players in the country. ------------------------------------------------------------------------- Correspondence regarding this program can be directed to: David W. Parsons 7 Peter Cooper Road #10G NY, NY 10010 Phone: (212) 475-8911 Please support Othello by joining the United States Othello Association and by playing in USOA tournaments. Membership in the USOA includes the quarterly magazine and is available for $6 per year. Subscription requests may be sent to: OTHELLO QUARTERLY 920 Northgate Avenue Waynesboro, VA 22980