This text is the electronic equivalent of a booklet created and distributed by Emmanuel Lazard and the French Othello Federation (F.F.O.). This copy is distributed with the authorization of Emmanuel and the F.F.O. The printed version of this booklet (with nice round discs) is available from the F.F.O. for 20 French Francs (shipping included) by check payable to the F.F.O.

FEDERATION FRANCAISE D'OTHELLO, BP 1383 75626 Paris Cedex 13, (1) 45 35 55 86

(C) Emmanuel Lazard (and the entire F.F.O. team) March 1993

Translated from French into English by Colin Springer with the permission of the author. This text may not be further distributed without the explicit agreement of the author.

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OTHELLO (r) : THE RULES OF THE GAME

Othello is a strategy game played by two players: Black and White. It is played on an 8x8 board (usually Green in colour), called the Othello board. The two players place 64 discs, each of which is black on one side and white on the other. For convenience, each player begins with 32 discs but these do not belong to him and if his opponent runs out of discs, he is obliged to give him some. A disc is black if the black side is visible and white if the white face is on top.

The Goal

The winner is the player who has more discs of his colour than his opponent at the end of the game. This will happen when neither of the two players has a legal move. Generally at this stage all 64 squares are occupied.

Starting Position

At the beginning of the game, two black discs are placed on e4 and d5 and two white discs on d4 and e5 (see fig. 1).

Figure 1 : the Initial Position

Black always begins, and the two players subsequently take turns moving.

Making a Move

At his turn, a player must place a disc of his colour on one of the empty squares of the othello board, adjacent to an opponent's disc. In addition, by placing his disc, he must flank one or several of his opponent's discs between the disc played and another disc of his own colour already on the board. He then flips to his colour all the discs which were flanked. The discs are neither removed from the Othello board nor moved from one square to another.

Fig. 2 : Black plays f5 ...

Fig. 3 : and flips e5 !

Black's first move may be, for example, to f5 (see figure 2). By playing f5, he flanks the white disc at e5 between the disc played and another black disc already on the board (here d5) ; he then flips this disc (see figure 3). Black could also have moved to e6, c4 or d3. However, these four black moves are perfectly symmetrical ; black needn't spend time thinking about his first move.

Fig. 4 : White f4, f6 or d6

Fig. 5 : if white plays d6.

Now it's white's turn to move. He has three possible moves (see figure 4). Each possible move flips at least one opponent's disc. White may play f4, f6 or d6. Note that discs can be flanked in all eight directions. Furthermore, in each direction several discs may be flanked (see figures 6 and 7). All these flanked discs must be flipped.

Fig. 6 : Black plays c6 ...

Fig. 7 : resulting in this position.

Black has played to c6. He turns the discs at b6 (flanked by the disc at a6), b5 (flanked by a4), d7 (flanked by e8), c5 and c4 (flanked by c3). Note that neither d6 nor e6 are flipped due to the empty square at f6.

There is no chain reaction : flipped discs may not be used to flip other discs on the same move. Thus, in figure 8, black moves to a5 :

Fig. 8 : Black plays a5

Fig. 9 : c4 remains white.

The discs at b5 and c5 are flipped since they are flanked. At this point, even though c4 is flanked, it is not flipped (see figure 9). The reason for this is that it is not flanked between the disc played and another disc.

If, at your turn, you may not make a move to flip at least one opponent's disc according to these rules, you must pass your turn and it's once again your opponent's turn to play. But if a move is possible, you must play it.

End of the Game

The game is over when neither of the two players has a legal move.

Generally, this happens when all 64 squares are occupied. However, it is possible that some empty squares will remain where neither player may move : for example, if all the discs are the same colour after a turn, or in a position such as the one below (see figure 10).

Fig. 10 : The game is over !

Neither of the two players can play to b1 since no flipped discs are possible. In this case, we count discs to determine the final score. Empty squares are given to the winner by convention. In this game, white has 29 discs and black has 34, with one empty square. Thus black wins 35-29.

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NOTATION

The game of Othello takes place on a board with 64 squares. We refer to these squares by a coordinate system : the rows are numbered from top to bottom by 1 to 8 ; the columns are indicated from left to right by 'a' to 'h'.

             a  b  c  d  e  f  g  h
          1 a1 b1 c1  .  .  .  . h1 1
          2 a2  .  .  .  .  .  .  . 2
          3 a3  .  .  .  .  .  .  . 3
          4  .  .  .  .  .  .  .  . 4
          5  .  .  .  .  .  .  .  . 5
          6  .  .  .  .  .  .  .  . 6
          7  .  .  .  .  .  .  .  . 7
          8 a8  .  .  .  .  .  . h8 8
             a  b  c  d  e  f  g  h

             a  b  c  d  e  f  g  h
          1  .  C  .  .  .  .  C  . 1
          2  C  X  .  .  .  .  X  C 2
          3  .  .  .  .  .  .  .  . 3
          4  .  .  .  .  .  .  .  . 4
          5  .  .  .  .  .  .  .  . 5
          6  .  .  .  .  .  .  .  . 6
          7  C  X  .  .  .  .  X  C 7
          8  .  C  .  .  .  .  C  . 8
             a  b  c  d  e  f  g  h

    a  b  c  d  e  f  g  h
1  45 32 19 18 31 24 44 43  1
2  46 36  9 11 16 15 42 56  2
3  17  8  3  4 10 22 38 51  3
4  20 13  5 o  x   6 23 40  4
5  21 14  7 x  o   1 39 41  5
6  34 30 12  2 28 29 53 52  6
7  35 47 33 26 25 37 59 55  7
8  50 49 48 27 54 60 58 57  8
    a  b  c  d  e  f  g  h

The diagram above represents the game Penloup-Juhem game from the 1992 World Championships. The first player listed is black, here Penloup. The '1' on f5 indicates that the first move was played on this square ; then white responded with d6, followed by c3 d3 c4 ...

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INTRODUCTION TO STRATEGY

The rules stipulate that the winner of an Othello games is the player who has the most discs of his colour at the end of the game. Newcomers to the game too often have the tendancy to transform this long-term objective into a short-term tactic : they try to have the most discs at each stage of the game. To do this, they play at each move the move which turns the greatest number of discs possible. This is called the maximum disc strategy. Fortunately for the game's interest, after several games against an experienced player, one clearly sees that this strategy is not good, as we will try to demonstrate with an example.

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MAXIMUM DISC STRATEGY

In diagram 1, black has only one disc with only four moves to go. Surely white has a certain win ?

Diagram 1. Black to play

Black may play a1 or h8, and in this manner, he may play all the remaining moves (since white must pass after each move), for a final score of 40-24 for black ! It's therefore clear that having lots of discs, even very close to the end of the game, does not absolutely guarantee an ultimate victory. In the example of diagram 1, white indeed has many discs, but they are vulnerable : they can be flipped back by the opponent. What's important is therefore not to have many discs but rather to have many discs which can not be flipped back by the opponent, no matter what happens for the rest of the game. Such discs are called "stable discs". Of course, it's often very difficult to acquire stable discs before the last few moves of the game ; but first let's see some examples of stable discs.

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STABLE DISCS -- POSITIONAL STRATEGY

It is impossible to flip a disc placed in a corner since it can never be flanked between two opponent's discs. A disc played in a corner is therefore the most simple example of a stable disc. In addition, once a corner is occupied by a disc, adjancent discs of the same colour often also become stable discs.

Diagram 2 : Stable discs

In the example of diagram 2, the 26 black discs are stable, independent of the colour of the other discs on the board, and black is assured to keep at least 26 discs at the end of the game.

Diagram 3 : Black to play

In diagram 3, black may play to h8, creating 23 stable discs (the g and h columns, rows 7 and 8, and the disc f6) (see diagram 4).

Diagram 4 : After a black move to H8

Black is now in a very good position to win this game. Indeed, he already has 23 stable discs ; if he can hold just 10 more discs at the end of the game he will be assured at least 33 discs, and victory. In Othello, discs played in the corners are therefore extremely important : they permit subsequent edge moves which lead to even more stable discs. However, this rule has exceptions (as we shall see later), but remember never to give a corner to your opponent without compensation (unless of course you have no better moves...). The simplest way to avoid giving up a corner is to avoid playing to the squares adjacent to a corner, that is to the weaker X and C squares (see diagram on page 2). You may only move to a square which is adjacent to an opponent's disc (which you will flip) ; thus your opponent will not be able to take a corner unless at least one of the three adjacent squares are occupied. In diagram 5, black has unwisely played to the X-square b7, believing that white cannot take the corner a8 since there is no white disc along the diagonal. However, white may play d8 (see diagram 6), which flips (among others) d5 and allows him to take the corner a8 on his next move, black having no method to flip back the disc on d5.

Diagram 5 : White to play

Indeed, the isolated disc on b1 will permit white to take the a1 corner : white plays c1, threatening to play a1 on the next move. To prevent this, black has only one possibility : he must flip back the disc by playing d1. However, thanks to the disc at e1, white may still play a1. Black has made a terrible error by playing the C-square b1. To be more precise, the danger of playing a C-square is greatest when it is an isolated C-square, that is to say not connected to other discs along the edge. Thus in diagram 3, black has played several C-squares but he risks nothing since black discs occupy the entire edge.

Diagram 6 : After a white move to D8

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WEDGES

We have already seen that the corners are very important. This immediately translates into a method by which edges must be played. Consider for example the south edge in diagram 7. If black plays c8, he can take the corner a8 no matter what white does. The reason is that the disc at c8 cannot be flipped back, since it is flanked by two white discs. One says that the black disk is wedged. What about the east edge? If black plays h6, he cannot wedge because white takes back with h5 (and similarly, if black plays h5, white will respond h6). Now consider the north edge. If black plays c1, white may take back with d1 to avoid losing the a1 corner. However black may now wedge with e1, winning despite everything the corner on his next move.

It seems clear therefore that whenever there are an odd number of empty squares between two discs of the same colour (here white), the other player may get a wedge (as in the south and north edges), while when there are an even number of empty squares, the wedge may be avoided (as in the east edge).

Diagram 7 : Black to play

From the principal that one should avoid playing C and X-squares, many beginning players deduce an incorrect strategy which consists of assigning to each square a fixed value in advance which does not take into consideration the position on the board. In this method, corners are the best squares, followed by edge squares other than C-squares, the central squares are given a neutral value, while the C-squares and especially X-squares are considered to be bad. At each move, they play to the square with the greatest value (assuming it is a legal move of course).

Unfortunately, this strategy is badly flawed for reasons which will soon become apparent.

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MOBILITY

We have already said that to avoid giving up corners to your opponent, you should avoid playing to squares adjacent to a corner. There is however one case where you may be obliged to do this : if it is your only legal move. Consider the position in diagram 8.

Diagram 8 : Black to play

White has very few possible moves. If black plays to e8, there will be only two remaining moves for white, b2 and g2 (see diagram 9).

Diagram 9 : After black's move to E8

Now, according to the rules of the game, white is forced to play one of these teo moves. If he plays b2, black may take the a1 corner and if white plays g2, black may take the h1 corner. Furthermore, because of the six black discs on the north edge, as soon as black takes one of the corners a1 or h1, he will be able to take the other on his next move.

At this stage we can begin to develop a good strategy for playing Othello. Your opponent will not play to a C-square or an X-square if he may play elsewhere. Your objective is therefore to force him to play there. To this end, you must reduce his different move choices to the point where he only has poor moves remaining, as is the case for white in diagram 8. Now he will be obliged to play one of these (bad) moves and you will be well on your way to a final victory.

Diagram 10 gives another example.

Diagram 10 : Black to play

If black plays to g6, there is only one legal move for white : b2. Of course, as black has no disc on the b2-e5 diagonal, he cannot immediately take the a1 corner, but he will have no trouble in recovering this diagonal, for example with e1 which flips c3 (see diagram 11).

Diagram 11 : after G6-B2-E1

In diagrams 8 and 10, black has very good mobility as he has the choice between numerous (good) moves, while white has few options and all these moves are mediocre : he has very bad mobility.

As a general rule, your objective is to limit the number of liberities (that is, the number of moves) available to your opponent, while at the same time increasing yours. This is what we call the mobility strategy. When this objective is attained, one is said to have control of the game. However, don't forget that you must force your opponent to make a bad move : it's not enough if he has even one non-disasterous choice at each move ; he must have no good moves at all.

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FRONTIERS

Each move is played to an empty square adjacent to an opponent's disc. This is the principal which will guide us in the choice of a good move.

At each move you must flip at least one of your opponent's discs. It is therefore clear that the more opponent's discs there are neighbouring empty squares, the more possible moves you will have, and hence the better your mobility will be. Conversely, if very few of your discs are adjacent to an empty square, your opponent will have very few possible moves. A disc adjacent to an empty square is called a frontier disc ; the others are called internal discs. The set of frontier discs is called the frontier. From what we just said, it seems natural to try and minimize your number of frontier discs.

In diagrams 12, 13 and 14, we show three positions which appear similar. What can we say about a black move to a6 in each of these three positions?

Diagram 12 : Should black play A6 ?

In diagram 12, a move to a6 seems disasterous : after white responds with g1, blck will be forced to give up a corner to white (since his only remaining legal moves are b1, g2 and h2). Playing a6 is very poor since it flips a large number of frontier discs (those on row 6) and establishes on this row a large black frontier adjacent to which black may no longer play.

Diagram 13 : Should black play A6 ?

Playing a6 in diagram 13 is much more reasonable since, among the flipped discs, only b6 and c6 are frontier discs. However, this move still deprives black of access to some squares which may become important later on, for example a7. Perhaps it would be better to play e7 which flips fewer frontier discs.

Diagram 14 : Should black play A6 ?

By contrast, the best move in diagram 14 is a6. If white responds with b2 or g2, black can immediately take a corner, and if he responds with g1 (the only other legal move), black may respond with a7 and white is now forced to give up a corner to blck (he can only play b2 or b7). In this diagram, the move to a6 is called a perfectly quiet move, since it flips no frontier discs (after playing a6, b5 is no longer a frontier disc). Now we can see the limits of an evaluation of moves based simply on a positional strategy : what's important isn't just where you play but especially what discs which you flip. We can now better understand the weakness of white in diagram 8. All the frontier being white and black having many moves at his disposal (7 moves in addition to those to an X-square or C-square). He has a perfectly quiet move to e8 which adds no discs to his frontier. White now sees the consequences of his enormous frontier : he is obliged to play b2 or g2. Similarly, in diagram 10, a large part of the frontier is white (largely because of the white wall on the east), and by playing g6 black offers no new moves to white.

One of the methods of reducing your opponent's mobility (and especially of not reducing yours by much) will be to avoid flipping too many frontier discs. It's better to have internal discs (that is, discs which are not adjacent to an empty square) than frontier discs. This is what we call the strategy of control of the center. Of course, it is not an accident that all the black discs in diagram 8 are internal discs.

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TEMPO, WAITING MOVES

Consider diagram 15. The frontier to the north is equally divided between the two players.

Diagram 15 : Black to play

It's black to play. He may consider a move to the north (e2, d2, or c2 are reasonable), but of course he would prefer white to play first into this region and lengthen his frontier. This is one of the paradoxical characteristics of Othello : it is often unfavourable to have to move since you flip discs of your opponent and risk giving a number of new moves to your opponent. Now, if black doesn't want to play to the north, the only remaining option is to play to the south. He has the choice between two reasonable moves there: c8 and d7. What will happen if black plays c8? White, who doesn't want to play to the north either, will respond with d7 (diagram 16), and black must open the game to the north first. By contrast, if black plays d7, the only plausible move to the south for white is c8 to which black may easily respond b8 (see diagram 17). We say that black has gained a tempo in the southern region. Now it is white who must initiate play to the north.

Diagram 16 : Black to play