Things to remember: DIAGONALISATION! by David Haigh

February 1995

``Othello is a game of chance.'' Who said that? Someone who hasn't played much Othello? Maybe. But I in fact heard it said by a very good player, good enough to be in the top ten of the rating list.

``What do you mean?'', I asked. ``Well,'' he said, ``suppose it's your move and you have two equally good-looking moves. Try as you can, you can't decide which is better. So you mentally flip a coin and make one of the moves. Now, unknown to you, one of those moves was really a game-winning move and the other a game-losing move. So the outcome of the game has been decided your mental coin flipping, i.e. chance. This happens more often than you might think, to players of all abilities.''

So what distinguishes a good player from a poor player? One answer is that the good player encounters fewer situations where moves look equally good. To a beginner, with very little experience, many of his/her moves will look indistinguishable, impossible to choose between; I'm sure you know what I mean! Read on, and I'll describe one thing you should bear in mind, which could help you to decide between otherwise equally good-looking moves.

One thing Othello novices soon learn is that the X-squares, the squares next to the corners but not on the edge, are very often bad places to go to, so one delays going there as long as possible. But eventually someone will have to go there. What will happen when they do?

That depends. One thing that it depends on is what the two main diagonals, i.e. the squares from c3 to f6 and c6 to f3, are like. There are three types of main diagonal to watch out for:

1) it is all one colour;

2) as you look along it from one end, there is exactly one change of colour, as on c3-f6 in figure 1;

3) there are two (as on c6-f3 in figure 1) or more changes of colour.

In figures 1 and 2, only the discs on the diagonals are shown.

........
........
..W..W..
...WB...
...WW...
..W..B..
........
........

Figure 1

........
.B....W.
..B..W..
...BB...
...WB...
..W..B..
........
........

Figure 2

Type 3's are dodgy for both players. If either player goes to an X-square on this type their opponent will be able to take the corner. In figure 2 white has had to go to g2 (by flipping pieces not shown) and black will now be able to go to h1.

Type 1's are good for the player whose colour they are. This player can go to each X-square in turn and not immediately give away a corner. These extra two moves will very often be very useful. Conversely, type 1's are not good for the other player.

Type 2's are more interesting. Whoever goes to the right X-square first can make the diagonal all his/her colour, so it effectively becomes a type 1. This type is potentially good for either player. It's a sort of race, the winner being the player who has the foresight and/or courage to go to the X-square first! In figure 2 black has won this race by going to b2.

The lesson to be learned from this is that it can be good to have the main diagonal all your colour. This is called diagonalisation. Apart from allowing you some extra safe moves at the end of the game, it is also an essential ingredient in one of the ways used to attack a weak edge. So, if you are trying to decide whether to make a particular move, one thing to consider is what it will do to the main diagonals. Will it help you to diagonalise? Or will it stop your opponent from achieving this, or even ruin his/her existing diagonalisation? If the answer is yes, the move is probably better than an otherwise equally good-looking move which has no such effect on these diagonals.

However, it should be stressed that you should not try to diagonalise too early in the game, because in the early stages it is too easy for the opponent to cut accross your diagonal. Diagonalisation is a ploy best left to the later stages of the game.

To finish, here are two very similar looking positions. In both positions it is Black to play. There is just one difference between these positions. In figure 3, White has managed to use diagonalisation to fool Black. If Black had been more careful and kept a piece on the c6-f3 diagonal then the win would be easy. Instead, Black will have to give away all the corners, and White wins. In figure 4, Black has been more sensible. This time White is made to pay for taking all those weak edges, as Black simply takes all the corners and wins easily.

.WWWWW..
W.WBBBWW
WWWBWWWW
WBWBWWWW
WBBWBWBW
WBWBBWWW
WWBBBW.W
..WWWWW.

Figure 3: Black to play

.WWWWW..
W.WBBBWW
WWWBWWWW
WBWBWWWW
WBBBBWBW
WBWBBWWW
WWBBBW.W
..WWWWW.

Figure 4: Black to play

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