This article is intended to be a beginners guide to some strong ways to sacrifice corners against players who take a lot of pieces and a lot of edges (certain poor Othello programs, for example). But many of the ideas can be used in ordinary positions also.
The first example we shall consider is the one I usually use to demonstrate that having lots of pieces and lots of edges is not a good thing.
..OOOO.. ..OOOO.. OOOOOOOO OOO##OOO OOO##OOO OOOOOOOO ..OOOO.. ..OOOO..
Black to play
In this fairly extreme example, White has a position which may seem ideal
to many beginners. He has 44 pieces to Black's 4, he has the beginner's
favourite edge structure on each edge (a balanced four), and it even looks
fairly certain that Black will lose all four corners.
But, this position
is a very easy win for Black. Black has a particularly strong type of
sacrifice available. Black's best line begins with an x-square, e.g.
45.b7. White now has the choice of taking the corner, or giving it to Black
(by playing a7 or b8). The latter choice is, at least in this case, clearly
suicidal: Black can then win easily by taking the corner and
working round the
edges (White has to keep sacrificing corners).
So let us assume that White takes the corner with 46.a8. Black can now play both the moves a7 and b8, and should do so. This gives Black wedges in two edges, more than enough compensation for his corner. The feature that made this sacrifice so good was that all of the pieces in the b column and the 7th row were white. Note that this sacrifice can be used in the midgame in order to play three out of four moves near a corner, and force White to find two moves elsewhere. In this endgame, however, White simply passes, and there is more work to do.
After 47.a7 pass 48.b8 pass, Black plays 49.g7. This time the pieces on the seventh row are not White, but after 50.h8, Black has access to g8 along the bottom edge, and so we have 51.g8 pass and black can save h7 for later. After 52.b2 a1 a2 pass Black has two excellent moves saved up: he only needs one to make the last region play the way he wants. In order to get the last move in the North-East region, Black "feeds" White with some self-destructive moves. 55.g1 h1 h7 g2 b1 pass h2 completes the perfect play line. Black has sacrificed all four corners and won 46-18.
..OOOO.. ..O#OO.. OOOOOOOO O#O##OOO OOO##OOO OOOOOOOO ..OOOO.. ..OOOO..
Black to play
Let us see another example. This time three of the x-squares available to Black are inferior to the fourth. Since the pieces in the g column and the seventh row are all White, the best first move for Black is 45.g7. Now, as before, perfect play continues with 46.h8 g8 pass, but this time Black will need to save his available move at h7, and feed White immediately in one of the other regions. Best is 48.b1 a1 h7 b2. Note this has made all the second row White, and so g2 now becomes available as a good sacrifice. After 52.g2, White should consider h2, but 53.h1 h2 pass g1 pass is better for White. Note Black still has his move at a2 saved up, and so he can feed White in the last region. Surprizingly, the best way is to unwedge with 56.b8, giving White the fourth corner, and the whole South edge. But after 57.a8 a2 b7 a7 Black wins 43-21.
When there are no obvious strong x-square sacrifices, the wins in this type of position are hard to find, if they are even there. I would suggest that you should try to avoid ending up in the following kind of position, either by making sure the opponent's edges are worse than this, or by taking an edge yourself at some point.
..OOOO.. ..O#OO.. OOOOOOOO O#O##O#O OOO##OOO OOOOOOOO ..O#OO.. ..OOOO..
Black to play
I will admit that when I typed this position into my computer, I thought it was a win for White! But it turns out that Black can win 33-31. The perfect play line begins 45.b1 a1 a2 b2 b7 b8. Here White turns down the corner in order to cut accross Black's plans. But Black simply continues with 51.a8 a7 g8 g7 h8 h7 h2 g2 g1 h1, and wins, barely, 33-31.
..OOOO.. ..O#OO.. OOOOOOOO O#O##O#O OOO##OOO OOOOOOOO ..O#OO.. ..OOOO..
Black to play
What happens if White grabs corners instead? After 50.a8, Black sacrifices with 51.h7 and perfect play is then 52.b8 g8 h8 g7 g1 (feeding time again) h1 a7 g2 h2 34-30.
..OOOO.. ..O#OO.. OOOOOOOO O#O##O#O OOO##OOO OOOOOOOO ..O#OO.. ..OOOO..
Black to play
If instead 52.h8, then 53.g8 g7 b8 pass g1 h1 a7 g2 h2 is 36-28 to Black.
I would not like to have to find that over the board.
Now, for a change, let us look at a real position from a serious game.
..OOOO.. #.O#OO.. ##OOOOOO #O###OOO .OO#OOOO OOOOOOOO ..#OOO.. .###.O..
Bhagat (Black) to move
This position is from Bhagat-Feinstein in the 1987 Cambridge international tournament. I wouldn't really want this position for either side! Pete had outplayed me in the mid-game, and in desperation I had walled myself off from both regions in the East, after making sure that he had no good x-square sacrifices. We had now arrived in the endgame with Black to play. Pete tried 45.b2, (this is indeed a 33-31 win). But after 46.a1 Pete played the natural 47.b1 and after 48.a5 I was winning all the way. Black urgently needs a plan from the start, and it is very difficult to find one.
..OOOO.. #.O#OO.. ##OOOOOO #O###OOO .OO#OOOO OOOOOOOO ..#OOO.. .###.O..
Bhagat (Black) to move
The perfect play line is 45.b1 a1 a5 b2 g1 g2 b7 a8 a7 e8 h1 h2 h7 g7 g8 h8 37-27, but the question is: what happens if White plays 50.h1 instead?
..OOOO.. #.O#OO.. ##OOOOOO #O###OOO .OO#OOOO OOOOOOOO ..#OOO.. .###.O..
Bhagat (Black) to move
Well, it's very sneaky. Black plays 51.b7 a8 e8 a7 and Black gets both of g2 and h2. Play finishes 55.g2 pass h7 (feed) h8 h2 g7 g8 and Black wins 38-26. If you saw all of that, you are an endgame expert!
..OOOO.. ..O#OO.. OOOOOOOO OOO##OOO OOO##OOO OOOOOOOO ..OO#O.. ..OOOO..
Black to move
Finally, a tricky little exercise for you. Would you be able to find a win for Black in the following position? Black can win 33-31.
(Warning: after 45.b1 a1 a2 b2 b7 b8 White gets a draw. So you need another plan).
A solution (well, clearly there is more than one!) can be found by clicking just the forward (>) button