El sistema vial generado por proyectos de desarrollo hidroeléctrico

Let us delve into some of the theory of this endgame. Maybe it will kindle the

reader's interest in studying endgames as it did with me.

From the previous diagram:

l.If8+ He8

2.Hf7

Black loses i f he tries to passively hold the back rank. For instance:

2 . . . * c 8

2...Hh8 loses immediately to 3.Ha7 Hh6+ 4. A e 6 and Black is mated or loses his rook.

3. Ha7!

Switching sides is a natural way to ex- ploit the fact the rook is only protecting the back rank on one side of the king

3...Id8+

4. * c 6 * b 8 5.1b7+ * a 8

P A R T 3. E n d g a m e Explorations

6. Hb5!

Black will be shortly mated thanks to the bishop's X-ray to a8

6...*a7

6...Hc8+ 7 . * d 7 + loses the rook, and any other sixth move loses to <4)c7+

and l a 5 #

7. * c 7

Threatening checkmate and the rook.

7...*a6

The only try. 8.1c5!

A n d when the black rook moves the black king will be mated by jfcc4+ (or A b 7 + ) followed byHa5#.

The lines are a little tricky at first but after playing over them a few times you will see the mating patterns more easily.

We will return to the last diagram and look for other defenses:

Position after 2.2f7

The only other defensive try is to move the rook somewhere down the e-file, to meet 2 f 8 + with He8 back. Three squares are available ( e l , e2 and e3).

If you will trust me for now, I will tell you about these three options:

> The worst square is e3. They key reason for this (other than the fact it loses to a forced sequence) is that the white bishop controls some important squares on the third rank, which will be denied to the defending rook.

> e l is the next best square. White's goal then is to force the rook from e l to the inferior e3 square.

> The most flexible and best square is e2. In this case White is looking to force the rook first to e 1, then to e3.

E n d g a m e E x p l o r a t i o n 1: M y Favorite E n d g a m e

Are we clear?

O K , let's see why e3 is so bad, and what the forced sequence is:

Starting from 2.2f7:

2...1e3?!

Not changing the theoretical assess- ment (losing for Black) but rather com- pliant.

3.1d7+!

Remember this. When the black rook goes to the third rank, we force Black to make a decision with his king with a check between the kings. As it turns out it's not much of a decision...

3...*e8

3...<4)c8 4.Ha7 is mating immediate-

ly. Notice here that the black rook can- not go to b3 to guard against the mate. If the rook was on the first or second rank then it could, but I did tell you the third rank was the worst choice!

4.1a7

4.Hb7 is the same. The key point is that although 4.Hg7?! may appear as i f it mates as in the previous note, it does not because of the reply 4...<4)d8. White

has actually made zero progress in that case. So we commit the rook in the same direction no matter which way Black moves his king.

4...*f8

The only move; anything else is mat- ed immediately.

5.1f7+! *e8

5...4>g8 loses the rook to a discov- ered check, so our forced sequence con- tinues.

The next step is to retreat the rook down the f-file. This will threaten A c 6 + followed by Hf8+ and mate since the e8 square will be attacked twice. Which square we move to on the f-file is impor- tant though:

P A R T 3. E n d g a m e E x p l o r a t i o n s

Now Black has a choice of defenses to the threat of A c 6 + . He can pin the bish- op with Hd3 so it cannot move, or he can move his king back to d8 immediately.

6...*d8

6...Hd3 goes down quickly after 7.Hg4, and again the perils of the third rank are shown; Black is denied the f3 square for his rook. Note that this 6...Hd3 defense would lose i n the same way no matter where White retreated his rook on the sixth move.

7. Ae4!

But this key interference move would not be possible with the rook otherwise placed on the f-file. The threat is Hf8 and mate!

7...*e8 8. A c 6 +

A n d Black is mated.

Returning to the position after 2.Hf7.

Position after 2.1f7

Now we know on 2...He3, we initi- ate a winning sequence of forced moves with 3.Hd7+! We saw how clumsy the third rank is for the defender's rook i n those variations. N o w we should try:

2...1el

The same idea with 3.Hd7+ doesn't do White any good here. Black's best way to exploit the extra flexibility of his rook is to follow an analogous line to the previous one until close to the end: 3...*e8 4.1a7 * f 8 5.1f7+ * e 8 6.1f4 ^ d S 7.Ae4 and now exploiting the ex- tra mobility the rook enjoys on e 1 by the simple 7...Hdl+.

It turns out that White's rook is per- fectly positioned on f7 for this. We will first see how the concept works, then we will look at how White would implement it if his rook was not so favorably placed.

The idea is to create a Zugzwang position. If Black can't move his king, and the white bishop controls both the e2 square and the checking square d l ,

E n d g a m e E x p l o r a t i o n 1: M y Favorite E n d g a m e

then...maybe Black will be forced to put his rook on e3.

Can we avoid playing 3...He3? The only try seems to be to move the king. 3..(4>c8 4.Bf8+ ends the game immedi-

ately, but perhaps we can try 3...(4>e8.

3...*e8

The rook clearly must retreat, and on to the fourth rank becomes the reflex move. The threat is A c 6 + and B f 8 + .

4 . . . * d 8 Forced.

5.1a4

5.Bb4 is the same, but it always pleasant to create these patterns where both bishop and rook control the back rank mating square (in this case a8)

5 . . . 1 c l

5...*c8 6.1a8# is still mate. 5...*e8 loses to 6. A d 5 threatening Ba8# 6.. f8

7.Bg4! with a beautifully coordinated and unstoppable mate on g8.

6.Ag4!!

A quite wonderful scene. Complete coordination of the white forces! Notice how Black's pieces are totally dominated.

6...*e8 7. Bf4 B e l

8. A h 5 +

Or 8.Ad7+. Mate follows.

We should go back to the position af- ter White's 3.Af3:

P A R T 3. E n d g a m e E x p l o r a t i o n s

The only remaining try is to fall in with White's wishes and play:

3...1e3

The white bishop is on f3 though, not on d5. So it's not quite the same as before, perhaps Black can survive?

4 . A c 6 !

4. Hd7+ would be premature with the bishop still on f3. First a sequence of threats will bring us to a familiar posi- tion.

4...1d3+

5. A d 5 2 e 3

5...4>e8 6.Hg7! is another nice mat- ing pattern.

A position we have seen before. White wins, as we know, beginning with 6.1d7+

Getting the correct geometry