## Saturday, November 02, 2013

### TGIF Brain Teaser

White to move and win! How should White proceed?

7K/2p5/4p3/2p2kPP/8/4P3/2b5/4n3 w - - 0 1

This puzzle was presented by Andreas.

Anand Gautam said...

What is wrong with g6, g7, h6, h7, exchanging one pawn for the Bishop and promoting the other to Queen?

Yancey Ward said...

This is a tough puzzle! And, right now, I don't have a good, clean solution.

Obviously, white would want to advance a pawn here. The obvious place to look first is to push g6:

1. g6

Now, the question is back on black- can he stop the pawn at g8? He can try the combo of e5 and Bb3:

1. .....e5
2. g7 Bb3
3. h6

Now white is threatening h7 followed by g8Q. At this point, black's best bet is to gobble up e3 and try for a draw with the knight and the extra pawns vs K+Q, but this is likely lost because of the weak pawns and the fact that none have yet crossed the 4th rank:

3. .....Ke4
4. h7 Ke3
5. g8Q Bg8
6. hg8Q Nd3 (any better?)
7. Qd5

And, at this point, since I didn't really want to spend a lot time analyzing a dead end line, I just confirmed that this is surely lost by putting in various analogs of this position into the Nalimov tablebase where black has dropped the backward c-pawn to the white queen, and I couldn't find a single one where white doesn't win in 20-30 moves. However, this would be a tricky ending to finish off.

So, at move 1, black's next most obvious defense to me is Bd1. The idea being to win the h-pawn, allow white his queen, and try to gobble up the e-pawn later and try for a draw like the one above, but this time having the bishop in addition to the knight:

1. g6 Bd1
2. g7 Bh5
3. g8Q

Now, black has a decision to make and not an easy one. Black cannot play Ke4 here since Qh7 wins the bishop and the game. Black could play Nd3 now. Note, this is somewhat speculative on my part, but I think black can't really do better than what follows after 3. ...Nd3:

3. .....Nd3
4. Qh7 Bg6 (forced)
5. e4 Kf6
6. Qg7 Qg5
7. Qe7 Kh5
8. Qe6 Nf4 (almost forced?)
9. Qc4

And I don't see how black retains the pawns here. The ending, K+Q vs K+N+B is won in almost all instances that I am aware of, and certainly the ones that might arise here. So black cannot play 3. ...Nd3 in my opinion and hold.

At this point, I don't see a good defense for black after 1. g6, however, the pedestrian but tedious nature of white's win after the two defenses discussed above leads me to believe I am missing a more tenacious defense that either leads to a draw, or a white win after a more "clever" continuation after 1.g6, or maybe even a different first move for white. Right now, I don't know what either one might be. Back to the drawing board.

debborah brega said...

h4

Yancey Ward said...

Ok, maybe I found the right thread:

1. g6 Kf6

When you have exhausted the obvious, it is time to look at the non-obvious. This defense looks silly, but I was looking for ways to get the knight involved, and I stumbled onto one way to do it. With Kf6, black is threatening Bxg6, and he can't guard the g-pawn with the king without pinning it to the bishop, so g7 seems required:

2. g7 Bh7

Not crazy at all if you think about it for a moment. Continuing:

3. Kh7 Nf3!

This is a pretty position:

4. g8Q Ng5!

And what can white do here? If he plays Kh6 or Kh8, black checks from f7 and then g5 endlessly, so white will have to take the knight with the queen if he wants to try for a win. He can take the knight now, or he can take it at f7. Let's run through the possibilities:

5. Qg5 Kg5
6. h6 c4! (the only move)
7. Kg7 c3
8. h7 c2
9. h8Q c1Q

And, this has to be a draw. Back at move 5:

5. Kh8 Nf7
6. Qf7 Kf7

And black will win since black will queen in time before white can threaten any stalemate:

7. h6 c4
8. h7 c3
9. e4 e4
10.c2 e5
11.Ke7 Kg7 (or Kg8)
12.c1Q h8Q
13.Qg5 Kh7
14.Qh5 and black will exchange and win with the second passed c-pawn.

Finally, at move 5:

5. Kh6 Nf7
6. Qf7 Kf7
7. Kg5 c4 and the pawn can't be stopped because white's e-pawn is in the way, and even if it weren't, white can't catch the c-pawn without dropping the h-pawn and the game anyway.

So, after 1. ....Kf6, white can't win with 2.g7. I think I see the solution in this line for white to win, but I need some time to analyze a few of the variations, and I have an appointment I can't delay any longer this morning:

Lucymarie said...

My first try at this produced:

1. g6 e5 2. g7 Bb3 3. h6 Nf3 4. h7 Ng5 5. g8=Q Nf7+ 6. Kg7 Ke4 7. h8=Q Nxh8
8. Qxb3

It is clear, I think, that White's strategy was correct, but that Black's leaves something to be desired.
Black was correct in having the bishop take the queen on g8, but incorrect in having the knight try to get to the White pawns.
Instead, Black should use the knight, along with his king, to try to marshall his own pawns home.

So back to the drawing board again. This looks like it's going to be quite complicated.

Yancey Ward said...

I think the critical line really does start with 1.g6 Kf6. At first I thought white can't win with 2.g7, but I now see my error. From the top:

1. g6 Kf6
2. g7 Bh7

And I showed that white can't win with 3.Kxh7. White has three other moves here- g8Q, h6, and e4. Now, g8Q just loses since white will also lose the h and the e-pawns afterwards. Also, 3.h6 allows black to support the bishop with Kg6 and white will be forced eventually to play g8Q allowing black to win both pawns for the bishop. This leaves......

3. e4!

Black can't really move the king now since he needs the king on f6 just to enforce the threat of perpetual check with the knight. What black can do is get the knight moving, take at e4, or start pushing the c-pawn. Let's just take each in order:

3. .....Nf3
4. e5! and the black king must give up f6, or black must divert the knight to e5. After every reply, white just takes at h7 and queens the g-pawn afterwards to win.

Or, at move 3:

3. .....Be4
4. g8Q and though not trivial, this ending is won for white.

And finally at move 3 is.....

3. ......c4
4. e5 again forces the king to give up f6, or diverts the knight.

I hope I am not overlooking something there.

Michael Freeman said...

Yancey,

In your 1. g6 Kf6 2. g7 Bh7 line does 3.e4 help?

If ..e5 then your line continues but after ..Ng5 then Qxg5 wins as their is a Qh6+ winning the black queen on c1.

Idea of e4 is playing e5 deflecting the black king.

KWRegan said...

Yancey Ward is warm here---nice composition.

Anonymous said...

1.g6 Kf6 2.g7 Bh7 3.e4 Nf3 4.e5+ Nxe5 5.Kxh7 Nf3 6.g8Q Ng5+ 7.Qxg5+ Kxg5 8.h6 +-

1.g6 e5 2.g7 Bb3 3.h6 Nf3 4. h7 Nh4 5.g8Q Ng6+ 6.Kg7 +-

Blogger said...

1. g6,e5;
2. g7,B3;
3. h6,Nf3;
4. h7,Ng5;
5. g8=Q,Nf7+;
6. QxF7,BxF7,
7.Kg7 after this h pawn cannot be stopped from becoming a queen

Lorfa said...

The problem is:

g6 Kf6 g7 Bh7 Kxh7 Nf3 g8=Q Ng5+ where the best that can be had is Qxg5+ Kxg5 h6 c4 Kg7 c3 h7 c2 h8=Q c1=Q and this is drawing.

Notice here that if the e pawn wasn't there a nasty skewer on h6 would be available. The king had to go to g5 to recapture after queen takes knight (enabling the skewer), and if the king moves to avoid this white's extra tempo will allow him to stop c1=Q.

Luckily the e pawn can be moved and can gain a tempo by attacking the king.

So with that in mind:

g6 Kf6 g7 Bh7 e4!! Nf3 e5+!! Nxe5 Kxh7 Nf7 g8=Q Ng5+ Qxg5+ Kxg5 h6 c4 Kg7 c3 h7 c2 h8=Q c1=Q Qh6+ 1-0

Lucymarie said...

Hi, Yancey. I'm sure you have seen this by now:

1. g6 Kf6!? 2. g7 Bh7 3. e4!! Nf3 4. e5+ foils Black's plan.

Yancey Ward said...

The really funny thing about this composition, and it is a really beautiful one, is that, all things considered, I think black actually puts up more resistance with 1. ...Bd1 than with Kf6.

Anonymous said...

So this is the chess problem that was presented to Magnus for training purposes. It gave him troubles too, he could not solve it!