Endgame analysis

[ernest]

I can't find a way for White to win the first game.

I'd be VERY surprised if there is!!!

[michiguel]

I can't find a way for White to win the first game.

I'd be VERY surprised if there is!!!

Qa1 and Qxc3 seems to be an easy win. Depending how black recaptures, b4 or d4 at the appropriate time will break black's position.

Miguel

[Tom Barrister]

I can't find a way for White to win the first game.

I'd be VERY surprised if there is!!!

Qa1 and Qxc3 seems to be an easy win. Depending how black recaptures, b4 or d4 at the appropriate time will break black's position.

Miguel

The the direct approach doesn't work: 1 Qa1 Kd7, 2 Qxc3 dxc3, 3 d4 exd4, 4 Ke2 Kd6, 5 Kd3 Kc5!, 6 e5 Kd5, 7 e6 Kxe6, 8 Kxd4 Kd3, and Black has the Opposition.

----

I finally figured out the winning combination.

Note that White can't get in via a4 (Black simply refuses the pawn and if Qxb4 axb4), d4 (Black recaptures with the e-pawn) or f4 (ditto), and in all three cases, White can't get through.

White has two main entrance points, c3 and h4/g5. Black's King needs to be able to defend against both.

When White's King is at e2, and the Queen is able to play Qxc3, Black must be on either b6, c6, or d6--in other words, able to play Kc5. For example: 1 Kd2 Kd7, 2 Qa1 Ke6?, 3 Qxc3 dxc3, 4 d4 exd4, 5 Kd3 Ke5, 6 Kc4, and Black's pawn falls. This won't work if Black's King is on d6: 1 Kd2 Kd7, 2 Qa1 Kd6, 3 Qxc3 dxc3, 4 d4 exd4, 5 Kd3 Kc5!, 6 e5 (else no progress) Kd5, 7 e6, Kxe6, 8 Kxd4 Kd6, and Black has the Opposition and draws.

When White plays Qh4, Black's King must be no further away than the d-file: For example: 1 Qe2 Kd7, 2 Qh2 Kc6?, 3 Qh4 Kd6 (3... gxh4, 4 g5) , 4 Qxg5 hxg5, 5 h6 wins for White. On the other hand, 1 Qe2 Kd7, 2 Qh2 Kd6, 3 Qh4 Ke6, 4 Qxg5 hxg5, and Black is close enough to stop the pawn.


Here's a crucial position. Ignore who the position states is to move:

[D]8/8/3k3p/p3p1pP/Pp1pPpP1/1PpP1P2/2P1K3/4Q3 w - - 0 1

This position is a key to the ending; it's mutual Zugzwang, although White's isn't fatal to a win. Note that White's queen targets both c3 and h4. If White moves, either the King has to move a tempo away from penetrating after Qxc3, or the Queen has to give up its position targetting both key squares. If Black moves, he must give up protection of one threat or the other: every move but Kc6 allows Qxc3. The move Kc6 allows Qh4. See the above for more details.

Knowing those things, it's simple enough to find the correct combination and plain enough to see how Black can defend against other possibilities.

1 Ke2!

Actually, White can fool around and still win. However, the given Queen sequence must (I believe) eventually be played.

1 ... Kd7 (or Ke7)

Otherwise, 2 Qd1, and Black can't get to c6 or d6 in time.

2 Qh1! Ke6 (or Ke7)

Forced. If 2 ... Kd6, 3 Qd1, and White has reached the Zugzwang position. Any other move but those allows 3 Qd1, followed by Qxc3, d4, and Kd3 as above.

3 Qa1!!

And now Black has a problem. Since White is threatening Qxc3, Black must reach a square that allows him to play Kc5, and d6 is the only one that's available.

3 ... Kd6

Other moves lose, i.e.: 3 ... Kd7, 4 Qxc3 dxc3, 5 d4 exd4, 6 Kd3 and Kxd4.

4 Qd1!

We've reached the Zugzwang position, with Black to move.

4 ... Kc6

We've seen what happens if Black isn't on c6 or d6, so the other alternative is examined:

5 Qh4! Kd6

Or 5 ... gxh4, 6 g5 Kd6 (6... gxh6, 7 h6, and Black's out of range) , 7 gxh6, and the pawn promotes, while White's King is able to stop Black's pawn.

6 Qxg5 hxg5
7 h6

The pawn promotes.

(Pardon any move-typos that may exist)

[Arpad Rusz]

Nice work, Tom!
Now show me an engine thinking like him!

[Arpad Rusz]

First try it without computer (the engines find the solution very fast):

4.M.Matous, Shakmaty v SSSR, 1986
[D]1q6/p4B2/8/pp6/k7/8/5Q2/K7 w - - 0 1
White wins

(Hint) After 1.Ka2 b4 some very nice play is comming.

5.M.Matous, Duras MT, 1982
[D]7k/2q3pP/6P1/8/8/8/6Pp/2RR3K w - - 0 1
White wins

(I have the solution, but I don't really understand what is going on... )

[IGarcia]

3.O. Bláthy, Vielzügige Schachaufgaben, 1890
[D]1k6/1P3ppp/P1p5/1pP5/p1p3p1/2P1K1P1/1P3P1P/8 w - - 0 1

White wins

This is easy to solve... by the human players.

hello

Its sarcasm?

maybe white is wining, but i think a human in white cant win any computer with a strong engine as black. There are too many combinatios of pawn moves to calculate, where humans can miss a move and computer not...

[Arpad Rusz]

No, it wasn't sarcasm. Anybody can win this against a strong engine. In this position if you understand the idea, you don't need to calculate variations.

[Arpad Rusz]

This is a simplified version of the previous position:
3a.
[D]8/kP6/P1p5/1pP5/p1p5/2P5/1P6/1K6 w - - 0 1

White wins

[Tom Barrister]

maybe white is wining, but i think a human in white cant win any computer with a strong engine as black. There are too many combinatios of pawn moves to calculate, where humans can miss a move and computer not...

Black can only move the King back and forth from b8 to either a7 or c7. Other than that, he only has pawn moves. This allows White to triangulate at a1/b1 and penetrate at b5 to force Black to use a pawn move. Here's a short example:

1 Kd2 Ka7
2 Kc1 Kb8
3 Kb1 Ka7
4 Ka1

White must triangulate (spend a tempo) here:

4 ... Kb8
5 Ka2 Ka7
6 Ka3 Kb8
7 Kb4 Ka7
8 Ka5

Black must now spend a pawn move, as Kb8 Kb6 mates next.

8 ... g5

If 8 ... b5, 9 Kxb5, or if 8 ... a3, 9 bxa3.

Black can, of course, dole out the Kingside pawn moves one at a time. Whenever he does so, White goes back via b4/a3/a2/a1/b1 (triangulation) and returns via a2/a3/b4/a5, leaving Black on the move again. If Black interrupts the King's tour with a pawn move, White goes back to a1/b1 and starts back again. Rather than play out the entire 104 moves, we'll make all the pawn moves now to show White's handling of various Black threats:

9 Kb4 f5
10 Ka5 f4
11 Kb4! f3

Or 11 fxg3, 12 fxg3

12 Ka5 h5
13 Kb4 h4
14 Ka5 h3
15 Kb4

Note that 15 b8=Q+ Kxb8, 16 Kb6 doesn't work because of 16 ... b4!, 17 Kxc6 (17 cxb4? c3 wins) a3, 18 bxa3 b3, 19 Kd7 b2, 20 c6 b1=Q, 21 c7+ Ka2, 22 c8=Q+ Qf5+ with a perpetual.

White triangulates.

15 ... Kb8
16 Ka3 Ka7
17 Ka2 Kb8
18 Ka1 Ka7
19 Kb1! Kb8
20 Ka2 Ka7
21 Ka3 Kb8
22 Kb4 Kb7
23 Ka5

Now something must give. 23 ... Kb8 is mate after 24 Kb6 any, 25 a7#.

23 ... b4

Or 23 ... a3 bxa3.

24 Kxb4

White must be careful. 24 cxb4?? a3 wins for Black.

With Black's pawns dismantled, White wins easily.

[Jouni]

In 1. position after executing and taking back some moves

Analysis by Stockfish 2.0 JA 64bit:

1.Ke2 Kf7 2.Qb1 Kg7 3.Qa1 Kg8 4.Qe1 Kg7 5.Qxc3 dxc3 6.Kf2 Kf6 7.d4 Kg7 8.Ke1 Kf6 9.Ke2 Kf7 10.d5 Ke7 11.Kd3 Kd7 12.Kc4 Kc7 13.Kc5 Kc8 14.d6 Kb7 15.Kb5 Ka8 16.d7 Ka7
+- (124.04) Depth: 47/80 00:01:15 232mN

Jouni