we need the white bishop to stop covering h1 -- our queening square. so we move our king to g4 and after the white bishop moves, we take the pawn on h5 leading to an equal ending...

Man, I shouldn't be up this late :P

The first question to ask yourself looking at this position is, "Are we going for a win or a draw?"

After a minute or so, I think that black will play for a draw in this position. From what I can tell, the idea is to put white into zugzwang in order to win one tempo.

Currently the bishop guards both a2 and h1. If black simply plays 72...Kxh5 then play will go 73 Kxf5 Kg3 74 Kg5 h4 75 f5 h3 76 f6 h2 77 f7 a2 78 f8=Q a1=Q 79 Qf3#.

But, by playing

72...Kg4

white finds himself having to move. The king can't take either pawn, and should the king move to either f6 or h6, then black will be able to capture the pawn on the same file without fear of losing one of his own pawns. So it seems that the bishop must move, but when it does, it must continue to guard a2. So I'm guessing...

73 Bc4

Now that the bishop no longer guards h1, black plays

73...Kxh4 74 Kxf5 Kg3 75 Kg6 h4 76 f5 h3 77 f6 h2 78 f7 h1=Q 79 f8=Q

and now black has the move (the tempo gained by forcing the bishop to abandon h1) and the game should be drawn.

I'm mentioning this because I thought Black might be able to pull off a Shirov

Topalov vs Shirov, 1998

But there’s another (cruel) way black loses with first playing 73…Kxf4, below, when pursuing the strategy of trying to chase the bishop off of c4.

click for larger view

74 Kxh5 Ke3 75 Kg5 f4 76 h5 f3 77 h6 Kd4 78 Bf1 a2 79 h7 a1Q 80 a1Q+.

click for larger view

A) 77... a2 78.f8=Q a1=Q 79.Qf4+ Kh3 80.Qh4 mate.

B) 77... h1=Q 78.Bxh1 (78.f8=Q Qxd5+) a2 79.f8=Q a1=Q 80.Qf4+ Kh3 81.Qh4 mate.

Perhaps 72... Kg4 can save the game:

A) 73.Be6 Kxf4 74.Kxh5 Ke5 75.Bc4 Kd4 76.Be6 f4 77.Kg4 Ke4 78.h5 f3 79.h6 f2 80.h7 (80.Bc4 a2 81.Bxa2 f1=Q winning) f1=Q 81.h8=Q Qg1+ 82.Kh4 Qh2+ 83.Bh3 Qf2+:

A.1) 84.Kg4 Qf4+ 85.Kh5 Qe5+ 86.Qxe5+ Kxe5 winning.

A.2) 84.Kg5 Qg3+ 85.Bg4 Qe5+ 86.Qxe5+ Kxe5 winning.

A.3) 84.Kh5 Qf3+ and Black draws at least.

B) 73.Bc4 Kxh4 74.Kxf5 Kg3

B.1) 75.Kg5 h4 76.f5 h3 77.f6 h2 78.f7 h1=Q 79.f8=Q Qc1+ and draw.

B.2) 75.Kg6 h4 76.f5 h3 77.f6 h2 78.f7 h1=Q 79.f8=Q Qc6+ and draw.

C) 73.Kf6(h6) Kxf4(h4) 74.Kg6 Kg4 looks bad for White.

Second, from the puzzle position, Black needs a maximum of seven moves to queen after capturing the h pawn (one king move and six pawn moves). White needs only six moves after capturing the f-pawn (one king move, four pawn moves and a bishop move). For example, 72. ... Kxh4 73. Kxf5 Kg3 74. Kg5 h4 75. f5 h3 76. f6 h2 77. f7 h1=Q 78. Bxh1 a2 79. f8=Q a1=Q and White has all the chances for winning. That analysis eliminated 72. ... Kxh4.

That left 72. ... Kg4. Any other move loses material and the game to Kxh5. At first, I feared that White could move his king in response to Kg4. But Kh6 or Kf6 just lost material (e.g. 72. ... Kg4 73. Kh6?? Kxh4 (73. Kf6?? Kxf4)). That meant White's bishop had to move after 72. ... Kg4.

72. ... Kg4 73. Bc4 (best since it attacks f1). Black still needs seven moves after capturing either pawn. But with White's bishop attacking f1, playing Kxf4 allows White to queen in six. But if Black plays Kxh4, White will also need seven moves to queen (one king, four pawn and two bishop moves including Bd5).

The point is that white's bishop is perfectly positioned to kill black's pawn promotion efforts at a2 (of course), and more subtly, at h1. Also, white's king is perfectly positioned to take either Pf5 or Ph5.

And when your opponents pieces are so perfect, you want to force him to move one of them to a less-perfect square by burning up a tempo. That's what 72...Kg4! accomplishes:

White is in a little zugzwang. He can't move his king (which would give up a pawn for nothing) nor can he take his bishop off the a2-g8 diagonal (which would allows ...h2 & ...h1=Q), so he must move the bishop to some square where it DOESN'T guard h1.

Portisch vs H Westerinen, 1963 (72…?)

Black to play and draw

Material: P for B. Neither K is in any immediate danger in this sparse endgame. Presently, Bd5 is completely restricted to the a2-g7 diagonal by the threat of Pa3-a2-a1=Q and wins. Black should try to get a passed K-side P, so with 2 passed Ps, he can deflect the White B with one to permit the second to queen. For brevity, the following omits infeasible variations permitting either of these wins.

Let us perform a thought experiment, removing Bd5 and Pa3 until further notice, to analyze the resulting K+P endgame. First, the candidate 72…Kg4 is now transparent: as usual in a K+P endgame, Black seizes the opposition to prevent the capture of his Ps. Second, Black has a choice: which P to capture? Because of symmetry, after White captures the complementary P, White queens his P just after Black.

Now, put Bd5 and Pa3 on the board. The B alone cannot mate. So, if Black can queen first as above, the resulting Q+B vs. Q is a draw: Black just keeps checking, ensuring that the B never interposes with check (e.g., by placing his K on a dark square).

Candidates (72…): Kg4

72…Kg4

If White moves Kg6, he does no more than draw because Bd5 alone cannot mate.

(1) 73.Kf6 Kxf4 then …Kxh4

(2) 73.Kh6 Kxh4 then …Kxf4

(3) 73.Be6 Kxf4 74.Kxh5

[74.Kf6 Kg4 then …Kxh4 and Black at least draws]

74…Ke5

If White lets Black capture Be6, the Black Pa3 queens first, winning.

75.Ba2, e.g.

[75.Bc4 Kd4 can not be better, because the Black K can protect Pf5 from e3]

75…f4 76.Kg4 Ke4 77.h5 f3 77.Kg3

[77.h6 f2 78.Bc4 f1=Q 79.Bxf1 a2 and Black wins]

<[According to the Nalimov tables at http://www.k4it.de/index.php?topic=... I went wrong with 77…Ke3, trying to win, which loses against

78.h6 f2 79.Kg2 Ke2 80.Bc4+

The correct play (easily found to ensure a draw) is

77…f2 78.Kxf2 Kf5]>

(4) 73.B moves along the a1-h8 diagonal but not to e6, e.g., 73.Bc4

Black can force a draw, because White must expend a tempo to stop h1=Q.

73…Kxh4 74.Kxf5 Kg3 75.K moves off the f-file

75…h4 76.f5 h3 77.f6 h2

(threatening h1=Q with at least the Q+B draw above)

First, notice that the white bishop controls two important squares: a2 and h1. Second, f and h pawns are exactly in the middle of the board. Black and White easily force a passed pawn (72... Kxh4 73.Kxf5 Kg3 - the only move to pass the black pawn - 74.Kg5). In a pawn race, both have 4 squares ahead to be crowned. The black pawn would crown first, but the white bishop denies it or takes it (Bxh1). In either case, the a-pawn goes to a2 and White crowns first (f8=Q and a1=Q). Draw seems inevitable, but a mate net is setup (Qf3+ and Qg2#, or Qf3# if the h-pawn still occupies h2). So, if White crowns first and Black crowns on a1, Black is lost.

So, Black must force White to move the bishop away from h1, losing one tempo. With 72... Kg4, White has got the opposition and forces Black to move the bishop. If not, a white pawn falls, Black keeps the opposition again (73.Kf6 Kxf4 or 73.Kh6 Kxh4), and White has no way to defend its last pawn.

Now, the bishop has to move over the a2-g7 diagonal to keep a2 under control. Any square of that diagonal allows Black to win one tempo. But 73.Bc4 introduces a trap. The bishop now controls f1 and the mate net is unset. Now, Black is able to take the h-pawn and draw is ensured.

Oh, yes, I forgot the trap. If the mate net is unset, Black could crown after White by taking the f-pawn. Wrong. Now, White crowns its h-pawn controlling the a1-h8 diagonal and avoiding Black to crown on a1.