After leading the World Team's search for the White win against 58...Qf5 that Kasparov is expected to reveal in his published analysis later today (Wed. 10/27), I have to say that I have not found it. I suspect, however, that it follows one of the possibilities presented below, beginning with the Zugzwang maneuver ascribed to me on the World Team Strategy Bulletin Board. (If it does not use 59. Kh6 then I am and we all are really surprised!) The main winning point seems to be that White can be very flexible about whether his king goes to hide from checks on the Q-side or runs down the board to hide near h1---the latter being what IM2429 carried through in his "funerals after 62...Kc2" post, preserved by 99% Energy at http://www.gamersx.com/messages/view.asp?id=wnwcg. Several of the basic concepts are:
On Black's turn at Move 58, White had his King on g7, pawn on g6, and Queen on d4, while Black had Queen on f5, King on b1, and pawn on d5. With Irina Krush's analysis never being posted by MSN, the World chose the inferior 58...Qe4?, which was already known to lose albeit in long lines. Krush and the St. Petersburg GM School had worked out a much tougher defense with 58...Qf5, one that would have forced Kasparov to exhibit his best chess.
58. ... Qf5 59. Kh6 Qe6
This is the so-called "GM-School Position", a holding strategy exploiting the fact that White's blocking Queen on d4 does not protect g6, so that Black can force White's King to stay near the g-pawn with checks. The only square Black can hold from is e6, however, so Black is susceptible to the Zugzwang motif, which White uses to force Black to move his King away from the safest square, b1. An illustration of all this is what may be an equally accurate series of moves: 60. Kg5 Qe7+ 61. Qf4 Qe3+ 62. Qf4 Qe7+ 63. Kh6 Qe6 and now 64. Qd4! Another way to get there may be 60. Qb4+ Ka2 61. Qf4, when 61...d4 is impossible owing to 62. Qf7+! (see point 3. above), and Black seems to have nothing better than 61...Kb1 62. Qd4! Sentiment on the BBS favored the pretty triangulation sequence 60. Qd3+ Kc1 61. Qc3+ Kb1 62. Qd4, though it gives Black possible extra chances by 60...Kb2!? Simplest to me seems:
Kasparov confirmed in his chat today that this was his line.
60. Qg1+ Kb2 61. Qf2+ Kb1 62. Qd4! ...
(on 61...Kc1, White can at least reach the same position by 62. Qf4+ Kb1 63. Qd4). This Zugzwang leaves Black not much more than 62...Kc2 or 62...Ka2 since 62...Qh3+ seems to help White and other Queen moves cede ground. Now the drawback of 62...Kc2, which was part of the original GM-School strategy, is revealed by 63. Kg5 Qe7+ 64. Qf6 Qe3+ 65. Qf4 (65. Kg4! looks even better) Qe7+ 66. Kg4 (Kh5 may also be good), when the hoped-for liberating 66...d4 simply meets 67. Qxd4! with a computer-proven checkmate in 45 moves! http://chess.liveonthenet.com/scripts/chess_egtb_endings?8/4q3/6P1/8/3Q2K1/8/2k5/8+b The post by IM2429 on the BBS mentioned above gave a nearly-complete demonstration of a White win after 62...Kc2---there was a possible loophole but I do not know the final analysis of it---and so attention shifted to:
62. ... Ka2 63. Kg5 Qe7+ 64. Qf6 Qe3+ 65. Qf4 ...
Now going back by 65...Qe7+ runs into a diabolical problem: 66. Kh6 Qe6 67. Qf3! White's last move prevents 67...d4 by the 68. Qf7+ motif, and equally importantly, covers the squares h3, e4, and f5, one of which Black needs to continue his holding strategy after Kh7 by White. There appears to be no sturdy defense left here. Fritz's idea of 65...Qc3!? also bears mention, but seems not to be better than options Black gets later on below. Thus it seems Black must press ahead with checking strategy from behind:
65. ... Qg1+
Now White's four independent options are all promising in different ways. We save for last what currently seems to be the most dangerous option, 66. Kh5.
A. 66. Kh6. This was felt to be OK for Black after 66...Qh1+ 67. Kg7 d4, intuitively because White's King is still on g7, Black's Queen controls the important square d5, and Black has many checking options when White's King moves. However, in view of positions below where White wins by controlling d4 even when Black gets in ...d3 before White can play g7, there may be hidden poison here.
66. Kf6 Qb6+ 67. Kg7! Qe6!
B. 66. Kf6, when Black can stop a run to the Q-side but cannot play ...d4 as in A, so this "runaround" by White's King displaces Black's Queen. It is worth displaying as a main line:
Here 67...d4 does not quite work: 68. Kh7! and now Black cannot stop g7 (68...Qb1 69. Qf7+ leads to a trade of Queens and win). All lines seem to meet fates similar to: 68...d3 69. g7 Qb7 70. Qd2+ Ka1 71. Qc1+! (to cover h1) Ka2 72. Kh8 and Black cannot stop White from queening. Rafael Gorski sent me 68...Qb5!? (here or on Move 67), but White seems to have a bust with 69. Qg4!? d3 70. g7 Qb7 71. Qd4!, a theme that comes up in other lines. Even if White played 71...Qh1+ 72. Kg8? Black would still be unable to let the d-pawn fall with check (this note is relevant to A.), but 72. Kg6! sets up the theme of running White's King around to capture Black's d-pawn, after which the position is a known EGTB win.
However, Black's last move seeks to re-establish the GM-School holding strategy. Were White's King on h6 White's next would be winning as mentioned above, but even here it is strong:
68. Qf3! ...
Now available checks all seem to put Black's Queen "on the wrong circuits." For instance, 68...Qe5+ 69. Kh7! Qh2+ 70. Kg8! leaves Black unable to stop g7 after 70...Qb8+ 71. Qf8---Black's Queen needs to be on c8 when White interposes on f8. The major question, however, is whether White is winning after 71...Qe5! here. This critical position
(WKg8, Qf8, Pg6; Bka2, qe5, pd5; White to move) is
one even I have not been able to exhaust, nor the position resulting
from 72. g7 d4---the latter was also relevant to the viability of
56...Qe3 if I recall correctly. If White plays 72. Qf7 Black just
resumes checking, and all other non-check Queen moves allow ...d4. If
White has a win here then this is a major step toward proving the
whole ending won for White, but if not then several lines of defense
besides this one become open for Black. (All diagrams are
screen-captured from MacChess 5.0.1.)
It is worth noting that 70...d4 seems to fail quickly once again: 71. Qd5+! Kb1 (allowing d4 to fall with check is a computer-proven loss, and ...Ka3 is no help) 72. g7 Qb8+ (weirdly, 72...Qg3!? 73. Qxd4? Qb8+ is a computer-proven draw, but 73. Kf7 leaves Black nothing but transposition into this line) 73. Kf7 Qf4/c7+ 74. Kg6 Qg3+ 75. Kf6!, and Black is gone after 75...Qh4+ 76. Qg5. And 68...d4 is still impossible owing to 69. Qf7! Black has one other option whose point is to meet 69. Kh7 by ...Qc2!, when from prior analyses of lines with 51...Ka1 Black looks fine. Although it seems inferior to 68...Qe5+ and is probably a forced loss, the lines it leads to are interesting and potentially important enough to warrant mainline treatment here:
68. ... Qc8!?
It is a paradox of this ending that Black willingly hangs his pawn with check: 69. Qxd5+? is a computer-proven draw. Now White's King is contained for the moment: 69. Kh7 Qc2! seems so good as to be an easy draw for Black, 69. Kf7 simply meets ...Qc7+ if not ...Qd7+, and 69. Kh6 Qh8+ 70. Kg5 Qe5+ 71. Qf5 Qe7+ is not great progress for White. Thus it is time for White to re-position his Queen with checks. Three target squares seem particularly inviting: e2, b4, and b6; the last of these seems the one to fear.
It is worth inserting Black's defenses to the first two, since they also show rich themes: 69. Qe2+ Ka1/b1 70. Qd1+ Ka2/b2 71. Qd2+ Kb1 72. Qb4+ is met by 72...Ka2! and on 73. Kf6 Qc6+ 74. Kf7 Qd7+ 75. Qe7 Qf5+ we transpose into positions White could have had long ago, in which Black is able to block White's King from going to the Q-side. The other line leads to pretty play if Black moves our King to b1: 69. Qe2+ Kb1!? 70. Kf6(!)(?) Qf8+ 71. Kg5 Qd8+ 72. Kf5! Qf8+ 73. Kg4 Qc8+ 74. Kg3 Qc7+ 75. Kf3! Here 75. Kg2 allows ...d4! since Black has a forking check at c6, but now that check will be met by the cross-check Qe4+ trading Queens. Of all Black's tries, the best seems to be the immediate 75...Qg7!, when 76. Qd3+ Kb2 77. Qf5 d4(!) 78. Qf7 Qh6! 79. g7 Qh3+ is a pattern the World Team found to be good in other lines with White's Queen at f7---Black can deny White a useful interposition, and 80. Ke4 Qe3+ 81. Kf5 Qf3+ 82. Kg6 Qg3+ 83. Kh6 Qe3+! 84. Kh7 allows Black both the defense 84...Qe4+ 85. Qg6 Qh4+ 86. Qh6 Qe4+ 87. Kh8 Qe5 that the misguided 58...Qe4? originally sought to achieve, and the probably better 84...Qh3+! 85. Kg8 d3! and Black seems to have caught up in the pawn race. Nor does 79. Kg4? d3! seem to work as Black is queening with check. Moreover, 69. Qe2+ Ka1 looks possible on account of 70. Qe5+ d4!, and this is a case where Black draws even if the pawn falls on d4 with check, and Black also appears able to avoid the dreaded "Pin Battery" idea (White running with his King so as to play Kxd4 and a discovered check) because the Queen on e5 is not guarding g6. But enough of second-best moves for White...
69. Qf2+! Ka1 70. Qa7+! Kb1 71. Qb6+! Ka2
Now the ONLY difference from White's option of playing 59. Qb6+ right back at the beginning is that Black's Queen is on c8 not f5. Also note that 70. Qd4+ Kb1 71. Kh6 Qe6! makes White have to start all over again. But here White's King can emerge effectively. As in the first alternate line above, Black avoided 71...Ka1 in order not to get crosschecked on a1 or drop d4 with check, but finds the King on a2 sensitive again. Moving to the c-file seems to lose quickly as in our present game---see below.
72. Kf7! Qf5+!? 73. Ke7 _ Qe5+
Now 74. Qe6!? Qc7+ leads to a desperate battle of "Tablebase Chess" against the Pin Battery that I think Black survives: 75. Ke8 Qb8+ 76. Kd7 Qb7+ 77. Kd6 Qb8+! 78. Kc5! Qf8+! 79. Kc6! Qa8+! 80. Kb5 Qb8+! In all cases Black has played only-moves to avoid EGTB losses---e.g. it is curious that 79...Qg7 80. Kxd5! wins while it didn't win the previous move with Black's Queen on f8! (Someone please double-check all this...) Now 81. Qb6 seems not so clear: 81...Qe8+ 82. Ka5 Qe1+ 83. Qb4 Qe5! looks like nothing special for White, and ditto 83. Ka6 Qe2+ 84. Ka7 Qe7+ 85. Qb7 Qe3+! 86. Ka8 Qe8+ 87. Qb8 Qc6+ etc. White may have a way of winning in this line, so it certainly needs attention too, but the following seems a more precise and incisive means of reaching the desired goal, if the final position in my mainline is winning for White. Note that 74. Kd7?! gives Black an extra option by 74...Qg7+! 75. Kc8 d4!? 76. Qe6+ Kb2 (White can attempt to force this anyway on 76...Ka1 77. Qe1+ Kb2 78. Qf2+ Ka1 79. Qf1+ and then 80. Qf7; for 76...Ka3!? here see more below) 77. Qf7 Qh8+! 78. Kb7 Qh1+ and it doesn't look clear to me: 79. Kb6 Qh6!? or 80. Ka7 Qg1!? or ...d3!? 81. Qf2+ Kb3! are all obscure. (My MacChess 5.0.1 has examined 41 million nodes after 78...Qh1+ and is currently allowing Black to queen with check in a 4Q position, so don't ask me for any computer evals.:-) White "must" be winning somewhere here, but if not, then White is probably not winning in lines C or D either.
Since 74. Qe6!? Qc7+ 75. Kf8?! Qb8+ 76. Kf7 Qc7+ 76. Qe7 Qf4+ 77. Kg8 Qb8+ 78. Qf8 Qe5 enables White to force the above-marked critical position, Black cannot be better off here than with 68...Qc8, but the resulting positions are still relevant to White's general strategy of running Q-side with his King.
73. Ke7 _
74. Kd8(!) Qh8+ 75. Kc7 Qg7+ 76. Kb8 Qh8+ 77. Ka7 Qg7+ 78. Ka6 d4!?
Notice alas that 76...d4 was impossible yet again owing to Black's King being on a2 on account of 77. Qa7+! Black has other checking options in these moves as well, ones I haven't had time to explore yet---hopefully they could produce an e-file hold like in the 74. Qe6!? variation given above. But the position now on the board seems highly thematic, and my final question is whether White's master plan of 79. Qe6+ and an eventual Qf7 is winning here. I see:
(a) 79. Qe6+ Kb2 (or ...Ka1 80. Qe1+ Ka2/b2 81. Qe2+ Ka1/b1 82. Qf1+ Kb2; other King placements may be worth mention here) 80. Qf7 Qh6!? 81. Qh7!? Qg5(!)---is this winning after 82. g7?! or 82. Qb7+!? ---?
(b) 79. Qe6+ Ka3!? 80. Qf7 Qh6 81. Qh7?! Qe3! and maybe better 81...Qg5! 82. Qh3+ Kb2 both deny White useful checks.
(c) In both (a) and (b), White can make a King
move after 80...Qh6, and things get hairy. For instance, 79. Qe6+ Kb2
80. Qf7 Qh6 81. Ka7 d3 is desperate stuff, staring 4Q losses in the
eye, but 82. g7?! Qe3+! 83. Ka6 d2 84. g8=Q Qd3+! seems to be one of
those weird 1Q-vs.-2Q perpetual check or trade-of-Queens draws. And
Black may be even better off in the analogous 79. Qe6+ Ka3 line with
80. Qf7 Qh6 81. Ka7 Qe3! and suddenly White does not have so many
useful checks. Anyone see a quick kill for
White hereabouts---or simply a winning line? 66. Qg4 Qc1+ 67. Kh4 Qh6+ 68. Kg3 Qe3+ 69. Kg2/h2 d4!?
C. 66. Qg4
This try seems inferior to line D, but is worth including since some themes are similar. Both 66...Qe3+ and 66...Qc1+ seem acceptable in reply, with not much to choose between them. Now running Q-side with White's Queen only on g4 seems not to work, e.g. 66. Qg4 Qc1/e3+ 67. Kf5 Qc2/d3+ 68. Ke5 Qc3+ 69. Qd4 Qc7+! 70. Ke6 Qc6+ 71. Kf5 Qd7+ 72. Kf4 Qd6+ 73. Kg5 Qe7+ resets the game back to Move 63, and 69. Kd6 Qa3+! leads to no better as Black has enough room for checks. Hence most thematic seems:
Black avoided 67...Qh1+?! on account of 68. Qh3! Qe4+ 69. Kg5! and suddenly Black is in a spot of bother after 69...Qe7+ 70. Kh6! since White's Queen controls key squares, or 69...Qe5+?! 70. Qf5! with themes from Line D. And Black is avoiding 69. Kg2 Qd2+ (or 69. Kh2 Qh6+ 70. Kg2 Qd2+) on account of 70. Kf1! Qc1+ 71. Kf2!, when 71...Qc5+ 72. Kg2 leaves Black no checks---although black may still be OK with 72...d4. This version of ...d4 is quite a bit better, however, and leads to a twin pair of positions that to me seem critical for line C:
I haven't had time to analyze it all, but these
lines offer good comparison to themes in line D:
70. g7 Qd2+/h6+ is perpetual check along the c1-h6 diagonal, as White never gets a chance to interpose profitably.
69. Kh2 d4 70. Qg2+ Ka1 71. Qg1+ trades Queens but does not win, while 71. g7 Qh6+ is perpetual on h6, e3, and c1, and 71. Qa8+ Kb2 72. Qb7+ Ka1 73. g7 Qh6+ sets up a block and perpetual using h5,g5,f5,c2,c1.
69. Kh2 d4 70. Qg3!? Qh6+! 71. Kg2/g1 d3! seems to draw as White has no productive checks and 72. g7 Qc6+ 73. Kf2 Qc5+! 74. Kf1 Qc1+ 75. Qe1 d2 76. g8=Q+ Kb2! and 74. Kf3 Qd5+ 75. Ke3 Qc5+! (...d2 76. g8=Q d1=Q is a 4Q loss) 76. Ke4 Qc6+, and since White cannot do better than EGTB= on taking Black's d-pawn, we do not see what White is accomplishing: 77. Kf5 Qd7+ 78. Kg6 Qe6+, and the best White has is a "known pattern" typified by 79. Kh5 (Kg5? d2!=) Qf5+ 80. Kh6 Qe6+ 81. Qg6 Qe3+ 82. Qg5 Qe6+ 83. Kh5 Qh3+ 84. Kg6 Qg4+ 85. Kf7 Qd7+ 86. Qe7 Qf5+ 87. Ke8 Qc8+ "etc."---even with Black's pawn at d4 we suspect this is holding.
69. Kg2 d4 70. Qg3!? Qe6!? Now 71. g7 yields a perpetual check that constitutes Black's main defensive idea hereabouts: 71...Qc6+ 72. Kf1 Qc4+! 73. Kg1 Qc1+ 74. Kh2 Qh6+ 75. Kg2 Qc6+ 76. Kf2 Qc2+ 77. Kf3 Qc6+! 78. Kf4 Qd6+ 79. Kg4 Qg6+ 80. Kh3 Qh6+! 81. Kg2 Qc6+!, and Black is always able to reach the squares needed to prevent White from escaping without losing his g-pawn.
The first question is whether 71. Qg5 wins with White's King on g2 the same way it does with White's King on h2 in line D. if Black tries 66. Kh5 Qh1+ 67. Kg4 Qg2+? 68. Qg3! Qe4+ 69. Kh3 Qe6+ 70. Kh2! d4. Black's only possible defense seems to be 71. Qg5 Qe4+ 72. K-any Ka1!, when 73. g7 seems to yield a perpetual again---I think I can illustrate all the many points in one line: 72. Kg1 Ka1! 73. g7 Qb1+ 74. Kf2 Qc2+ 75. Kf1 Qd3+! 76. Ke1 Qc3+! 77. Ke2 (Qd2 Qg3+ 78. Kd1 is not close enough to give mate) Qc4+! 78. Kd1 Qb3+! 79. Kd2 Qc3+ 80. Ke2 Qc4+ 81. Kf3 Qd3+ 82. Kg4 Qe4+ 83. Qf4 Qg6+ 84. Qg5 Qe4+ 85. Kh3 Qh7+! 86. Kg2 Qe4+ 87. Kg3 Qd3+ 88. Kf4 Qd2+! 89. Kf5 Qc2+! 90. Ke5 Qc7+! 91. Ke4 Qc2+ 92. Kd5 Qc6+! 93. Kf4 (here Qd5 is not check and loses the g-pawn) Qc1+! 94. Kg4 Qd1+! 95. Kf5 Qc2+ 96. Ke6 Qc6+ 97. Ke7 Qc7+ 98. Ke8 Qc8+ 99. Qd8 Qe6+ 100. Qe7 Qc8+ 101. Kf7 Qf5+ 102. Qf6 Qd7+ 103. Kf8 Qc8+ 104. Ke7 Qc7+ 105. Ke6 Qc6+ 106. Ke5 Qb5+! (handle Pin Battery by keeping contact with the counter-skewer ...Qb2+) 107. Kf4 Qf1+ 108. Kg5 Qg2+ 109. Kh6 Qh3+, and hopefully by now it is clear (without my having to show King-run lines with White's Queen on e7 as well as g5,f6) that Black can always reach the needed squares.
The second question is whether Black survives being pinned down on g8 after 71. Kg1!? d3 72. g7 Qg8 because White cannot hop to d4 in one move, and 73. Qf2+ Kb1 74. Qf8 fails to 74...d2! 75. Qxg8 d1=Q+ and perpetual! This was a needed resource in some GM-School lines, but maybe with Black's king further away on a2, White has a way to use his King too... However, facts like 73. Kf2 d2 74. Ke2 Qe6+?! 75. Kxd2 Qd5+ being EGTB= (notice also 8/6P1/4q3/6Q1/8/8/k7/3K4+b with White's Queen better placed on g5: Black still draws with ...Qb3+) give Black cause for optimism.
69. Kg2 d4 70. Qf3!? Qe5!, and now the sneaky 71. Qf2+ Ka1 72. Qg1+ Kb2! does not win. Now 71. Qg3 Qe6 transposes into the most-delicate last variation, while supporting g7 from f7, b7, or a7 seems to yield Black a perpetual after ...Qg5+, a fact that was crucial to certain GM-School lines. I don't see how White makes progress after 71. Qd3 Kb2---since once Black's King escapes a2 White cannot win by opposing Queens---though this may contain hidden venom. And other non-checking moves allow ...d3, which seems always to be an EGTB draw if it is captured.
Whew! I'll admit that the above volume far from exhausts this line---and any one hole I may have missed makes the whole thing go blooey! (Please someone test it with better computer-chess software than I have.) But that's my manifesto for a Black draw in Line C.
66. Kh5 Qh1+ 67. Kg4 Qd1+! 68. Qf3 Qc2!
D. 66. Kh5!?
Along the way, Black has avoided a pretty loss with
67...Qg2+? 68. Qg3! Qe4+ 69. Kh3 (White's plan is to retreat the King
to the first rank, when Black may be forced to block White's pawn by
...Qg7 but will have no check in response to Qf2+/f1+/f7. This seems
inexorable unless Black can take evasive action.) Qe6+!? 70. Kh2! d4
71. Qg5! as found by JQB last Sunday. All defenses other than
71...d3 72. g7 Qg8 run out of checks as White gets a new Queen,
but now 73. Qd2+ Ka1 74. Qc3+ Ka2 75. Qd4! leads to a standard winning
theme in which Black is hogtied: losing the pawn with check is an EGTB loss
when White's Queen returns to d4, and otherwise Black cannot stop White's
King from wandering over and munching the pawn. In particular,
75...Qf7 76. Kg3 is another Zugzwang.
The amazing point of 68...Qc2! is that 69. Qxd5+ is EGTB=, even though the move seems to lead either to 69...Kb1 70. Qf5 pinning the Queen and game-over, or 69...Ka1/b2 70. Qd4+ K-any 71. g7 setting up the same win I just mentioned, or 69...Ka3 70. g7 and Black has no really useful checks and will soon die from the King's exposure on a3. The point is that 69...Kb1 70. Qf5 Ka1! escapes the pin by stalemate! Also amazing is that then 71. Qe5+ and 72. g7 is not enough to win---White's Queen needs to be on d4 for the EGTB trap to close. Hence this is actually a critical position too:
Now it is important to note that White
may have made progress after 69. Qf5(!), because the Queen
on this square assists White's King into f6. A second nasty point is
that if White's King gets to g2, then Black has absolutely no checks
at all! Hence Black may have to hope that 69...Qg2+ followed by
70...d4 works, or if 70. Kf4 Qf2+ 71. Ke5, that 71...Qb2+ is OK.
Update: There seems to be no reason why 69...Qg2+ 70. K-any d4! shouldn't work---with Black's Queen on g2 this seems the best possible form of the resource that Black could imagine. And 69. Kg5 and Kh5 seem at best to transpose into line C (which admittedly is very tenuous for Black---Kasparov said in his chat today that the analysis was "incredibly delicate", so this being the line may be no surprise. Hence my current belief (Wed. 10/27 late-night) is that 68...Qc2! completely shuts down this major branch for White!---and White has to go looking for wins in line B or line C---where quite possibly they may still be found, either by winning the critical position in line B or by punching a hole in my fragile line-C defense.
In any event, the above lines seem to be the major backbone of White winning plans, and bears analysis. I will post this on both the MSN and 99%'s bulletin boards, but if you have major additional analysis, please also send it to me by e-mail to firstname.lastname@example.org. Hopefully we're getting to the core of this fascinating endgame.
This article is copyright (c) Kenneth W. Regan, 10/19/99. Permission to reproduce in whole or in part is granted for non-commercial uses. The analysis here is expressly not copyrighted---although virtually all of the above was originated by me as far as World Team members go, Kasparov probably had it all long ago...and I would like to encourage other World Team members to add more to this analysis...maybe FIND A DRAW!!