Computer Challenge 01

by Karsten Müller
4/25/2023 – Our "Iniyan Challenge" saw a lot of readers getting interested, and we received some excellent analysis from them. Today we want to give you a Computer Challenge. It is a position in which your chess engines will not give you the solution if you ask them — even if you run them for a very long time. You have to come up with the logic and strategy of the solution yourself, and then confirm everything with the help of the computer. Can you do that?

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Here's the position, which actually occurred in a high-level game:

To get a feel for the problems that White is faced with, you can try winning the game from the above position. You can move the white pieces and the diagram will defend for Black.

1.Nxb6+? does not win, as you will quickly see. After 1...cxb6 the position is completely locked and White would have to sacrifice his queen to open it up.

How about using the h3 square for the queen to penetrate? 2.h4!? But Black plays 2...gxh4 and then 3...h3 to lock up the position. You may consider sacrificing the queen on a5, but Black can easily block the passed b-pawn and hold the draw. So what to do?

You can analyse the position comprehensively in the following replay window:

Here you can start the engine (fan icon) and enter variations. If you come up with a solution, you can download the full analysis you have done (disk icon below the notation) as a PGN file. You can also simply download the PGN as is and use your favourite engine to search for the solution.

Please submit your analysis in PGN to puzzle2@chessbase.com. The subject should be "Computer Challenge 01". Please give your name and your place of residence!

Magical Chess Endgames Vol. 1 & 2 + The magic of chess tactics

In over 4 hours in front of the camera, Karsten Müller presents to you sensations from the world of endgames - partly reaching far beyond standard techniques and rules of thumb - and rounds off with some cases of with own examples.

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<< Sixth edition of the Salamanca Festival with Topalov, Khadem and Ivanchuk
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Karsten Müller is considered to be one of the greatest endgame experts in the world. His books on the endgame - among them "Fundamentals of Chess Endings", co-authored with Frank Lamprecht, that helped to improve Magnus Carlsen's endgame knowledge - and his endgame columns for the ChessCafe website and the ChessBase Magazine helped to establish and to confirm this reputation. Karsten's Fritztrainer DVDs on the endgame are bestsellers. The mathematician with a PhD lives in Hamburg, and for more than 25 years he has been scoring points for the Hamburger Schachklub (HSK) in the Bundesliga.
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World Championship, Playoff - Ding Liren takes the crown!

4/30/2023 – By winning game 4 of the rapid tiebreakers — after three draws — Ding Liren became the 17th undisputed world chess champion! Ian Nepomniachtchi seemed to have things under control in the deciding game, and even a bit of an advantage at times, but he overestimated his chances and allowed Ding to get a dangerous passer. Ding kept his nerves and converted his advantage brilliantly. | Replay the games with computer-assisted analysis. Full report to follow shortly.
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The Iniyan Challenge

4/9/2023 – Recently young grandmaster P. Iniyan visited our company and showed us a position from one of his games which should be won by White. But he needed to work very hard to do so. It was a remarkable rook ending from which there was a lot to learn. We challenged our readers to find a comprehensive solution, and received some excellent analyses. This we present you today, with Iniyan's own analysis. Don't miss the wonderfully instructive video at the end.
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60m The London System

If you are looking for a new attacking plan against the popular Queen’s Gambit, then this download is for you. Completely new ideas after 1.d4 d5 2.Bf4 turn the solid London system into a serious weapon. New approaches and Fritz analyses will catch out an unprepared opponent. Henrik Danielsen used this system to win the Icelandic blitz championship in 2011. Some strong GMs and IMs didn't realise the danger before it was too late. Even after Black’s best defence White will be able to fight for an advantage. After watching 60 minutes you have a total opening plan against the Queen’s Gambit.

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Karsten Müller Karsten Müller 5/2/2023 04:47
The solution is now published:
https://en.chessbase.com/post/computer-challenge-01-anaslysis
Karsten Müller Karsten Müller 5/2/2023 12:10
oxygenes: Good question. Of course there is the printed ACM magazine. But I do not know, if it is available as e.g. PDF. I will ask.
oxygenes oxygenes 5/2/2023 10:57
EmilV wrote: With the queen on b6, the bishop can't move much because of Nxb6.
If we forget all (computers too) fear of b5-b6, it literally means, that 46.Qb1 Qb7 give to black bishop possibility to move. :) Then direct idea 47.h4 Bxh4 48.Qh1 Kb8 49.Qh3 Qc8 do not works. And 47.b6 really seems good, but again Bf2 48.Qb5 Kd8 49.bxc7 Qxc7 looks hard enough to crack.
@Karsten Müller Is somewhere pdf/png/txt version of Prohaszka full analyses for check? I did not found it and try to invent wheel second time myself has not much sense.
Karsten Müller Karsten Müller 5/2/2023 06:51
oxygenes, EmilV: Peter Prohaszka's analysis from 2021 published in American Chess Magazine 21/2021, p.67-73 is very long and does mention b6 wins. In the document mentioned by EmilV below only the main line is given. But oxygenes may nevertheless have a point that the solution found is a bit easier...
EmilV EmilV 5/1/2023 09:48
Methodically, Black should play Qa7 only after Nb2, otherwise White would refute it with b6.

This is neither in my analysis nor in Prohaszka, where Black can always play Qa7 after Qf1, even if it is just a demonstration and he has to come back Qb6 quickly.

That's why I like oxygenes' suggestion to go straight king on f1 the best.
46.Kb1 Kb7 47.Kc1 Kb8 48.Kd1 Kc8 49.Ke2 Kb8 50.Qb1 h4 51.Qb3 etc...

First of all, the Qa7 option is nowhere to be found.

Second, it turns out that Qf1 is a redundant move.
With the queen on b6, the bishop can't move much because of Nxb6.
oxygenes oxygenes 5/1/2023 08:14
We have faster and simpler solution. :)
In Prohaszka analysis white can easily lost right track, if black play 46.Qb1 h4 47.Kb3 Qa7!? 48.Kc2?! -48.Df1! - Bf2!? 49.b6 Qa6 50.Nc3 a4 51.Qb5 Qxb6 52.Qxa4 Be1! I was not able to find win for white. 53.Qe8 Kb7 54.Nb5 Qa5 55.Qc6 Kb8 56.Kb3 Bd2.
Karsten Müller Karsten Müller 5/1/2023 06:06
EmilV, oxygenes: Many thanks for locating Prohaszka's analysis directly! Indeed both winning proofs are very similar...
oxygenes oxygenes 4/30/2023 05:44
Funny thing is, that main defence resource for black is Qa7. In Prohaszka variation 1.Db1 h4 2.Kb3 Kb7 3.Df1 Da7 4.Kc2 Db6 5.Kd3 Ka7 6.Db1 Bf2 7.Ke2 Bg3 8.Db3 Kb7 9.Nb2 etc. white must play precisely to force zugzwang and eventually white king must go to e2-f1. Black can play 2.- Qa7 too.
When white play 1.Kb1, we see, that king do not cross fire line at b6, black queen is paralysed over 5 moves and white has simple plan move king to e2-f1, no need calculate much and effect is the same.
EmilV EmilV 4/30/2023 02:33
I have found the analysis of GM Peter Prohaszka.
https://docplayer.org/228644639-Engine-an-kopf-aus-probleme-und-chancen-bei-der-verwendung-von-schachengines-von-tobias-voege.html
The analyses are very similar and arrive at a similar position:

We Qb3 Nb2 Kf1 / Kb7 Qa7 Bg3
Prohaszka Qb3 Nb2 Ke2 / Kb7 Qa7 Bg3

In both cases White loses tempo to attract Bh2, and even the next plan with g4 is almost the same.
Prochaszka has to find later a pretty difficult move anyway, Qc2.

We 56.Qc2! Bh2 57.g4 Bg3 58.Qb3 Qb6 59.a4
Prohaszka 56.Kf1 Bh2 57.g4 Bg3 59.Qc2! Qb6 60.Nd3 Qa7 61.a4

Somehow now I'm not able to comment if any plan is worse, but it's probably the same.
EmilV EmilV 4/30/2023 02:01
2 oxygenes

It depends on the purpose of the analysis.
If you play for example correspondence chess, it's certainly optimal to give your opponent room to make mistakes.
But I am looking for proof the position is won. Such a proof should be elegant and as simple as possible - and it's different there :-))
Karsten Müller Karsten Müller 4/30/2023 06:21
oxygenes, mtak, EmilV: Many thanks! Now it is solved and a solution article is already prepared for publication. Basically it is a version of the win published by Peter Prohaszka in 2021. Indeed White has several moves to preserve the win and so "your" win is similar but not identical to Prohaszka's, But the ideas are the same.
oxygenes oxygenes 4/29/2023 09:49
Ok, 46.Qb1 force h5-h4, which is my plan too. But from human view black "lost" possibility to make unforced errors like Bh4. Game was played by real players and i tried do my moves human-like and simple as possible too. I am really curious, how much human players will be capable calculate all these ultra sharp computers variations (where black can play Qa7 early+active g4+Bh4) and keep in memory 7-men-syzygy positions. :)
White need secure king first and keep passive Bg3 too, before start something complex. So Kb1-c2-d3-e2-f1 is normal human plan, while black has still good moves for king only. When is Bg3 paralyzed, then white has Knight more in action.
mtakt mtakt 4/29/2023 09:32
@EmilV: Don't worry, it's all ok.
Yes, now we have several moves which keep the win and appear to be game-theoretically equal. But not with all of them will White feel equal comfortable, for example with 46.Qd2 he has to play very precise, so that the result doesn't turn into a draw
EmilV EmilV 4/29/2023 07:38
2 mtakt
Sorry for my mistake arising by copying from big and a little chaotic system of lines and comments.
By the way, we have been waiting for years for ChessBase to build a feature to copy only some subline system to clipboard and not only the whole game :-((.

Otherwise, I don't believe any 46th move is the best.
If the position is won, then probably several moves win.
In some analyses (myself or oxygenes) Black is forced to play h4.
If this is the right step, then methodically it seems best to me to do it immediately playing 46.Qb1.
oxygenes oxygenes 4/29/2023 02:59
Ok, how see it human brain? :) Basic rule for endgame - do not rush. Black has 3 weak points b6, Bg3, pa5. Playing even against 2 weak points could logical lead into zugzwang.. Then forcing h5-h4 while black queen must guard b5-b6 and Bg3 must prevent h2-h4 is simple, no need computer.
So 46.Kb1 Kb8 47.Kc2 Ka8 48.Kd3 Kb8 49.Ke2 Kb7 50.Qb1 h4 - forced, now black lost power of strike g5-g4, Bg3 has accessible one square less, ph4 can be captured by Knight or Queen, white got nice square g4 for Knight. Four small plus added for white. 51.Kf1 Bh2 ( Black can just stay at g3, what lead into Werewolfs variation zugzwang, where Bh2 allows Nd3-f2-g4xe5) 52.g4 Kb8 53.Qb2 Bg3 and now white king can go to a4. 54.Ke2 Ka8 (Bh2 55.Kd3 Bg1? 56.Nxb6 cxb6 57.Qe2) 55.Qd2 Bh2 56.Kd3 Bg3 57.Kc3 Qa7 (Kb7 lead into the same position, just white can take Kxa4 too.) 58.Kb3 Kb7 59.Nb2 a4 (if black just wait, then Ka4,Nb2-d3-c1-b3) 60.Nxa4 Qa8 61.Nb2 - lure black to exchange queens (61.Nxc5!?) - Kb6 62.Nd3 and black is lost, because if black exchange queens, then Bg3 cannot protect pc5, pe5, ph4 simultaneously. If black just wait - then white is eventually forced to think very precisely and play Nxe5/c5.
Karsten Müller Karsten Müller 4/29/2023 02:42
EmilV, mtak: Many thanks! Indeed it now looks like a convincing winning proof, which is very similar to Peter Prohaszka's published one. Good point is that 48.Nc3? runs into ...a4+! as Black needs counterplay. This is the difficulty of the winning plan to bring the king to a4.
mtakt mtakt 4/29/2023 01:33
"A/ mtakt
46.Qd2 Qa7 47.Kb3 Kb7 48.Nc3 a4+! "
Hm, 48.Nc3? was not in the posted line.

And even 46.Qd2 can be considered, as mentioned, to be the second best move with complicated consequences. The best one is 46.Kb3!
EmilV EmilV 4/29/2023 11:24
Yes, the "short plan" with a5 winning seems to fail because of Black defence a4.

A/ mtakt
46.Qd2 Qa7 47.Kb3 Kb7 48.Nc3 a4+! 49.Nxa4 Bh4! (preventing the future Nxe5) 50.Nb2 Kb6! (preparing a4 Qa5!) 51.Nd3 Qa8! 52.a4 Qa5!

Very interesting moment - 51...Qa5? is premature before a4, for example
52.Qxa5+ Kxa5 53.Kc2 Bg3 54.Kd2 Kb6 (54...Ka4 55.Nxe5 dxe5 56.b6; 54...Bh2 55.h4 gxh4 56.Nf2) 55.Ke2 Ka5 56.Nb2 Kb6 57.Na4+ Ka5 58.b6 cxb6 59.Nc3

B/ forcing h4 first
46.Qc1 h4! 47.Qd2 Qa7! 48.Kb3 Kb7 49.Nb2 a4+ (also 49...Bh2!) 50.Nxa4 Bh2! 51.Nb2 Bg1!

(here not 51...Kb6? 52.Qc1!! - tempo, preventing Bg1 and heading to c3 - 52...Qa8 53.Nd3 Qa5 (53...Bg3 54.Qc3 Qh8 55.a4 Qa8 56.Nxe5) 54.Nf2 Bg3 55.Ng4 Qa8 56.Qd2)

52.Nd3 Bd4/e3=

So we have only the original plan, which I try to summarize in this pgn file
https://www.vlasak.biz/xxx/cbchallenge1.pgn
Anyone see any more defence out there?
Karsten Müller Karsten Müller 4/29/2023 10:58
oxygenes: OK. But White should very careful, when he allows ...a5-a4. Then matters can get very deep and sometimes it is even a draw. But your winning proof of course is correct.
oxygenes oxygenes 4/29/2023 09:33
Plan Ka4 works, if black is forced to play h5-h4, later Bg3-h2, allowing g2-g4. If bishop just stay at g3, then white plays for zugzwang, which lead to Knight sacrifice Nd3xc5/e5.
Karsten Müller Karsten Müller 4/29/2023 07:17
Charles Sullivan, mtak, oxygenes: Many thanks! Deep indeed. But the winning plan is not to bring White's king to a4...
Karsten Müller Karsten Müller 4/29/2023 07:10
trellim: But what about 1.Nc3 a4! ?
trellim trellim 4/29/2023 03:40
1.Nc3 Qa7 2.a4 Be1 3.Ne2 Bf2 4.Qd2 Bd4 5.g3 Be3 6.Qe1 Qa8 7.gxf4 exf4 8.e5 dxe5 9.Qb1 Kb7 10.Nc3 Bd4 11. d6 .....winning in all variations from here.
oxygenes oxygenes 4/29/2023 01:08
All these complications, hardly calculable by human brain, are consequences of allowing move 46.- Qa7 and later g5-g4. We need clean technical solution, what is understandable for average players too. :)
So best start will be 46.Kb1 keep black queen dance limited.
mtakt mtakt 4/29/2023 12:20
Had a look at 46.Qd2 (which seems to be the second best move after 46. Kb3) and with Lc0 v30-rc1 and Crystal 5 KWK I could work out the following line which points out that white still has a winning position:
46... Qa7 47. Kb3 Kb7 48. Kc3 Qa8 49. Kd3 Bh4 50. Qb2 Qe8 51. Qb3 g4
52. b6 gxf3 53. gxf3 c6 54. Nc3 Be1 55. dxc6+ Qxc6 56. Nb5 Bh4 57. Kc2 Bd8 58.
Qd3 Be7 59. Qc3 Kxb6 60. Qb2 Qd7 61. Nxd6+ Kc7 62. Nb5+ Kd8 63. Qxe5 Qxh3 64.
Qd5+ Ke8 65. Nc7+ Kf8 66. Ne6+ Ke8 67. Ng7+ Kf8 68. Nxh5 Qxf3 69. Qf5+ Ke8 70.
Nxf4 Qxa3 71. Qg6+ Kd7 72. Qe6+ Kd8 73. Qb6+ Kd7 74. Qb7+ Kd6 75. e5+ Kxe5 76.
Ng6+ Kf6 77. Qb6+ Bd6 78. Qxd6+ Kg5 79. Ne5 Qa2+ 80. Kd3 Qb1+ 81. Ke3 Qe1+ 82.
Kf3 Qh1+ 83. Ke2 Qe4+ 84. Kf2 Qh4+ 85. Kg2 Qe4+ 86. Nf3+ Kg4 87. Qg3+ Kf5 88.
Qg5+ Ke6 89. Qxc5 {and black is losing according to the 7-men-syzygy}
CharlesSullivan CharlesSullivan 4/28/2023 05:11
Regaqrding Karsten's comment about 45...Qb6 46.Qd2 Qa7 47.Kb3 Kb7 -- Even with a 32-core computer (Threadripper 3970X) and a current version of Stockfish (dev-20230329), the verdict is not clear because Black has many plausible defenses and White's winning methods are very subtle. That said, I will give you a line that *probably* wins for White: 48.Kc3 Qa8 49.Kc2 Bh2 50.Qc1 Bg3 51.Qd2 Bh2 52.Qd1 Bg3 53.Qf1 g4 54.hxg4 hxg4 55.fxg4 Qd8 56.b6 and Stockfish works this out to a win.
I also looked at 48.Kc3 Qb6, but White still seems to win: 49.Qb2 Kc8 50.Kd3 Kd8 (50...Kb7 also seems to lose: 51.Ke2 Ka7 52.Qb3 Kb7 53.Qb1 h4 54.Kf1, etc.) 51.Qb1 (Stockfish shows +5.48 at this point, if you can believe that!!) Qb7 52.Ke2 Bh2 53.Qe1 Kc8 54.Qh1 Bg3 55.Qb1 Kb8 56.b6 c6 57.Nc3 Bh2 58.dxc6 Qxc6 59.Kf1 Kb7 60.Qd3 Qxb6 61.Nb5 Bg3 62.Qd5+ etc.
oxygenes oxygenes 4/28/2023 05:07
This direct plan is good, but required strong nerves (calculation) and most of human players is probably not capable see all complications to very end.
Start is easy - 46.Qd2 Kb8 47.Kb3 Kb7 48.Nb2 a4 49.Kxa4 Qa7 50.Kb3 Kb6 51.Nd3 Bh4! - here bishop can be returned into play - and now silicon monster say 52.Nxe5! dxe5 53.d6 but 53.- g4! will force human player to play very precisely. 54.Qd5 Qb7 55.Qxe5 gxf3 56.gxf3 Qc8 57.dxc7!? (57.a4 lead to wild position) Qxc7 58.Qxh5 Bf2 59.Qg6+ Ka7 60.Qa6+Kb8 61.b6 Qd7 62.Qa7+ Qxa7 63.bxa7+ Kxa7 64.e5 Bd4 65.e6 Bf6 66.Kc2 Kb6 67.Kd3 Kc6 68.Ke4 Kd6 69.Kf5 Be7 70.a4 Bd8 71.h4
So it would be good human practical solution disable counter-play g5-g4 first. We need force h5-h4, then return to plan Kb3, Nb2.
Karsten Müller Karsten Müller 4/28/2023 01:28
EmilV, oxygenes: Fascinating idea! More critical seems to be the defense 45...Qb6 46.Qd2 Qa7 47.Kb3 Kb7 to meet 48.Nb2 with a4+. Charles Sullivan has analysed this to a draw a few years ago. I have asked him to check it again. To me it is still not clear, if there is a working winning plan with "always" Ka4. Fascinating question indeed!
oxygenes oxygenes 4/28/2023 12:08
@ EmilV Well, you eventually found a5-a4. :)
I as divan bed general, can to say, that any tactic is good, if silicon monster can see it. But game was played by human players, there is hard to predict, how precise could they play next moves, it was 46. move and both players could be probably tired too. So move like Bg3-h2 is normal human move, if black see zugwang and hope, that white will not find g2-g4.
EmilV EmilV 4/28/2023 10:50
The critical point of such plans is Black defence a4!?
For example
48...a4+ 49.Nxa4 Qa7 50.Nb2! Kb6 51.Nd3! (But not 51.a4? Qa5 52.Qxa5+ Kxa5 53.Nd3 Bh4! probably draw)
and now
51...Qa5 52.Qxa5+ Kxa5 53.Kc2 Bh2 (53...Ka4? 54.Nxe5) 54.h4 gh 55.Nf2!
51...Qb8 52.a4 Qa8 53.Nxe5
51...Qa8 52.Nxe5 de 53.d6 Qd8 54.d7
EmilV EmilV 4/28/2023 09:13
It seems there are different working short plans with a win of Pa5 combined with Nxe5.
For example
46.Qd2 Kb8 47.Kb3 Kb7 48.Nb2 Qa7 49.Ka4 Kb6 50.Nd3! and now:

50...Bh2 51.Nxe5! dxe5 52.d6! is enough to win.

50...Kb7 51.Qxa5 (Beause of Nd3, Be1 is not possible here)

51...Qxa5+ 52.Kxa5 Bh2 53.b6! cxb6+ 54.Kb5 Bg1 55.Nb2 Be3 56.Na4 Bc1 57.Nxb6 Bxa3 58.Nd7
51...Qb6 cannot be good - 52.Qc3 Bh2 53.Kb3 Bg1 54.a4 Bd4 55.Qd2 Be3 56.Qe1 Qa7 57.a5 Qa8 58.Qa1 Qd8 59.Qa4

Emil
Karsten Müller Karsten Müller 4/28/2023 06:59
oxygenes: Interesting! Can you give a complete sample line with your plan to bring the king to a4?
oxygenes oxygenes 4/28/2023 12:44
For first question: In variation from EmilV 52.- Bh2 53.g4 white can go with king to a4, try simply capture pa5 too, instead of forcing sacrifice of knight at e5/c5. White play Qd2 to control square a5, Bg3 has no more shelter behind pg2, after Na4-b2 black is forced sacrifice a5-a4, result is safe endgame: good knight vs bad bishop and tactical motives Nd3xe5/c5 are still ready to use. That i had in view in my first comment.
Of course, forcing zugzwang is shorter solution.
Werewolf Werewolf 4/27/2023 03:14
@ Karsten: On your point 3)below:

No, the issue is Alpha Beta will find this harder than MCTS.
Karsten Müller Karsten Müller 4/27/2023 11:15
By the way: the winning plan mentioned in
https://en.chessbase.com/post/solving-the-impossible
only draws and also the "winning analysis" in Dvorestky's Endgame Manual 4th edition only draws.
Karsten Müller Karsten Müller 4/27/2023 11:10
So 3 major questions remain:
1) Is this the only way to win by exploiting the zugzwangs EmilV gives?
2) Is there an earlier published winning proof than Prohaszka's?
3) Are there computer programs maybe specialised for fortress cracking, who can solve it nowadays and what does solve mean here?
Karsten Müller Karsten Müller 4/27/2023 11:07
EmilV: Deep discovery. Well done! Wolfram Schön had mailed this already to me. So the riddle is solved. Basically this is "a version of the win" Peter Prohaszka found in 2021 and published in American Chess Magazine 21/2021, p.67-73. To my knowledge this is the first correct published winning proof for this position.
EmilV EmilV 4/27/2023 09:14
Hi, all, I am back.

What about MickeyMous-defence? :-)

In Werewolf line, the best chance is 51...Kb8! (and not 51...Kb7?)
52.Qb3 Kb7 with the idea 53. Nb2 Qa7!, because 54.b6? Qxb6 is good for Black.
And after 54.a4? Kb6 55.Nd3 Qa8 56.Qc3 Qh8(e8) Black seems to hold.

Generally speaking, the position Qb3 Na4/Kb7 Qb6 has mutual zugzwang nature.

Black to move is easily lost
52...Qa7 53.b6!
52...Kb8 53.Nb2 Qa7 54.a4 Kb7 55.Qc3 Qa8 56.Nd3 Bh2!? for example 57.Nf2 Bg3 58.Ng4 zuzwang.
52...Bh2 - the toughest defence - 53.g4 Bg3 54.Qc2 zugzwang 54...Kb8 (54...Qa7 55.b6) 55.Nb2 Qa7 56.a4 Kb7 57. Qc3 Qa8 58.Nd3 Bh2 59.Kf2 Bg3+ 60.Kg2 with 61.Nxe5.

But Black can reach this position with White to move. After 53.Nb2 Qa7!

54.Kf2?! Bh2 55.Kf2 Bg3+ 56.Kg1? Be1!
54.Qc3? a4! draws.

It seems, the refutation is 54.Qc2! tempo the same time keeping a4 under control.
If 54...Kb6 then 55.Na4+ Kb7 56.b6
After 54..Qa8 55.Na4! Black has no more Qb6 and b6 is unstopable.
For example 55...g4 56.hxg4 Qh8 57.b6! h3 58.gxh3 Qxh3+ 59.Qg2 probably wins.

Maybe even easier is immediate 53.Qc2! with similar lines.

Emil
Karsten Müller Karsten Müller 4/27/2023 07:40
Sparsh-NewDelhi: Taking the queen does not win as Black can answer White's h4 with ...gxh4 and then close the kingside with ...h3 gxh3 h4 again.
Vinvin: OK but the question was White to move and win after ...Qb6.
Karsten Müller Karsten Müller 4/27/2023 07:28
Werewolf: Many thanks! That plan indeed seems to be winning. More details would be good. Wolfram Schön and Charles Sullivan are already working on it.
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