<Isaak Schulimowitsch Birbrager >

"Chess: Serious, for fun"

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Hi AylerKupp,

I'm sure you will find this post as you told me once you search for your name in case someone calls.

a couple of positions from Birbrager's book: "Chess: Serious, for Fun."

I've guessed a modern computer will get this in two seconds max. It will probably be less than that. According to Birbrager (page 40) in 1961 it took a computer 12 minutes to solve.

White to play and mate in 3.

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And this interesting one with a beautiful key idea . White to play and win.

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Does it come up with mate in X moves very quickly as well.

You're right, I guess I'm a glutton for punishment. Perhaps I should change my user name to <You Rang> but that's already taken.

At any rate, as far as the first position:

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It took the following for some modern engines to solve it in my somewhat archaic machine. FWIW the number in parenthesis reflect the engine's current ratings in the latest CCRL 40/40 version for the 64-bit version of the engine. Since my computer is only 32-bits, the actual rating would be somewhat lower. But remember that these ratings are based on engine vs. engine games and not engine vs. human games, so the engine ratings are not directly comparable to human ratings.

I also set the engines to use 4 threads, a 1024 KB hash table, and make use of the 5-piece Syzygy tablebases.

Houdini 6 (3399): [+M3], d=9, 00:00: 1.e8=B Kxd6 2.c8=R Ke6 3.Rc6#

Komodo 12.1 (3400): +M3], d=35(!), 00:00: 1.e8=B Kxd6 2.c8=R Ke6 3.Rc6#. I should add that although it Komodo until d=35 to find the mate in 3, it also got to d=99 (its highest) in 00:00.

Stockfish 9 (3438): [+M3], d=5:, 00:00: 1.e8=B Kxd6 2.c8=R Ke6 3.Rc6#. It also took Stockfish 00:00 to reach d=127 (it's highest).

Since the definition of "modern" is subject of interpretation, I thought I would also try that old warhorse, Rybka 4.1, was top dog in the chess engine world for many years but hasn't been updated since Mar-2011 (a lifetime in computer engine time), Rybka uses 5-Nalimov tablebases, everything else was the same as for Houdini, Komodo, and Stockfish..

Rybka 4.1 (3149): I let Rybka run for almost 20 minutes and MPV=5 but it could not fine a mate in 3, although it "found" 3 mates in 4 after 00:00:

1. [+M4]: 1.e8=Q+ Kxd6 2.Qe7+ Kc6 3.c8=Q+ Kb6 4.Qec5#

1. [+M4]: 1.g8=Q+ Kxd6 2.Qc4 Kd7 3.c8=Q+ Kd6 4.e8=Q. But that's not mate, it's stalemate!

After 19 minutes at d=49 this it what it got:

1. [+M4]: 1.c8=Q+ Kxf6 2.Qg4 Kf7 3.g8Q+ Kf6 4.Q4e6#

2. [+M4]: 1.e8=R+ Kxd6 2.c8=Q. Again, not mate but stalemate.

3. [+M4]: 1.c8=R Kxf6 2.e8=Q Kg5 3.Qh8 Kg4 4.g8=Q#

4. [+M4]: 1.e8=Q+ Kxd6 2.Qe7+ Kc6 3.Qc5+ (??) Kd7 (??) 4.c8=Q#. It looks more like a helpmate than a mate to me. Why not 3...Kxc5?

5. [+M4]: 1.g8=Q+ Kxd6 2.Qc4 Kd7 3.c8=Q+ Kd6 4.Q4e6#

Well, at least it got 3 out of 5 assessments correct. So it looks like Rybka 4.1, which was the top-rated engine until about Dec 2010 with the release of Houdini 1.5 had some serious endgame handling bugs. And it looks like Houdini 6 might have been lucky to find the mates because in 2 versions following the release of Houdini 6:

Houdini 6.01 (released Sep 2017) - Maintenance update with Nalimov EGTB correction and new output option..

Houdini 6.03 (released Nov 2017) - Correction for incorrect detection of stalemate in positions with white pawn capture moves..

Finally, the results given by Darky 0.5d, the second lowest rated engine at 1517 in the latest CCRL 40/40 engine tournament. It was last updated in Mar-2012. Unfortunately, the lowest rated engine (Saruman 2017.08.10 64-bit) was not available for download, nor could I run it on my 32-bit computer.

As far as I can tell (the documentation, as expected, is almost non-existent) Darky can only use one core, display only one variation, and has no tablebase support. And it is slooooow (it too it 15 secs to reach d=10 and then it apparently stopped running even though I let it continue to run for more than 30 minutes). But . . .

Darky 0.5d: [+99.95], d=8: 1.e8=B Kxd6 2.c8=R Ke6 3.Rc6#

So, the second lowest rated engine in the CCRL 40/40 engine tournament outperformed Houdini 6 (found mate in 3 at a lower search depth), Komodo 12.1 (ditto), and Rybka 4.1 (who couldn't find a mate in 3 at all and misassesed several positions which it thought were mate but weren't. Only Stockfish 9 found a mate in 3 at a lower search depth.

I'm not sure if the engine recognized that 3.Rc6 was mate since it didn't indicate it unless [+99.95] is its way of indicating mate. But mate in 3 it was.

Wonders never cease. And such an apparently simple position turned out to be quite a chess engine adventure!

As final comment, even though the position contains only 7 pieces, it was not recognizable by the on-line 7-piece Lomonosov tablebases (), saying that it was an invalid board because there were "Too many white pieces". So it looks like Issak Birbrager was prescient and came up with a position that stumped the 7-piece Lomonosov tablebase developers!

Hi AylerKupp,

Thought you might enjoy it.

Interesting about Rybka 4.1. Maybe there is a setting in it's options 'always promote to a Queen.'

If I ever pulled 'Birbrager' by setting a problem that required one to turn the board 45 or 90 degrees I would put a huge clue to do so in the text.

What would be a good position is mate in two with White playing up the board, then playing down the board, then playing from left to right and finally playing right to left.

Yes. You can downloaded from here: https://chessengines.blogspot.com/2.... It even includes the source code, assuming that you are interested. But be forwarned, while fairly well documented the comments are in Spanish, although the variables are named in English. Here is an example:

/* Aplico factor tiempo */
if (Darky_Pieces() < 7) TimeControl.factor = 2; /* si hay pocas piezas pienso mas */

And also note that there are two versions, one for the Winboard interface and one for the UCI interface. If, as likely, your GUI uses the UCI interface, make sure that you load the proper version.

It's also relatively new to the CCRL 40/40 tournament. While the link above indicates that the latest version was released in Oct-2012 it had not made an appearance in the CCRL 40/40 tournament by Mar-2018. Somewhere between Mar-2018 and Jul-2018 when I next downloaded the CCRL engine tournament results it appeared, and its rating in the Jul-2018 rating list was 1777, ahead of my previous whipping boy, Ziggurat 0.22, rated at 1768.

But Darky 0.5d has apparently not held up well under the stress of competition. Its rating in the Sep-2018 CCRL rating list was 1754 with 8 engines rated lower (and Ziggurat 0.22 rated above it at 1769). And by the Oct-2018 CCRL rating list its rating had dropped to 1517 with only Saruman 2017.08.10 64-bit rated below it at 1441. So it may be time for Darky 0.6 to make an appearance in order for it to avoid the cellar.

Yes, I did. And I liked your second position even better, and I'll have my comments hopefully shortly. You have been warned.

But I'm not done with this first position yet. I mentioned that the on-line Lomonosov tablebases could not handle the position. I tried to enter the position again but on my tablet instead of my phone (the app only runs on Android devices, go figure) and this time I got the message "Too many White pieces." Huh? I counted 5 White pawns and a White King for a total of six pieces, and the Black king makes it seven pieces so it should have been able to handle it. Then I remembered that some of the other 5 and 6 piece tablebases do not include positions that are clearly won for one side, e.g. KPPPPvK, so I suspect that the Lomonosov tablebases do not have an entry for the position of KPPPPPvK and hence "Too many White pieces". When I eliminated the Pg7 (i.e. KPPPPvK it then worked fine , indicating that White mates in 4 after 1.c8=Q+.

But why mate in 4 and not mate in 3.? Well, with the original symmetric position we have 1.e8=B Kxd6 2.c8=R Ke6 [forced] 3.Rc6#. And if 1.e8=B Kxf6 2.g8=R Ke6 3.Rg6#. But if you remove, say the Pg7, then after 1.e8=B Kxf6 Black's king has an escape square, g7 and there is no mate in 3 after, say, 2.c8=Q Kg7, although of course mate occurs shortly thereafter.

Then, in the reversed "trick" position without, say, the White Pg7, White mates in 11 by advancing either the Pf3, Pd3, or Pc2 (2 squares). No big deal.

As far as Rybka having a setting about always promoting to a queen that would be logical under the assumption that, all other things being equal, it will attempt to maximize its evaluation by selecting the continuation that results in the greatest material advantage. Only if that continuation results in stalemate or something equally undesirable in a winning position will it underpromote.

One exception is when it sees that the promoted piece will be immediately recaptured. In that case some engines, and I don't know if Rybka is one of them, underpromote to the lowest value piece that it will still force the recapture. I consider this as a way for the engine to either minimize its material loss after the recapture or show that it has a sense of humor. I know, I should not fall into the trap of anthropormizing chess engines.

Finally, I thought I would try one final tool in my endgame arsenal, the FinalGen tablebase generator. It is able to (theoretically) determine the results of endgames consisting of kings, one piece for either side, and an arbitrary number of pawns for either side. So in theory it's not limited to the current 7-piece table bases, it could theoretically perfectly evaluate a position consisting of 2 kings, 2 pieces, and 16 pawns; 20 pieces in total!. In practice some positions meeting the 2 kings, 2 pieces, and pawns criteria are unsolvable if sufficient computer resources (i.e. RAM) are not available, and the resulting analysis could take a very long time, possibly <years>(!).

But in this case the position is very simple so in 1 second or less it determined it was a win for White (meaning White achieves a position where a win is "obvious" and after 1.g8=Q+, 1.e8=Q+, 1.c8=Q+ and after 1.f7, 1.d7, 1.Kf3, 1.Kd4, 1.Kf4 White wins in 1 (which presumably means that after any of those moves White achieves a position where a win is "obvious"). But then I knew that and I just wanted to find out if it could find a mate in 3

Interestingly it said that a solution after 1.c8=R, 1.c8=B+, 1.c8=N, 1.e8=R+, 1.e8=B, 1.e8=N, 1.g8=R, 1.g=B+ were "Not available". Which I suppose it means "Hey buddy, I already gave you 10 solutions where White wins. I'm not going to bother giving you more." And I don't know why it didn't even bother to indicate that a solution after 1.g=N was not available.

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Definitely interesting and with a beautiful idea. It had so many variations, themes, and subtleties that, like a good novel, I couldn't put it down. I tried to analyze it with multiple engines, with varying amounts of success.

But first let <me> see. The Bf1 can't move because then Qxg2#. The Nh1 can't move because just Qxg3. And neither the Black pawns or Black's king can move until either the Bf1 or the Kg1 moves, and the Kg1 can't move until the Bf1 moves and that leads to mate.

So the only Black piece that can move is the Nh8 which can't stray too far and leave h8 unprotected so that White's Ph7 can queen. Which implies that White's king can move about at will and either capture Black's knight currently on h8 or force it away from guarding h8. So, by approaching h8 with its king White can put Black in zugzwang since its other pieces can't move.

Conversely, Black has set up a fortress and White is in a state of almost zugzwang also. White's queen and rook must stay where they are in order to continue to tie down the Bf1 by the threat of Qxg2#. ...Ng3, Qxg3 is possible, but that's about it since White's queen must protect its Rh2. Almost mutual zugzwang. So it's a battle between the White Ka1 and the Black Nh8, eyeing each other along the long a1-h8 diagonal. What a concept!

Having said that, let's try the same engines under the same conditions and see how long it takes them to figure this out if indeed that's the right approach for White.

<Stockfish 9>: [+132.62], d=29, 00:04:26: 1.Kb2 Ng6 2.Kc3 Nh8 3.Kd4 Ng6 4.Kc5 Nh8 5.Kd6 Ng6 6.Kc7 Nh8 7.Kb8 Nf7 8.Ka8 Nh8 9.Ka7 Nf7 10.Kb6 Nh8 11.Kc5 (we now reach the same position as after 4.Kc5 but Black's knight is already on h8 so it must move elsewhere) 11...Ng6 12.Kd4 Nh8 13.Ke5 (now the Black king has a straight path to f6 along the dark squares) 13...Ng6+ 14.Kf6 Nh8 15.Kg7 Ng6 16.Kxg6 Bd3+ (now Black can move the bishop with check but it doesn't matter) 17.Kh6 Kf1 18.Qxg2+ Ke1 19.Rxh1+ f1=Q 20.Rxf1+ Bxf1 and the simplest win is 21.Qxf1+ Kxf1 22.h8=Q.

At first I thought that the maneuver to a8 was extravagant and unnecessary, and that a simple triangulation, say 1.Ka2 followed by 2.Kb2 would be adequate. But then I realized that the White king must travel to f6 only along the dark squares to prevent any checks from the Bf1, even in "suicide mode", otherwise Black can promote its Pf2. And the only way that White could do the needed triangulation without being exposed to checks is via a8. A wonderful conception and finesse!

A word about Stockfish's evaluation of [+132.62]. It's an artifact of both Stockfish and the Syzygy tablebases which do not contain distance to mate (DTM) information so, while they know that the position is a win, they don't know the number of moves needed to mate. So all the tablebases can do is report a win and let Stockfish's normal evaluation function, as soon as its search depth is deep enough, determine the best move sequence to achieve mate in the shortest number of moves.

<Houdini 6>: [+250.00], d=15, 00:00:11: 1..Kb2 Nf7 2.Kc3 Nd6 (and odd choice in my opinion, just effectively giving up attempting to prevent or at least delay the h-pawn's promotion) 3.h8=Q Nb5+ 4.Kb4 Ng3 (this must be the horizon effect at work, recognizing that it is lost but giving up pieces to delay the inevitable) 5.Rxg2+ Bxg2 6.Qh2+ Kf1 7.Qxg3 Be4 8.Qxf2+ Kxf2

<Komodo 12.1>: [+250.00], d=19, 00:00:35: 1.Kb2 Nf7 2.Kc3 Ng5 (like Houdini, Komodo gives up trying to prevent the h-pawn from promoting but it tries to make itself more of a nuisance. 3.h8=Q Ng3 (Taking White's queen makes no difference! After 3...Nxh3 4.Rxh3 White has accomplished what it set out to do, chase Black's knight away from h8 to allow the promotion of the h-pawn. And Black is just as tied up as ever) 4.Rxg2+ Bxg2 5.Qh2+ Kf1 6.Qxg3 Ne4+ 7.Kd3 Nf6 (of course, if 7...Nxg3, 8.Qa1#) 8.Qxg2+ Kxg2

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Now 9.Qxf6 f1=Q+ leads to a draw so White's queen must approach the Black king a little bit more carefully. 9.Qg7+ leads to a mate in 8 (e.g. 9...Kh3 10.Qxf6 Kg4 11.Ke2 f1Q+ 12.Kxf1 Kh5 13.Qg7 Kh4 14.Qg6 Kh3 15.Qg5 Kh2 16.Qg2#) since once Black's king moves to the h-file then 10.Ke2 prevents Black's f-pawn from promoting and wins it. And if 9...Kf1 then 10.Qxf6 and another easy win for White. But at least Komodo presented more problems to White than Houdini, even though it took it an extra 24 secs to do so.

Time to give Rybka 4.1 another chance to redeem itself after its inability to not only find mates in 3 in the previous position but also by misevaluating some of the "mates" in 4. And I used to think around 2012 that Rybka played the best endgame of all the major engines! Here is how it did:

<Rybka 4.1>: [+3.52, d=24, 01:23:48: 1.Kb2 Nf7 2.Kc3 Nh8 3.Kd4 Ng6 4.Kc5 Nh8 5.Kd6 Ng6 6.Qh5 (not quite finding the winning approach) 6...Nh8 7.Rh3 Bd3 8.Qc5 Nf7+ 9.Ke7 Bxh7 10.Kxf7 (I would have thought that 10.Rxh7 might be better since it gets rid of the long range bishop and the Nf7 cannot easily survive when surrounded by all the White pieces, but what do I know?) 10...Bf5 11.Rf3 Bg4 12.Rf6 Kh2 13.Qe5+ Kg1 14.Qd4 Kh2 15.Qf4+ Kg1 16.Qe3 Now I'm not sure how White manages to avoid a draw by repetition and still prevent one of Black's pawn from promoting.

To see if Rybka could figure it out, I let it run overnight. But because Rybka is the slowest of the major engines (if it can still be considered a major engine) to reach a given search depth, after almost 11 hours it only advanced 2 ply and its principal variation did not change, although it did reduce its evaluation from [+3.52] to [+2.57]. So perhaps it recognized that it had encountered a fortress and could make no progress. So, to help it out, I restarted the analysis at the final position it had reached in its principal variation (my so-called "leaping forward" approach):

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[+2.67], d=26, 00:30:20: 16...Kh2 17.Qf4+ Kg1 18.Qd4 Kh2 19.Rh6+ Kg1 20.Ra6 Kh2 21.Qf4+ (Black's bishop is still immune since if 21.Qxg4, 21...f1=Q+ and 22...Qxa6) 21...Kg1 22.Qe3 (pinning the Pf2 is the only way for White to block its promotion) 22...Kh2 23.Rh6+ Kg1 24.Rh4 Ng3 (Black can apparently give up its bishop and still maintain its fortress) 25.Rxg4 (and this is a draw (!) per the 7-piece Lomonosov tablebases) 25...Nf5 26.Qb6 (White must maintain the pin on the Pf2 and moving to b6 gives it the chance to obtain its biggest material advantage) 26...Nh6+ (ooops!) 27.Qxh6 (pretty much forced since after, say, 27.Kg6 Nxg4 it is <Black> who mates in 14 per the Lomonosov tablebases!) 27...f1=Q+ (now the fight is a little bit more even, but it's still a draw) 28.Kg8 Qf2 29.Qc6 Kh2 30.Qd5 Kh1 31.Kg7 Qb2+

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I found this endgame so subtle and the performances of both Houdini and Komodo so disappointing that I thought I would try 2 other things. First, I wanted to try Houdini using Gaviota tablebases. Gaviota tablebases, unlike the Syzygy tablebases, contain DTM information so maybe it could find the line that Stockfish found and make it harder for White than the line it chose as "best". Second, I wanted to try Komodo 12.1 using Monte Carlo Tree Search (MCTS) just like AlphaZero uses. In a test 20-game match I earlier ran between Komodo 12.1 using MCTS vs. Komodo 12.1 using minimax with alpha-beta pruning (ABP) the latter won handily at a Classic time control, +12=8-0 and 80.0% scoring percentage, but maybe Komodo with MCTS might do better in endgames. Here is how they did:

<Houdini 6 with/without Gaviota Tablebases>: I couldn't get Houdini 6 with Gaviota tablebases to work, even though the documentation claimed that it still supported them. They worked fine with Houdini 4. So I tried Houdini 6 without tablebase support of any kind and, surprise!, it found the Stockfish winning line: [+2.74], d=24, 00:10:18: 1.Kb2 Nf7 2.Kc3 Nh8 3.Kd4 Nf7 4.Kc5 Nh8 5.Kb4 (seems like a step backwards, 5.Kb6, 6.Ka7, 7.Ka8 saves a tempo but it makes no difference in the end) 5...Nf7 6.Ka5 Nh8 7.Kb6 (back to the winning approach) 7...Nf7 8.Ka7 Nh8 <9.Ka8> (finally!) 9...Nf7 10.Kb8 Nh8 11.Kc7 and now 11...Nf7 would have prevented or at least delayed progress along the dark squares since both 12.Kd8 and 12.Kd6 would be prevented.

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But White still accomplishes its goal by 12.Kb6 (recouler pour mieux avancer) 12...Nh8 13.Kc5 Nf7 14.Kd4 Nh8 15.Ke5 so the incursion to g7 can't really be prevented. If Black tries 15...Ng6+ 16.Kf6 Nf4 then simply 17.h8=Q Nxh3 18.Qxh3

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and Black is in zugzwang since after either 18...Ng3 19.Qxg3 B(any) 20.Qxg2# or 18...B(any) 19.Qxg2#, White wins.

Instead Houdini played 11...Ng6 12.Kd6 Nh8 13.Ke7 Ng6+ 14.Kf6 Nh8 15.Kg7 Nf7 16.Kxf7 Bc4+ (the bishop is finally out with check but it's too late, White's h-pawn queens) 17.Ke7 f1=Q 18.Qe3+ Qf2 (if 18...Nf2 19.h8=Q and Houdini evaluates the resulting position at [+M17], d=23 after 19...Qb1 20.Rh6 Qb4+ 21.Kd7 Qb7+ 22.Kd6 Qd5+ 23.Kc7 Qa5+ 24.Kb8 Kf1 25.Qc1+ Qe1 26.Qha1 Qxc1 27.Qxc1+ Ke2 28.Qxc4+ Nd3 29.Rd6 g1=Q 30.Qxd3+ Kf2 31.Rf6+ Ke1 32.Re6+ Qe3 33.Rxe3+ Kf2 34.Qd2+ Kg1 35.Re1#) 19.Qxf2+ Kxf2

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And this position, per Houdini, results in a mate in 10: [+M10], d=22 after 20.h8=Q Bd5 (seems like the horizon effect at work, delay the inevitable as long as possible regardless of how many sacrifices it takes) 21.Qd4+ Kg3 22.Rh5 g1=B (an example of Houdini's "sense of humor") 23.Qxg1+ Kf4 24.Rxd5 Kf3 25.Qxh1+ Ke3 26.Qf1 Ke4 27.Kd6 Ke3 28.Rd3+ Ke4 29.Qf3#

So instead 6.Rh1+ and mate in 5 follows after 6...gxh1=Q 7.Qxg3+ Bg2 (if 7...Qg2, 8.Qhh2#) 8.Qa1+ f1=N (if 8... f1=Q then 9.Qd4+ and mate on f2 follows) 9.Qd4+ Ne3 10.Qgxe3+ (or 10.Qdxe3+ Kf1 11.Qef2#) 10.Kh2 11.Qd6#. An amusing position.

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The ChessBase.com (who acquired Komodo) propaganda ... er, marketing for Komodo MCTS says that "it plays more aggressively and more human-like". Does it? I think that you are in a better position than I am to agree or disagree with that statement. :-)

Finally, in case lightning can strike twice here's how the appropriately named dark horse contender did:

<Darky 0.5d>: [+5.35], d=10, 00:00:18: 1.Kb2 Nf7 2.Kc3 Nh8 3.Kd4 Nf7 4.h8=Q Nxh8 5.Qxh8 Ng3

Unfortunately that's as far as it got. After 18 secs of calculation, if apparently crashed. No indication whatsoever, but after 2 hours it made no progress. And the Windows Performance Monitor did not indicate any CPU activity. I restarted the analysis and kept an eye on the Windows Performance Monitor, and after about 00:01:40 the CPU utilization went down to zero again.

But Darky's line was the most straightforward with regards to promoting the h-pawn and after 6.Qh3 we get the same zugzwang position with, alas, Black to move. And that makes all the difference after 6...Ne4 since the knight is immune because after 7.Kxe4 it's once again a tablebase draw (7...Bd3+ and 8...f1=Q). Black has maintained his fortress and any move other than 7.Ke3 is evaluated by Stockfish at [0.00], d=53. After 7.Ke3 we get another amusing position after 7...Nf6 8.Qf3 Kxh2 9.Qf4+ Kh3 10.Kxf2 Ng4+ 11.Kg1 Kh4

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Stockfish evaluates the position at [+2.13] (winning) but White's king is trapped and as long as Black's king can dance around the Ng6 protecting it then White can make no progress. The rest of the (long) line went 12.Qf3 Kg5 13.Qe4 Kh4 14.Qf4 Kh3 15.Qf3+ Kh4 16.Qd5 Kg3 17.Qd2 Kh4 18.Qd8+ Kg3 19.Qd6+ Kf3 (I think 19..Kh3 would have been safer but it clearly doesn't matter) 20.Qc7 Ke4 21.Qb7+ Kf4 22.Qf7+ Ke4 23.Qe8+ Ne5 (and this, allowing White's king to escape, doesn't seem wise. But chess engines have no fear, they just calculate! At any rate, White's king can't stray from f2 or the g-pawn promotes) 24.Kf2 Kf4 25.Qb8 Kf5 26.Qf8+ Ke4 27.Qe7 Kf5 28.Qh7+ Kf6 ( I get the feeling that Black's king is going after White's queen!) 29.Qh8+ Ke6 30.Qc8+ Kf6 31.Qf8+ Ke6 32.Qe8+ Kd5 33.Qa8+ Kd6 34.Qb8+ Ke6 35.Qb3+ Ke7 (Black's king has no fear!) 36.Qb4+ Ke6 37.Qe4 Kf6 38.Qf4+ Ke6 39.Qe3 Kf5 40.Qc5 Ke4 41.Qb4+ Kf5 42.Qa5 Kf6 43.Qb6+ Kf5

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And as of d=70 Stockfish's evaluation is still [+2.13] although the final position is slightly different. But it seems clear that White can make no progress, so 6.Qh3 is not the way for White to get any winning chances, that gain of a tempo made all the difference.

I am, however, gratified that I figured out White's winning plan without any help from the engines. True, I did not envision the need for triangulation to lose a tempo, much less that this must happen at a8. So maybe I could not have won this position from White's side either. But now, if I ever find myself in such a position playing White, I'll know what to do. :-)

Hi AylerKupp,

"did Isaak Birbrager have all this analysis in his book?"

No, he just explained with one variation why White had to keep off a light square and gave the winning line.

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To win White must reach a position akin to this...

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....with Black to play. So from the first diagram.

1. Kb2 Nf7 2. Kc3 Nh8 3. Kd4 Nf7 4. Kc5 Nh8 5. Kb6 Nf7 6. Ka7 Nh8 7. Ka8

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Onto a light square without allowing a Bishop check.

7... Nf7 8. Kb8 Nh8 9. Kc7 Nf7 10. Kb6

Having lost the tempo this is a simple outflanking move to reach the critical position.

10... Nh8 11. Kc5 Nf7 12. Kd4 Nh8 13. Ke5

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There we have it. The crucial position with Black to play. From here the win is fairly straight forward.

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I played the winning idea v a computer and noticed it had an under promotion in a line of analysis. This appeared in one of the tries getting the King to e6 and playing Qh4.

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White threatening 1.RxN+ PxR=Q 2.Qxf2 Mate. But Black can play 1...PxR=N and there is no mate, the h1 Knight cover f2.

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Hi Olavi,

White to move and win:

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The solution would be 1.Ka1! which immediate accomplishes the required triangulation reaching the original position of Birbarger's (I hope!) but, critically, with Black to move. Then the solution is "simple": 1...Nf7 2.Kb2 Nh8 3.Kc3 Nf7 4.Kd4 Nh8 5.Ke5 reaching the position in your second diagram above. Then either 6... Nh7 or, if Black wanted a spite check, 5...Ng6+, 6.Kf6 Nh8 (or, if Black wants to gain useless material, 6...Ng5 (if 5...Nh7) or 6...Nf4 (if 5...Ng6+). Then comes 7.h8=Q Nxh3 8.Qxh3 and we again reach the by now well-known zugzwang position:

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Too bad that "The Immortal Zugzwang Game" is already taken. But maybe this one could become known as "The Immortal Zugzwang Position" or at least and certainly more modestly "My Zugzwang Beats Your Fortress". All I now have to figure out is a <plausible> way to get from chess' initial position to this one, a task probably harder than coming up with the solution to the puzzle!

And the direct White king march from a1 to f6 and g7, while perhaps not as impressive as its march to a8, has it's own charm. It appeals to my engineering sensibilities. After all, without having read Birbrager (and, modestly, my posts), how many would figure out that 1.Ka1! is the winning move? Once again, "reculer pour mieux avancer".