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Analysis by Stockfish 051119 64 BMI2:

1. = (0.00): 25...Kg6 26.Ke2 f5 27.Ke3 Kf6 28.exf5 Kxf5 29.h3 f6 30.b3 e5 31.f3 Ke6 32.g4 f5 33.g5 h4 34.f4 e4 35.a3 Ke7 36.b4 Kf7 37.Kd2 a5 38.bxa5 bxa5 39.a4 Kg6 40.Ke3 Kf7 41.Ke2 Kg6 42.Ke3

2. = (0.00): 25...Kh6 26.Ke2 Kg5 27.Kf3 f5 28.e5 f6 29.h4+ Kg6 30.Kf4 a6 31.a3 b5 32.cxb5 axb5 33.b3 fxe5+ 34.Ke3 f4+ 35.gxf4 exf4+ 36.Kxf4 Kf6 37.f3 e5+ 38.Ke4 Ke6 39.Ke3 Kd6 40.Kd2 Kd5 41.Kc3 Kc6 42.Kd3 Kd6 43.Ke3 Ke6 44.a4 c4 45.a5 cxb3 46.Kd3 Kd6 47.Kc3 Kc6 48.Kxb3 Kc5 49.Kc2 b4 50.a6 Kb6 51.Kb3 Kxa6 52.Kxb4 Kb6 53.Kc4 Kc6

After 27 moves

Analysis by Stockfish 051119 64 BMI2:

1. ⩲ (0.43): 28.h3 a6 29.h4+ Kf6 30.Ke3 Ke5 31.exf5 Kxf5 32.f3 a5 33.b3 f6 34.Kd3 Kg6 35.g4 Kh6 36.Ke2 Kg7 37.Kf1 Kh6 38.Kf2 Kg6 39.Ke1 Kh6 40.Kd1 Kg6 41.Kd2 Kf7 42.Kd3 Kg6 43.Ke4 Kh6 44.a3 Kg7 45.Kf4 Kg6 46.Kg3 Kh6 47.Kf2 Kg6 48.Ke2 Kh6 49.Kf1 Kg7 50.Kg2 Kg6 51.Kf2 Kh7 52.Ke3 Kh6 53.Ke2 Kg6

<Straclonoor> When you say "27 moves" I am not sure whether you indeed mean moves or plies. Engines typically report search depth in terms of plies and not moves, so it makes a big difference. Stockfish typically needs 30+ (preferably 40+) search depths in order for one to be able to have high confidence in its evaluations.

You did not indicate whether you enabled 6-piece Syzygy tablebase support or not. I'm assuming that you did but, just in case, make sure that you did so. It makes a big difference in the accuracy of the evaluations, although in this position it may take a very deep search to reach positions in which the number of pieces on the board is 6 or less.

The critical White winning attempt seems to be 27...f5 28.e5 instead of 28.h3 as played in the game or other moves, reaching the following position with Black to move:

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Could you please re-run the analysis starting from the position above and let it run to a depth of at least 40 ply? You can probably just let it run overnight and check it in the morning. And I'm interested in knowing how much RAM and how many cores your system has.

I don't know if you are familiar with the FinalGen tablebase generator but it can, within certain restrictions, generate a tablebase of a given position which by looking at every possible sequence of moves, conclusively determine whether the position is a draw or a win for one side or the other. The restriction, in principle, is that the position cannot have more than one piece for either side, both kings, and up to 8 pawns per side. So the position above certainly meets that requirement.

I said "in principle" because it considers certain positions to be "too complex". I had some correspondence with the FinalGen author some years ago explaining this but I don't remember what the explanation was, and I lost the correspondence after a disk crash some years ago when I didn't have sufficiently up to date backup. I know, I know ...

Now I have an ancient 32-bit computer with only 4 GB RAM to the "too complex" message might mean that I don't have enough RAM for FinalGen to analyze the position so, since I suspect that you have more than 4 GM of RAM, you might be able have FinalGen analyze the position and so get a definitive answer as to whether 28.e5 leads to a win or not. If interested you can download FinalGen from http://finalgenchess.ovh/home_ing.php. It's free.

<HOWEVER>, there is a big caveat or two. It can take a long time to run and require a lot of disk space if the position is complex, as this one certainly is, even though it can theoretically analyze it. And the program is single threaded and therefore does not benefit from having more than 1 core. In fact the ideal system to run this program in is an overclocked 2-core system with lots of RAM and a multi-TB, fast access SSD (FinalGen is apparently a very heavy disk user if the amount of RAM available is low).

Before it starts to analyze the position FinalGen thankfully gives you an estimate of how long it will take to analyze the position and how much disk space it will require. But FinalGen indicated that the position above was "too complex" so I inched towards it by starting with the 4 k-side pawns and increasing the number of q-side pawns by two for each starting position. To give you an idea of how the required time and disk utilization increases as a function of position complexity and Normal vs. Search for Draw modes, I got the following estimates as I inched towards the final position. The second column is the estimated time required and the third column the estimated amount of <uncompressed> disk space required. Fortunately the folder used by FinalGen can be compressed and so the real amount of disk space required is about 50% - 75% of the indicated number.

<Normal Mode>

4 pawns, all k-side 4 hrs 18 GB

5 pawns, all k-side + c-file pawns 130 hrs 426 GB

6 pawns, all k-side + c-file & b-file pawns - position too complex –

7 pawns - position too complex -

<Search for Drawl Mode>

4 pawns, all k-side 1 hr 10 GB

5 pawns, all k-side + c-file pawns 12 hrs 12 GB

6 pawns, all k-side + c-file & b-file pawns 1150 hrs 567 GB

7 pawns - position too complex -

Memory 8 GB 2400 MHz DDR4
Processor 3.4 GHz Intel Core i5

Anyway, at 72/60 188:59 (maybe it gives up after three hours?) 40948 MN SF10 spits out a 0.00. The continuation given is:

I said after 27, I meant after 27....f5
Plies in my analysis (8 cores, 16 threads) is around 50.

<Could you please re-run the analysis starting from the position above and let it run to a depth of at least 40 ply?>

<keypusher> I also ran it overnight after 28.e5 using Stockfish 10 on my ancient 32-bit, 4-core Intel Q9400. With only 4 GB memory, a 2.6 GHz clock rate, and 5-piece Syzygy tablebases (the 6-piece tablebase code apparently doesn't work with 32-bit computers) after 8 hours it got to d=43/34 and it also gave an eval of [0.00] after 28...f6 29.h4+ Kg6 30.Kf4 a6 31.b3 (here "my" Stockfish deviated from "your" Stockfish) 31...Kf7 32.a3 Kg6 33.f3 b5 34.a4 bxa4 35.bxa4 a5 (now the White king is prevented from penetrating on the q-side) 36.exf6 Kxf6 37.g4 e5+ 38.Kg3 Kg6 39.g5 Kf7 40.Kf2 Kg6 41.Ke2 Kf[bad FEN: 78/5k2/8/p1p1ppPp/P1P4P/5P2/4K3/8]

And this clearly is a draw. White cannot force matters in the k-side or arrive at a zugzwang position since attempts such as 41...Kg6 42.Ke3 Kf7 43.f4 is met by 42...e4 and Black also gets a protected passed pawn, with no points of entry into Black's position.

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So it seems to me (and Stockfish, of course), that the assessment of 28.e5 as possibly winning are wrong, assuming perfect play by Black which of course is not always a good assumption even at this GM level. But 28.e5 provides the best <practical> chances for a win, which might be the best we should expect. To reinforce this opinion after 28.e5 only 28...f6 draws, Stockfish evaluates its next two top moves to be clearly losing as follows:

2. [+13.38]: 28...h4 29.h3 a6 30.b3 Kg6 31.Kf4 Kh5 32.a3 Kg6 33.g4 fxg4 34.Kxg4 (now Black simply loses the h-pawn without any compensation) 34...b5 35.a4 b4 36.f4 a5 (with the q-side now locked White can concentrate on the k-side) 37.Kxh4 Kf5 38.Kg3 Ke4 (an interesting attempt to penetrate but fruitless since there is no way to stop White's passed h-pawn without the king) 39.h4 Kd4 (the game is over, White's h-pawn will queen first) 40.h5 Kc3 41.h6 Kxb3 42.h7 Kxc4 43.h8=Q Kb3 44.Qf6 c4 45.Qxf7 (how nice to be able to calculate deeply and see that you have enough time to go pawn grabbing!) 45...c3 46.Qxe6+ Kb2 47.Qc4 c2 48.e6 c1=Q 49.Qxc1+ Kxc1 50.e7 b3 51.e8=Q b2 52.Qe1+ Kc2 53.Qe4+ Kc1 54.Qc4+ Kb1 55.Qb3 Ka1 56.Qa3+ Kb1 57.Qf8

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White's last move seems very odd to me, blocking the f-pawn's queening square. Why not 57.Qb3? Then if 57...Kc1 or 57...Ka1 simply 58.f5 pb1=Q 59.f6 and White will get its 4th queen. Maybe it's the horizon effect in action because the Syzygy tablebases don't have distance-to-mate information so they can't report the shortest mate sequence, just that the position leads to a mate. So if the engine blindly follows the Syzygy information it can go round and round in circles without making much progress.

3. [+14.21] 28...a6 29.h4+ Kg6 30.Ke3 (note, not 30.Kf4, after the spare tempo-wasting of 28...a6 White starts off by triangulating to set up a zugzwang position) 30...Kg7 31.Kf4 Kh6 32.f3 Kg7 33.Kg5 (White's king is through and the h-pawn falls, the game is over) 33...f4 34.Kxf4 b5 35.cxb5 axb5 36.Kg5 f5 37.exf6+ Kf7 38.Kf4 b4 (I'm not sure why not just 38...Kxf6 but it just transposes) 39.b3 Kxf6 40.g4 e5+ 41.Ke4 c4 (another version of the horizon effect, Black sees that it is lost and tries to push the inevitable beyond its horizon) 42.bxc4 Ke6 43.g5 Kd6 44.Kf5 e4 45.Kxe4 Ke6 46.f4 Kd6 47.Kf5 b3 (more horizon effect) 48.axb3 Kc5

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One point of possible interest. Some engines report the search depth in the form dd/ee and some just in the form dd, where dd = search depth and ee = search extension. ee is supposed to be the maximum depth reached after extending the search depth to take into account captures, forced moves, etc. but the catch is that is the maximum search depth reached during that depth and not necessarily the maximum search depth for the line listed. Therefore I don't see much use for it.

But your analysis (and later mine) was the first time I noticed a situation where dd > ee which I would think could never happen. So I am no longer sure what ee really means.

After 34.b3 f4+ 35.Ke4 Stockfish 10 at d=40 suggests 35...fxg3 36.fxg3 Kf6

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Now White must give way since 37.a4 results in 37...c4 and Stockfish with 5-piece Syzygy tablebase support evaluates this at d=47 as a forced mate for Black:

1. [-M18]: 38.bxc4 bxa4 39.c5 a3 40.c6 Ke7 41.c7 Kd7 42.c8Q+ Kxc8 43.Kxe5 a2 44.Kd4 a1Q+ 45.Ke3 Qc3+ 46.Kf4 Qd3 47.g4 Qd4+ 48.Kf3 hxg4+ 49.Kg3 Qg1+ 50.Kf4 g3 51.h5 g2 52.Ke5 Qc5+ 53.Kf6 g1Q 54.Kf7 Kd7 55.h6 Qcf2+

2. [-M17]: 38.b4 bxa4 39.b5 Ke7 40.b6 Kd6 41.g4 a3 42.gxh5 a2 43.b7 Kc7 44.b8Q+ Kxb8 45.h6 a1Q 46.h7 Qe1+ 47.Kf3 Qxh4 48.Ke2 Qxh7 49.Kd2 Qd3+ 50.Ke1 Qe3+ 51.Kf1 c3 52.Kg2 c2 53.Kh2 c1Q 54.Kg2 Qcg1+

3. [-M16]: 38.a5 cxb3 39.Kd3 e4+ 40.Kc3 e3 41.a6 e2 42.Kd2 b2 43.Kxe2 b1Q 44.a7 Qa2+ 45.Kd3 Qxa7 46.Ke4 b4 47.Kd3 b3 48.Kc3 Qe3+ 49.Kb2 Qxg3 50.Ka3 Qc3 51.Ka4 b2 52.Kb5 b1Q+ 53.Ka4 Qca1+

So after 36...Kf6 at d=41 Stockfish evaluates the top 3 White moves, all winning for Black, to be:

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1. [-14.72]: 37.Kf3 Kf5 38.Kf2 b4 (with White's king far away on the k-side, Black decides to try a breakthrough on the q-side) 39.a4 c4 40.a5 cxb3 (and now Black queens first and, 2 pawns up, Black should win easily) 41.a6 b2 42.a7 b1=Q 43.a8=Q Qc2+ 44.Ke3 Qc3+ 45.Ke2 b3 46.Qg8 b2 47.g4+ Kf4 48.Qg5+ Ke4 49.Qg6+ Kd4 50.gxh5

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And restarting the analysis from this position Stockfish indicates that it's a mate in 10 after 51...Qe3+, mate in 13 after 51...Qc4+, and even mate in 14 after the non-forcing 51...Kd5

2. [-14.76]: 37.Kd3 Kf5 38.a4 e4+ 39.Kc2 bxa4 40.bxa4 Kg4 (with the situation clarified on the q-side, Black turns his attention to the center and k-side – not that he has much choice at this point) 41.a5 Kxg3 42.a6 e3 43.a7 e2 44.a8=Q e1=Q 45.Qd8 (it may seem that White some drawing chances with forcing moves but Stockfish can't find a perpetual after 45.Qa3+) 45...Qe4+ 46.Kc1 Qe3+ 47.Kb1 Kg4 48.Qg8+ Kxh4 (3 pawns down, White has no hope) 49.Ka2 e5 50.Qd8+ Kg3 51.Qg8+ Kh3 52.Qc8+ Kg2 53.Ka1 Qd4+ 54.Kb1 Qd3+ 55.Kc1 Qf1+ (this seems like a silly move that does not help advance Black's pawns) 56.Kb2 Qf2+ 57.Ka3 Qf3+ 58.Kb2 h4 59.Qg8+ Kf2 60.Kc2 h3 61.Qh8 Qe4+ 62.Kb3 Qf4 63.Ka2 h2 64.Qh7 Qd2+ 65.Kb3 Qd5+ 66.Ka3

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3. [-15.78]: 37.Ke3 Kf5 38.a4 c4 (a recurring theme) 39.a5 cxb3 40.Kd2 e4 (now White is in a quandary, he can stop either the b-pawn or the e-pawn from queening, but not both, and Black queens first, maintaining the initiative and a pawn advantage) 41.a6 e3+ 42.Kxe3 b2 43.a7 b1=Q 44.a8=Q Qe1+ 45.Kd3 (an odd decision IMO, White allows Black to capture all the k-side pawns) 45...Qxg3+ 46.Kc2 Qxh4

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And now Black theoretically mates in 29 moves per the Lomonosov tablebases. But I'll give the rest of Stockfish's line just to make another point about tablebases.

47.Qf3+ Kg5 (I thought that 47...Ke4, centralizing the king and threatening the queen exchange with 48...Qe4+ would be better but it has no practical advantage, White is lost in either case. Besides, the Lomonosov tablebases, with distance-to-mate (DTM) information, agree with Stockfish's decision.) 48.Qg2+ Qg4 49.Qd2+ Qf4 50.Qg2+ Kf5 51.Qh3+ (here the Lomonosov tablebases suggest 51.Qb7 indicating that Black mates in 23 moves) 51...Qg4 (here the Lomonosov tablebases suggest 51...Ke5 indicating that Black mates in 19 moves.

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I suspect that since the Syzygy tablebases do not have DTM information Stockfish can't find the shortest path to mate with either White or Black) 52.Qf1+ Kg5 53.Qc1+ Qf4 54.Qg1+ Kf6 55.Qg8 h4 56.Kb2 Qe5+ 57.Kb1 Kf5 58.Qh7+ Kg4 59.Qg6+ Kf3 60.Qh6 Qe4+ 61.Ka1 Qd4+ 62.Kb1 Kf2 63.Qf8+ Ke2 64.Qg8 Qe4+ 65.Kb2 Qe5+ 66.Kb1 Kf3 67.Qd8 h3 68.Qd1+ Qe2 69.Qh1+ Kg4 70.Qg1+ Kf4 71.Qc1+ Qe3 72.Qd1 Qe4+ 73.Kc1 Qc4+ 74.Kb2

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Here the Lomonosov tablebases indicate that Black mates in 17 moves. Twenty three moves earlier, after 51.Qh3+, had Black played 51...Ke5 instead of 51...Qg4 as played by Stockfish, Black would have theoretically mated in 19 moves. So, after 22 moves, Black has only succeeded in reducing the number of moves to mate from 19 to 17. At this rate, if the 50-move rule is taken into account, the game will last a long, long time, showing the advantages of having DTM information in the tablebases.

What's the penalty for using, say, 6-piece Nalimov tablebases with DTM information compared with 6-piece Syzygy information without DTM information? Disk storage, for one. The 6-piece Syzygy tablebases require about 161 GB of disk storage and the 6-piece Nalimov tablebases require about 1.2 TB of disk storage, about 7.5X more. However, high-performance (7200 RPM) 4 TB internal disk drives are going for < $ 90 so I'm not sure that the tradeoff in cost/performance is worth it, although it probably was back in 2013 when the 6-piece Syzygy tablebases were releases. And 7-piece Syzygy tablebases have been available since Aug-2018 and require about 17 TB of disk storage while the 7-piece Lomonosov tablebases require about 140 TB of storage, about an 8.2X storage ratio between a tablebase containing DTM information an one that does not contain DTM information. But either, I believe, is beyond the budget of most of us at this site.

However, 8-piece tablebases, presumably without DTM information, are estimated to require about 1 PB. Definitely beyond the reach of most of us!