Cooks and finds with 8-piece tablebases

by Albert Silver
5/16/2022 – One of the fascinating aspects of new iterations of tablebases is submitting known positions to their 'divine' evaluation. The words "better" or "worse" cease to have any meaning and not only are all evaluations perfect and absolute, but so are the solutions. In the following article a share of cooks of studies as well as famous endgames and analyses are placed under the spotlight of the 8-piece tablebases.

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The value of 8-piece tablebases

It would be easy to dismiss the interest and point of 8-piece tablebases in view of the powerful engines available together with 6-piece or 7-piece tablebases. But it really is not as simple as it sounds. Most people today do not have a complete 7-piece set at home, still requiring a hefty 18.4 TB, and while you can consult it online, the engine won't be using it to render judgement should you do so. However, even with a properly powerful setup, and a 'mere' 6-piece set, it will be unable to give you that absolute-ism you so desire in a position. 

Consider the following position and analysis shared by Marc Bourzutschky, the producer of the 8-piece tablebases and analysis.

 
Rodriguez Herreros, V. vs Kallio, H.
Mate in 370

In this position, taken from a game in the 1998 World Under-18 Championship, Black had a mate in ... 370 moves. Naturally, he had no way of knowing this, and even the 6-piece set was not publicly available, much less the 8-piece set that this requires. Black's only winning move here is 51... ♜a2!

So what does a strong engine using 6-piece tablebases say? The good news is that after a minute on a modern laptop with 16 threads, the engine does indeed choose the best play 51... ♜a2! Yay. The bad news is that even with all gears turning at full speed, it is only able to evaluate Black as slightly better.

A player analyzing without the benefit of a larger tablebase set may be led to believe there is no win, and the engine is doing that funny dance where it shuffles around the board for the next 100 moves before coming to terms with reality. Yet it is winning as we know.

Full replayable solution

 
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White loses in 369 moves. 50.Bg6 Black wins in 348 moves. 50.Kd6 hangs on slightly longer. 50...Rg2 White loses in 371 moves. 50...Kg7 is slightly faster. 51.Be4 Rg5+? 51...Ra2! is the only winning move. 52.Bd5!= the only drawing move. Kg7 53.Nd2 Rg3 54.Nf3 Rh3 55.Kc4 Rh1 56.Kc5! the only drawing move. Rh3 57.Kc4 Rh1 58.Kc5! Rd1 59.Bc4! Ra1 60.Nxd4 ½–½
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Rodriguez Herreros,V2280Kallio,H2360½–½1998A08Wch U187

 

Analyzing positions with opposing pawns

In his interview (see below) and email to ARVES, Marc Bourzutschky explained that two reasons motivated his research into positions with opposing pawns.

The first is that by its very nature, the only way one of the pawns will free itself of the blockade is by capturing an enemy piece, and in so doing, this would mean one piece less and therefore a 7-piece endgame for which a ready solution is available. In computation terms, this meant a huge savings in time and space.

An example can be found in the 1990 World Championship match between Kasparov and Karpov:

 
Kasparov, G. vs Karpov, A. (1990 WCh - Game 16)

The position is indeed winning for White, and Kasparov accounted very well for himself by converting it in under 40 moves. 

The second reason is that a survey of positions found in databases showed that such endgames with a pair of blocked pawns represented as much as 50% of practical positions seen in play. A wonderful payoff when you consider that together with the pawnless endgames, they took up only 70 TB of space, while the complete 8-piece tablebases are expected to exceed 700 TB.

Looking at some of the positions and solutions, one is left with a strange feeling. A feeling not of inadequacy, but rather of how astonishingly rich chess is even in its paths to victory. Consider this next position:

 
White to win in 273 moves

If you are told that it is a tablebase win for White, it won't come as a complete shock. White's pawn is on f6, just a couple of squares away from promotion, and is up an exchange as well. You might try to imagine how that win might be converted. Perhaps White must set up a timely sacrifice to free his pawn, while covering its advance. But then you are told that while this may indeed be a win it will take no fewer than 273 moves to reach a clearly winning position. What will inevitably leave readers not a little confused is how that win is reached and what it consists of.

Indeed, the white king will race around the back of the pawns to h6 and then all the way down to f2... 

After a staggering 129 moves to reach this position:

So how does White progress from here? White just needs to... race the king all the way back up via h6, from where it came, and through f8 come back to the queenside where it will end up cornering the king with mate threats and forcibly win the bishop after 273 perfect moves. Obvious! (This is stated entirely tongue-in-cheek).

How easy is that? I enjoin you to replay the solution.

 
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1.Bc7 Bc8 2.Rh5 Ke4 3.Re5+ Kf3 4.Re1 Kg4 5.Kc6 Kf5 6.Rf1+ Ke6 7.Bg3 Bd7+ 8.Kc7 Bb4 9.Rd1 Ba4 10.Rd4 Ba5+ 11.Kb8 Bb3 12.Rd3 Bd5 13.Re3+ Kd7 14.Be5 Bb4 15.Re2 Be6 16.Kb7 Bg4 17.Re3 Bd2 18.Ra3 Bf5 19.Ra4 Bh6 20.Ra2 Bd3 21.Ra1 Bf5 22.Bg3 Be4+ 23.Kb8 Bf8 24.Rd1+ Ke6 25.Re1 Kf5 26.Kc8 Bd3 27.Bh4 Bb4 28.Ra1 Be2 29.Ra2 Bc4 30.Rc2 Bd3 31.Rg2 Ke6 32.Rg3 Bc4 33.Rf3 Ba5 34.Ra3 Bb6 35.Ra4 Bf1 36.Re4+ Kd6 37.Re1 Bh3+ 38.Kb7 Bd4 39.Rd1 Ke5 40.Kc6 Bf5 41.Rd2 Bc3 42.Rf2 Bh3 43.Rc2 Bd4 44.Kc7 Ke6 45.Rc6+ Kf5 46.Kd8 Kg6 47.Ke7 Bf5 48.Rc7 Be6 49.Rc2 Kf5 50.Rg2 Bc5+ 51.Kd8 Bb4 52.Ke8 Bc4 53.Rb2 Ba3 54.Rb1 Bd6 55.Rc1 Bd5 56.Kd7 Ba3 57.Rf1+ Kg4 58.Be1 Bc4 59.Rg1+ Kf5 60.Bc3 Bc5 61.Rh1 Kg6 62.Kc6 Bf8 63.Rh4 Be6 64.Ra4 Bb3 65.Ra8 Bh6 66.Kd6 Bg5 67.Rb8 Bc4 68.Rb4 Be6 69.Rb2 Bf4+ 70.Ke7 Bd5 71.Re2 Bg3 72.Bd4 Bh4 73.Rh2 Bg5 74.Rf2 Bc1 75.Kd6 Bb7 76.Rf1 Bg5 77.Rg1 Kf5 78.Ke7 Bd5 79.Kf8 Bh6+ 80.Kg8 Be6 81.Bc3 Bd5 82.Kh7 Bf4 83.Ra1 Bb3 84.Ra5+ Ke4 85.Kg7 Be6 86.Rb5 Bd5 87.Rb1 Be6 88.Rf1 Bc4 89.Rf2 Be3 90.Rh2 Kd3 91.Be5 Be6 92.Rh1 Bd2 93.Rh4 Be3 94.Bf4 Bd4 95.Rh2 Bd5 96.Bc1 Be6 97.Rg2 Ke4 98.Re2+ Kd3 99.Rh2 Bd5 100.Rh3+ Kc2 101.Bg5 Be6 102.Rg3 Bd5 103.Kh6 Bc3 104.Rh3 Bd4 105.Ra3 Bb2 106.Ra6 Kd3 107.Bf4 Bc4 108.Rb6 Bd4 109.Rd6 Ke4 110.Kg5 Bd5 111.Bc1 Bc4 112.Rd8 Be6 113.Re8 Bc5 114.Rb8 Bd4 115.Rb4 Kd3 116.Ra4 Bd5 117.Ra3+ Ke4 118.Rh3 Bc4 119.Rh4+ Kd5 120.Rh1 Ke4 121.Re1+ Kf3 122.Re8 Bd5 123.Rb8 Ke4 124.Rb4 Kd3 125.Bb2 Be3+ 126.Kg4 Be6+ 127.Kg3 Bc4 128.Ra4 Bd2 129.Kf2 Be3+ 130.Kf3 Bd5+ 131.Kg3 Bc4 132.Ra5 Bd2 133.Rc5 Bb3 134.Kg4 Be6+ 135.Kf3 Bb3 136.Rb5 Bc4 137.Re5 Kc2 138.Bd4 Kd3 139.Bf2 Bc3 140.Re3+ Kc2 141.Bh4 Bd5+ 142.Kg4 Bd4 143.Re8 Kd3 144.Kg5 Be3+ 145.Kf5 Bd4 146.Rd8 Kc4 147.Bg3 Be6+ 148.Kg5 Be3+ 149.Bf4 Bd4 150.Bc1 Bc3 151.Rd1 Bd5 152.Bf4 Bd4 153.Re1 Bc3 154.Re2 Bb4 155.Bc7 Bc6 156.Rc2+ Kd5 157.Ra2 Kc4 158.Be5 Be4 159.Ba1 Kd5 160.Ra8 Bd2+ 161.Kg4 Bb4 162.Rd8+ Bd6 163.Bb2 Ke6 164.Re8+ Kd5 165.Kg5 Bg6 166.Kh6 Bf5 167.Rd8 Kc6 168.Ra8 Be6 169.Ra1 Bc5 170.Kg7 Kd5 171.Re1 Bf2 172.Re2 Bc5 173.Kg8 Kd6 174.Rd2+ Kc6 175.Rd1 Bb4 176.Rd3 Ba5 177.Kf8 Kb5 178.Ke7 Bb4+ 179.Ke8 Bc5 180.Rd2 Kc4 181.Rc2+ Kd5 182.Re2 Kc6 183.Rd2 Bb4 184.Rd3 Ba5 185.Bc3 Bc7 186.Rd2 Bd6 187.Rd1 Ba3 188.Be5 Bc5 189.Bh2 Ba3 190.Bg3 Bb4 191.Bf4 Bc5 192.Rd2 Bc4 193.Be5 Be3 194.Rd1 Kc5 195.Bd6+ Kc6 196.Re1 Bd2 197.Re4 Bd5 198.Re2 Ba5 199.Bf4 Bb4 200.Be3 Bd6 201.Rc2+ Kb5 202.Bd4 Be6 203.Rc1 Bc4 204.Rb1+ Kc6 205.Rb6+ Kc7 206.Be3 Bd5 207.Ra6 Bc4 208.Ra1 Kc6 209.Rc1 Kb5 210.Rb1+ Kc6 211.Rb6+ Kc7 212.Bd4 Bg3 213.Bc5 Be5 214.Ke7 Bd5 215.Rb1 Kc6 216.Rc1 Kb5 217.Be3 Bc4 218.Rd1 Be6 219.Bd4 Bg3 220.Rg1 Bf4 221.Re1 Bd5 222.Be5 Bg5 223.Bh2 Bh6 224.Kd6 Ba2 225.Re5+ Kc4 226.Re2 Bb3 227.Re4+ Kd3 228.Rh4 Bd2 229.Rh3+ Kc2 230.Rf3 Bb4+ 231.Kc6 Be6 232.Re3 Bc4 233.Be5 Bd2 234.Rf3 Bb4 235.Rf4 Kb3 236.Bd4 Bd2 237.Re4 Bb4 238.Ba1 Ba6 239.Re3+ Kc4 240.Re5 Kd3 241.Rd5+ Kc4 242.Rd4+ Kb3 243.Kd5 Bc8 244.Rd3+ Kc2 245.Re3 Bg4 246.Kd4 Bd2 247.Re5 Bc1 248.Rc5+ Kd1 249.Ke4 Bd2 250.Bc3 Bc1 251.Bd4 Be6 252.Kd3 Bg4 253.Be3 Bb2 254.Bf4 Bh3 255.Rh5 Bf1+ 256.Ke4 Kc2 257.Rc5+ Kb3 258.Be5 Ba3 259.Rc3+ Ka4 260.Bd4 Bd6 261.Kd5 Bb4 262.Rc7 Kb3 263.Ba7 Be2 264.Kd4 Bh5 265.Rb7 Ka4 266.Bc5 Ba5 267.Kd3 Bd8 268.Bd4 Bg6+ 269.Kc4 Bh5 270.Bc3 Be2+ 271.Kc5 Bh5 272.Rd7 Kb3 273.Rxd8
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White to win in 273 moves--2022

 

Too many Cooks in the kitchen

In the world of endgame studies, a 'cook' is when an alternate solution is found, or when the desired outcome (win or draw) is proven wrong. In many ways, it is the bane of endgame composers, who attempt to marry mathematical precision with wonder and creativity, forcing them back to the proverbial drawing board.

The advent of tablebases and powerful engines has made this a much more common occurrence when analyzing older compositions, and modern composers work with such tools hand in hand by necessity. 

While Marc Bourzutschky found a number of cooks for studies with eight pieces or that ended in such, one peculiarity stood out because a previous cook... was cooked!

 
Tijdschrift v.d. (1938)
White to play and draw

This fascinating position, with far more than eight pieces, quickly dissolves to a much more manageable situation after 1. d7! d3 2. e2 g4

 
After 2... Rg4

In this position, the solution goes 3. f2!+ followed by a lovely line that ends in stalemate. However, a previous cook had been announced here with 3. h5!? suggesting this also sufficed to save the game. However, after the forcing line 3... xg5 (Marc Bourzutschky) 4. xg5 xd7 5. xa6 (what else?)

 
After 5. Rxa6 (analysis)

Marc notes here, "This position seems to be won for Black. Without the pawns, the 7-man EGTB indicates it would be won, and the presence of the pawns seems to favor Black, if anything."

It isn't over though, since the actual final position is itself completely cooked as well. 

 
The (cooked) solution

The given ending here is the aesthetically pleasing 9... xd8 with a lovely stalemate. The composer deserves our respect and applause for his imagination at the very least. But as to the solution itself, it is sadly cooked. In a persistent moment of blindness, the idea of not capturing the queen was so contrary to instinct that all other moves were not even considered, unless you are consulting an 8-piece tablebase that is. Indeed, both 9... d6! and 9... g3! are winning for Black. 

 
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Marc B: This cook is interesting because it seems to refute a previous cook claim. Instead of the study having an alternative solution, it seems to have no solution at all. Tijdschrift v.d. KNSB/9. U2: Garcia=M HHdbV#66506 24-9-2011. 1.d7 Rd3 2.Ne2 Rg4 3.Rf2+ 3.Kh5! Cook by MarcG: Rg2 3...Rxg5+ 4.Kxg5 Rxd7 5.Rxa6 MarcB: This position seems to be won for Black. Without the pawns, the 7-man EGTB indicates it would be won, and the presence of the pawns seems to favor Black, if anything. For example: Nf3+ 6.Kg4 Rf7 7.Rh6+ Kg2 8.Nf4+ Kf2 9.Nh3+ Ke3 10.Re6+ Kd4 11.a6 Nc5 12.Rb6 Ne5+ 13.Kh5 Rf1 14.Rb4+ 14.a7 Ra1 14...Kc3 15.Rb6 Kc4 16.Kh4 Ra1 17.Kg5 Nxa6-+ 4.Nf4 Rxd7 5.Nxg2 Kxg2 6.Rxa6 3...Rg2 4.Rxg2+ Nxg2 5.Nf3+ Kh3 6.Nfd4 Nxd4 7.Nf4+! Nxf4 8.d8Q Nf5+ 9.Kxh7 Rxd8 The drawn solution attributed is the one claimed for the study, and does not reflect the actual refutations. Cook by MarcB: 9...Rd6-+ Cook by MarcB: 9...Rg3-+ ½–½
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WhiteEloWBlackEloBResYearECOEventRnd
Van den Ende=J-(=0708.22h6h2) U2-½–½1938Tijdschrift v.d. KNSB#211

Conclusion

There is no question that the production of endgame tablebases brings us one step closer to absolute chess truth. The value of the work done thus far by Marc Bourzutschky cannot be understated, and it would be a huge lack of vision to think it of only academic interest even to competitive chess players.

The number of piece-pawn combinations to solve has ballooned with each iteration and he noted in the interview below that each could take days to resolve, even on his 'low-end' workstations with only 1.5 TB of RAM (no, you did not misread), and there are no fewer than 4795 to be exact.

Marc adds, in his original email to ARVES, that while some may be disappointed the record moves to a solution did not break any real ground, representing a modest hop forward, rather than a massive leap, this may be due to the symmetrical situation of even pieces inherent to the division of eight. With nine, we might indeed see solutions in the four digits, and he has already begun exploring this. That said, the full set of eight has yet to be solved, so should you wish to help finish this undertaking and have access to major resources, he is quite open to the prospect. As for now though, work on it has been put on pause.

Video interview with Marc Bourzutschky

Links


Born in the US, he grew up in Paris, France, where he completed his Baccalaureat, and after college moved to Rio de Janeiro, Brazil. He had a peak rating of 2240 FIDE, and was a key designer of Chess Assistant 6. In 2010 he joined the ChessBase family as an editor and writer at ChessBase News. He is also a passionate photographer with work appearing in numerous publications, and the content creator of the YouTube channel, Chess & Tech.

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