Fortresses

[Lyudmil Tsvetkov]

Yacov Murey vs Nigel Short, Brighton 1982.

This foretress is breakable.

[d]5Q2/4nbp1/4pk1p/3p4/3P1P2/2P5/8/2K5 w - - 2 54

https://lichess.org/MoY9bNEX#106

only if black makes some mistakes.

[d]3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - - 0 10

provided this one is a fortress, I don't see how white wins.

is that one a fortress, according to 7-men?

[Nordlandia]

Yacov Murey vs Nigel Short, Brighton 1982.

This foretress is breakable.

[d]5Q2/4nbp1/4pk1p/3p4/3P1P2/2P5/8/2K5 w - - 2 54

https://lichess.org/MoY9bNEX#106

only if black makes some mistakes.

[d]3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - - 0 10

provided this one is a fortress, I don't see how white wins.

is that one a fortress, according to 7-men?

White mates in 101 and captures occures before 50-move rule take effect, so theoretically white can win. Of course no human can do that.

[pgn][Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[SetUp "1"]
[FEN "3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - -"]

1.Qc8+ Kf6 2.Qc3+ Kg6 3.Kd4 Bd7 4.Qa3 Bf5 5.Qe7 Bg4 6.Kc5 Bh3 7.Kc6 Bg4 8.Kc7
Bh3 9.Qe1 Bf5 10.Qh4 Be6 11.Qg3+ Kh7 12.Qh2+ Kg6 13.Qg2+ Kf6 14.Qc6 Ke7 15.
Qc5+ Kf6 16.Qc3+ Kg6 17.Qc6 Kf6 18.Kb6 Ke7 19.Qc5+ Kf6 20.Qc3+ Kg6 21.Qc6 Kf6
22.Kb5 Ke7 23.Qc5+ Kf6 24.Qd4+ Kg6 25.Qb6 Kf6 26.Kb4 Ke7 27.Qc5+ Kf6 28.Qd4+
Kg6 29.Qb6 Kf6 30.Kc3 Ke7 31.Qb4+ Kf6 32.Qd4+ Kg6 33.Qb6 Kf6 34.Kd3 g6 35.f5
Kxf5 36.Qb2 g5 37.Qf2+ Ke5 38.Kc3 Bf5 39.Qd4+ Ke6 40.Kb3 Nd6 41.Kb4 Nf7 42.Kb5
Nd6+ 43.Kb6 Nf7 44.Kc7 Ke7 45.Qb6 Be6 46.Qf2 Kf8 47.Qf6 Bg4 48.Kc6 Bh3 49.Kc5
Bg4 50.Kc4 Bh3 51.Kc3 Bg4 52.Kd2 Bh3 53.Qc6 Bg4 54.Qe4 Bh3 55.Qe3 Bg4 56.Ke1
Kg8 57.Kf2 Bf5 58.Qd4 Bh3 59.Kg3 Bc8 60.Qc4 Bf5 61.Qd5 Bg6 62.Qe6 Bh5 63.Kf2
Kf8 64.Qe4 Kg7 65.Ke3 Bg6 66.Qd4+ Kg8 67.Qf6 Bh5 68.Qf5 Kg7 69.Kd4 Bg6 70.Qf2
Nd6 71.Qf3 Ne4 72.Ke5 Kh7 73.Qh3+ Kg7 74.Ke6 Be8 75.Ke7 Bf7 76.Qh2 Bg6 77.Qb8
g4 78.Qf8+ Kh7 79.Qf4 Kg7 80.Qxg4 Kh6 81.Qh4+ Kg7 82.Ke6 Nc5+ 83.Ke5 Nd7+ 84.
Kd6 Nf8 85.Qe7+ Bf7 86.Qe5+ Kh7 87.Qf6 Kg8 88.Qh6 Nh7 89.Kd7 Nf8+ 90.Ke7 Nh7
91.Qf4 Bg6 92.Qd4 Bh5 93.Qd5+ Kh8 94.Qxh5 Kg7 95.Qf5 Kh6 96.Qg4 Ng5 97.Kf6
Nh7+ 98.Kf5 Ng5 99.Qxg5+ Kh7 100.Kf6 Kh8 101.Qg7# 1-0[/pgn]

[Vinvin]

only if black makes some mistakes.

[d]3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - - 0 10

provided this one is a fortress, I don't see how white wins.

is that one a fortress, according to 7-men?

White mates in 101 : 1.Qc8+

[Nordlandia]

only if black makes some mistakes.

[d]3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - - 0 10

provided this one is a fortress, I don't see how white wins.

is that one a fortress, according to 7-men?

White mates in 101 : 1.Qc8+

The wK and wQ dances (triangulates) on the queenside, how do that force zugzwang?

How does the King maneuver on the queenside force zugzwang on the kingside

[Lyudmil Tsvetkov]

Yacov Murey vs Nigel Short, Brighton 1982.

This foretress is breakable.

[d]5Q2/4nbp1/4pk1p/3p4/3P1P2/2P5/8/2K5 w - - 2 54

https://lichess.org/MoY9bNEX#106

only if black makes some mistakes.

[d]3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - - 0 10

provided this one is a fortress, I don't see how white wins.

is that one a fortress, according to 7-men?

White mates in 101 and captures occures before 50-move rule take effect, so theoretically white can win. Of course no human can do that.

[pgn][Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[SetUp "1"]
[FEN "3Q4/5np1/4k3/5b2/5P2/4K3/8/8 w - -"]

1.Qc8+ Kf6 2.Qc3+ Kg6 3.Kd4 Bd7 4.Qa3 Bf5 5.Qe7 Bg4 6.Kc5 Bh3 7.Kc6 Bg4 8.Kc7
Bh3 9.Qe1 Bf5 10.Qh4 Be6 11.Qg3+ Kh7 12.Qh2+ Kg6 13.Qg2+ Kf6 14.Qc6 Ke7 15.
Qc5+ Kf6 16.Qc3+ Kg6 17.Qc6 Kf6 18.Kb6 Ke7 19.Qc5+ Kf6 20.Qc3+ Kg6 21.Qc6 Kf6
22.Kb5 Ke7 23.Qc5+ Kf6 24.Qd4+ Kg6 25.Qb6 Kf6 26.Kb4 Ke7 27.Qc5+ Kf6 28.Qd4+
Kg6 29.Qb6 Kf6 30.Kc3 Ke7 31.Qb4+ Kf6 32.Qd4+ Kg6 33.Qb6 Kf6 34.Kd3 g6 35.f5
Kxf5 36.Qb2 g5 37.Qf2+ Ke5 38.Kc3 Bf5 39.Qd4+ Ke6 40.Kb3 Nd6 41.Kb4 Nf7 42.Kb5
Nd6+ 43.Kb6 Nf7 44.Kc7 Ke7 45.Qb6 Be6 46.Qf2 Kf8 47.Qf6 Bg4 48.Kc6 Bh3 49.Kc5
Bg4 50.Kc4 Bh3 51.Kc3 Bg4 52.Kd2 Bh3 53.Qc6 Bg4 54.Qe4 Bh3 55.Qe3 Bg4 56.Ke1
Kg8 57.Kf2 Bf5 58.Qd4 Bh3 59.Kg3 Bc8 60.Qc4 Bf5 61.Qd5 Bg6 62.Qe6 Bh5 63.Kf2
Kf8 64.Qe4 Kg7 65.Ke3 Bg6 66.Qd4+ Kg8 67.Qf6 Bh5 68.Qf5 Kg7 69.Kd4 Bg6 70.Qf2
Nd6 71.Qf3 Ne4 72.Ke5 Kh7 73.Qh3+ Kg7 74.Ke6 Be8 75.Ke7 Bf7 76.Qh2 Bg6 77.Qb8
g4 78.Qf8+ Kh7 79.Qf4 Kg7 80.Qxg4 Kh6 81.Qh4+ Kg7 82.Ke6 Nc5+ 83.Ke5 Nd7+ 84.
Kd6 Nf8 85.Qe7+ Bf7 86.Qe5+ Kh7 87.Qf6 Kg8 88.Qh6 Nh7 89.Kd7 Nf8+ 90.Ke7 Nh7
91.Qf4 Bg6 92.Qd4 Bh5 93.Qd5+ Kh8 94.Qxh5 Kg7 95.Qf5 Kh6 96.Qg4 Ng5 97.Kf6
Nh7+ 98.Kf5 Ng5 99.Qxg5+ Kh7 100.Kf6 Kh8 101.Qg7# 1-0[/pgn]

thanks Jon.

interesting, how certain are we of the result?

after all, computers have calculated it, and computers are very much fallible, too.

it looks very much like a fortress to me.

the position I posted was one of many possible, what about the same one, this time with black king on h7 or g6?

sometimes the borderline between draw and win is just one more mobile square of a single piece, just a tiny bit better placed in terms of psqt piece, or maybe a king with location where it is not quite supposed to be.

very very tiny differences. how are humans and even engines able to distinguish between those, deep down the search tree?

in any case, I ran a small shooutout with SF and Komodo, 10 games each, 1 min.

result was: 7 white wins, 13 draws, SF drew almost all.

I still insist the position might be a draw, how reliable might be lichess analysis?

[Vinvin]

...

[d]1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - - 0 1
After 1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 e5
White bishop stays on e1-h4 diagonal so Knight cannot move and it is draw.

SF finds this one after 22m51s (6 cores @4 GHz).
Other moves become worse, so SF finds it by elimination.

Code: Select all

Stockfish_170930_x64_modern:
...
 37/60	03:02	 2 710 980k	14 894k	-10,37	1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6 4.Bc7 g2 5.Rb6+ Ka7 6.Rg6 Ng4 7.Bb6+ Kb7 8.Bg1 f4 9.Rb6+ Kc7 10.e6 dxe6 11.Rxe6 Ng3 12.Re8 Kd6 13.Rf8 Ke5 14.Rb8 f3 15.Rb5+ Ke4 16.Rb4+ Kf5 17.Rb5+ Kf4 18.Be3+ Ke4 19.Rb4+ Kd5 20.Rb5+ Kc4 21.Rc5+ Kd3 22.Rd5+ Ke4 23.Rd4+ Ke5 24.Rb4 Ne2 25.Ba7 Ke6 26.Re4+ Kd6
 38/62+	03:20	 2 985 476k	14 923k	-10,30	1.Rc4
 38/62+	03:33	 3 184 936k	14 931k	-10,22	1.Rc4
 38/62-	03:34	 3 208 169k	14 937k	-10,45	1.Rc4 g2
 38/64-	05:28	 4 963 653k	15 090k	-10,82	1.Rc4 g2
 38/72+	07:13	 6 560 683k	15 138k	-10,62	1.Rxb4
 38/72+	07:25	 6 744 982k	15 144k	-10,23	1.Rxb4
 38/72-	07:44	 7 039 746k	15 151k	-11,11	1.Rxb4 Ka8
 38/83-	12:16	 11 194 460k	15 209k	-11,76	1.Rxb4 Ka8
 38/83	15:00	 13 780 620k	15 304k	-11,83	1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6 4.Bc5 g2 5.Rb6+ Ka5 6.Rg6 Ng4 7.Rg8 f4 8.e6 dxe6 9.Bb6+ Ka6 10.Rd8 Kb7 11.Rd2 f3 12.Rd7+ Kc6 13.Rc7+ Kd6 14.Rc3 Ne5 15.Rc1 h4 16.Rd1+ Kc6 17.Rc1+ Kd5 18.Rd1+ Kc4 19.Rd4+ Kb5 20.Rxh4 Nd3 21.Ba7 Ne1 22.Rb4+ Kxb4
 39/70	15:14	 14 018 065k	15 321k	-11,83	1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6 4.Bc5 g2 5.Rb6+ Ka5 6.Rg6 Ng4 7.Rg8 f4 8.e6 dxe6 9.Bb6+ Ka6 10.Rd8 Kb7 11.Bg1 Kc6 12.Rd4 f3 13.Re4 e5 14.Rc4+ Kd6 15.Rc3 e4 16.Rc8 Ng3 17.Rd8+ Ke6 18.Rg8 Nf5 19.Re8+ Kd5 20.Ra8 h4 21.Ra5+ Kc4 22.Rc5+ Kb4 23.Rxf5 h3 24.Rf4 f2 25.Bxf2 h2
 40/60-	15:43	 14 492 860k	15 357k	-11,91	1.Rxb4 Ka8
 40/60	16:42	 15 434 926k	15 403k	-11,98	1.Rc4 g2 2.Rc1 Nh3 3.Rd1 f4 4.e6 dxe6 5.Rd2 f3 6.Rd3 Ng5 7.Rd8+ Kb7 8.Rg8 Ne4 9.Rg7+ Kc6 10.Re7 Kd6 11.Rf7 Nd2 12.Rh7 Ng3 13.Bc5+ Kc6 14.Re7 Nde4 15.Rxe6+ Kd5 16.Re8 h4 17.Rd8+ Ke5 18.Rh8 Nf5 19.Bg1 Ng5 20.Rh5 Ne6 21.Rh8 Kd5 22.Rh5 Ke4 23.Rh8 Nf4 24.Rb8 Kd5 25.Rxb4
 41/60+	17:12	 15 931 382k	15 433k	-11,85	1.Rxb4
 41/60-	17:13	 15 954 342k	15 435k	-12,05	1.Rxb4 Ka8
 41/60-	17:33	 16 244 506k	15 424k	-12,17	1.Rxb4 Ka8
 41/66+	18:51	 17 454 651k	15 424k	-12,04	1.Rxb4
 41/66+	18:51	 17 455 372k	15 425k	-11,82	1.Rxb4
 41/66-	19:17	 17 867 619k	15 431k	-12,32	1.Rxb4 Ka8
 41/78	19:26	 17 993 841k	15 424k	-12,19	1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6 4.Bc7 g2 5.Rb6+ Ka7 6.Rg6 Ng4 7.Bb6+ Kb7 8.Bg1 f4 9.Rb6+ Kc7 10.e6 dxe6 11.Rxe6 Ng3 12.Re7+ Kd6 13.Rf7 Ke5 14.Rb7 Ke4 15.Re7+ Kf3 16.Rh7 Ke2 17.Rf7 f3 18.Rg7 Ne4 19.Ba7 Nef6 20.Re7+ Kd3 21.Rb7 h4 22.Rxb3+ Ke2 23.Rc3 f2 24.Kxa2 f1Q 25.Rc2+ Kf3 26.Rc3+ Kf4 27.Bc5 g1Q 28.Bxg1 Qxg1 29.b3
 42/62-	19:35	 18 127 363k	15 424k	-12,27	1.Rxb4 Ka8
 42/65+	20:03	 18 557 450k	15 420k	-12,19	1.Rxb4
 42/67+	20:03	 18 559 679k	15 420k	-11,92	1.Rxb4
 42/76	20:16	 18 769 366k	15 424k	-12,34	1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6 4.Bc5 g2 5.Rb6+ Ka5 6.Rg6 Ng4 7.Rg8 f4 8.e6 dxe6 9.Rd8 Kb5 10.Bg1 Kc6 11.Rd4 f3 12.Rc4+ Kd6 13.Rf4 Ne5 14.Rd4+ Kc6 15.Re4 Nd3 16.Rxe6+ Kd5 17.Re3 Ne5 18.Rxb3 h4 19.Rb5+ Ke6 20.Bd4 Nc6 21.Rb6 Kd5 22.Be3 f2 23.Bxf2 Nxf2 24.Rb5+ Ke6 25.Rg5 h3 26.Kxa2 h2 27.Rxg2 h1Q 28.Rg7 Nb4+ 29.Kb3
 43/64-	20:48	 19 272 043k	15 439k	-12,41	1.Rxb4 Ka8
 43/64+	22:51	 21 217 964k	15 471k	-12,30	1.Rxh1
 43/64+	22:51	 21 218 086k	15 471k	-12,18	1.Rxh1
 43/64	22:51	 21 218 359k	15 471k	-12,22	1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 Kc6 5.Bh4 f4 6.Be1 f3 7.Bf2 Kd6 8.Be1 Kd7 9.Bh4 e5 10.Be1 Kc6 11.Bf2 Kd5 12.Bh4 e4 13.Bg3 Kd4 14.Bh4 Kc5 15.Be1 Kc4 16.Bf2 e3 17.Bg3 Kd4 18.Bf2 Ke4 19.Bg3 e2 20.Bf2 Ke5 21.Bh4 Kd5 22.Bf2 Ke4 23.Be1 Kd4 24.Bg3 Ke3 25.Bh4 Kd2 26.Bf2 Kd3 27.Bg3
 44/40+	22:51	 21 218 785k	15 471k	-12,14	1.Rxh1
 44/47+	22:51	 21 220 467k	15 472k	-12,06	1.Rxh1
 44/55	22:51	 21 221 034k	15 472k	-12,04	1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 Kc6 5.Bh4 f4 6.Be1 f3 7.Bf2 Kb7 8.Bh4 Ka8 9.Be1 Kb8 10.Bf2 Kc8 11.Bg3 Kd7 12.Bh4 e5 13.Be1 Kc7 14.Bh4 Kd6 15.Bg3 Kc5 16.Be1 Kd5 17.Bf2 e4 18.Bg3 e3 19.Bh4 Ke4 20.Bg3 e2 21.Bf2 Ke5 22.Bh4 Kd4 23.Be1 Kd3 24.Bf2 Ke4 25.Be1 Kd4 26.Bg3 Ke3 27.Bh4 Kd2 28.Bf2
 45/48-	22:51	 21 222 244k	15 472k	-12,12	1.Rxh1 Nxh1
 45/48-	22:51	 21 222 389k	15 471k	-12,19	1.Rxh1 Nxh1
 45/48-	22:51	 21 222 837k	15 471k	-12,30	1.Rxh1 Nxh1
 45/48+	22:51	 21 222 967k	15 471k	-12,21	1.Rxh1
 45/55	22:51	 21 223 721k	15 471k	-12,20	1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 Kc6 5.Bh4 f4 6.Be1 f3 7.Bf2 Kb5 8.Bh4 Kc4 9.Bf2 e5 10.Bh4 Kc5 11.Be1 Kc6 12.Bf2 e4 13.Bh4 Kb5 14.Bg3 Kc4 15.Bf2 e3 16.Bg3 Kd5 17.Bf2 Ke5 18.Bg3+ Ke4 19.Bf2 Kd5 20.Bh4 Kd4 21.Bf2 Ke4 22.Bg3 Kd3 23.Be1 e2 24.Bf2 Ke4 25.Be1 Ke3 26.Bh4 Kd2 27.Bf2
 46/53-	22:55	 21 283 098k	15 474k	-12,27	1.Rxh1 Nxh1
 46/53+	22:55	 21 283 308k	15 474k	-12,20	1.Rxh1
 46/64+	22:55	 21 286 505k	15 474k	-11,71	1.Rxh1
 46/64	22:55	 21 288 921k	15 474k	-11,70	1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 Kc6 5.Bh4 f4 6.Be1 f3 7.Bf2 Kd6 8.Be1 Kd5 9.Bh4 Kc5 10.Be1 Kc4 11.Bg3 e5 12.Bf2 Kd5 13.Bh4 Kc5 14.Bf2+ Kc6 15.Bh4 Kd6 16.Bf2 Ke6 17.Bg3 e4 18.Be1 Kd5 19.Bg3 e3 20.Bf2 Ke4 21.Bg3 Kd4 22.Bf2 Kd3 23.Be1 Kc4 24.Bg3 Kb5 25.Bf2 Kc6 26.Bh4 e2 27.Be1 Kd5 28.Bf2 Kc6
 47/69-	23:03	 21 414 283k	15 476k	-11,77	1.Rxh1 Nxh1
 47/69+	23:03	 21 416 164k	15 476k	-11,70	1.Rxh1
 47/69-	23:06	 21 451 730k	15 477k	-11,85	1.Rxh1 Nxh1
 47/69-	23:07	 21 480 003k	15 476k	-12,01	1.Rxh1 Nxh1
 47/69+	23:07	 21 480 166k	15 476k	-11,86	1.Rxh1
 47/69+	23:08	 21 484 463k	15 476k	-11,57	1.Rxh1
 47/71	23:08	 21 488 599k	15 476k	-11,55	1.Rxh1 Nxh1 2.e6 dxe6 3.Bc7+ Kb7 4.Bxg3 Kc6 5.Bh4 Kb5 6.Bg3 Kc4 7.Bf2 f4 8.Bh4 f3 9.Be1 Kd4 10.Bf2+ Kd5 11.Bh4 Kc5 12.Be1 Kb6 13.Bh4 Kb7 14.Be1 Kc8 15.Bh4 e5 16.Bf2 Kc7 17.Bg3 Kc6 18.Bf2 Kb5 19.Be1 e4 20.Bf2 e3 21.Be1 Kc4 22.Bg3 Kd3 23.Bf2 e2 24.Bg3 Ke3 25.Bh4 Kf4 26.Be1 Ke4 27.Bf2 Ke5 28.Bg3+ Kf5 29.Be1 Kf4 30.Bf2 Ke4 31.Be1 Kd4 32.Bg3

[Nordlandia]

Schlechter-Walbrodt, Vienna 1898

At first Sight, the position seems even more favourable for White.

But can white breakthrough?

[d]8/1p1b4/pPp2k2/P1PpN2p/3P1K1P/8/8/8 b - - 0 59

[d]8/8/8/1p1k1p2/pPn2Pp1/P2K2P1/8/2B5 b - - 0 1

[d]8/p2bk3/2p3p1/1pP1K1Pp/1P1N4/P7/7P/8 w - - 0 0