Penrose Puzzle

[peter]

Thanks, Jon!

But for the new version Arpad's puzzle isn't easy neither:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

Analysis by Stockfish MateFinder 64:

1.Kb1 Bd4 2.Kc2 Bc3 3.Kb1 Bc7 4.Kc2 B7e5 5.Kd1 Bd6 6.Ke2 Bf4 7.Kd1 Bce5 8.Kc2 Bd4 9.Kd1 Bfe5 10.Ke2 Bh2 11.Kd1 Be3 12.Kc2 Bd6 13.Kb2 Bd2 14.Kc2 B2f4 15.Kd1 Bf8 16.Ke2 Bh6 17.Ke1 Bg7 18.Kd1 Ba1 19.Ke1 Bd6 20.Ke2 Bh2 21.Ke3 Bb2 22.Ke2 Bhe5 23.Kf2 Bd6 24.Ke2 Bg3 25.Kd3 Bc7 26.Kd2 Bf6 27.Kc1 Bg7 28.Kd2 Bd6
-+ (-9.74) Depth: 56/56 00:05:03 10698MN

That's default and without tbs at 24 threads, will give it another try with Study Mode on and full Syzygys, but I don't think less LMR would help in this position, nor would tbs.

Sting

http://www.talkchess.com/forum/viewtopi ... 34&t=63438

and komodo with turned off nullmove pruning do succeed:

8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

Analysis by Komodo 10.4 64-bit:
...
1.Kb1 Bd6 2.Kc2 Bh2 3.Kd2 Bhg3 4.Ke2 Bgf4 5.Kf3 Bh2 6.Ke2 Bhg3 7.Ke3 Bge5 8.Kd3 Bd4 9.Ke2 Bf4 10.Kd3 Bde5 11.Kc2 Bd6 12.Kd3 Bfe5 13.Kc2 Bg3 14.Kd3
-+ (-10.49) Depth: 27 00:00:19 290MN
1.d6 Bxd6 2.e5
-+ (-10.42 ++) Depth: 27 00:00:20 301MN
...
1.d6 Bxd6 2.e5
-+ (-1.91 ++) Depth: 28 00:00:50 847MN
1.d6 Bxd6 2.e5
= (0.21 ++) Depth: 28 00:00:55 903MN
1.d6 Bxd6 2.e5
+- (3.17 ++) Depth: 28 00:00:58 942MN
...
1.d6 Bxd6 2.e5 Bc7 3.Kb2 Bg3 4.Kc2 Bb8 5.Kd3 Bf4 6.e6 Bfd6 7.e7 Bxe7 8.Ke4 Bd8 9.Kd5 Bdc7 10.Ke6 Bd8 11.Kd7 Bbc7 12.b8Q Bxb8 13.c7 Bbxc7 14.Kc6 Bb8 15.cxb5#
+- (#15) Depth: 29 00:01:18 1187MN
1.d6 Bxd6 2.e5 Bc7 3.Kb1 Bh2 4.Kc2 Bb8 5.Kd3 Bhxe5 6.Ke4 Bh2 7.Kd5 Bbc7 8.Ke6 Bhe5 9.Kd7 Bf6 10.b8Q Bxb8 11.c7 Kb7 12.c8Q+ Ka8 13.Qc6#
+- (#13) Depth: 30 00:01:19 1212MN
...
1.d6 Bxd6 2.e5 Bc7 3.Kb1 Bh2 4.Kc2 Bb8 5.Kd3 Bhxe5 6.Ke4 Bh2 7.Kd5 Bbc7 8.Ke6 Bhe5 9.Kd7 Bf6 10.b8Q Bxb8 11.c7 Kb7 12.c8Q+ Ka8 13.Qc6#
+- (#13) Depth: 99 00:02:02 2818MN

[peter]

and komodo with turned off nullmove pruning do succeed:

Here's komodo default at 22 threads (NM off before was with 24)

8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

Analysis by Komodo 10.4 64-bit:
...
1.Kb1 Ld6 2.Kc2 Lfe5 3.Kd2 Lc3+ 4.Kd3 Lg7 5.Kc2 Ld4 6.Kd3 Lf6 7.Ke2 Lb2 8.Kd3 Lh8 9.Kc2 Lf6 10.Kd3 Lc3 11.Ke3 Lg7 12.Kd3 Ld4 13.Ke2 Lh8 14.Kd2 Lc7 15.Ke2 Lc3
-+ (-11.37) Tiefe: 29 00:00:34 533MN
1.d6 Lxd6 2.e5
-+ (-10.46 ++) Tiefe: 29 00:00:34 533MN
...
1.d6 Lxd6 2.e5 Lfxe5 3.Kb1 Lc3 4.Kc2 Lf6 5.Kd3 Lf4 6.Ke4 Le7 7.Kd5 Led6 8.Ke6 Lb8 9.Kd7 Lfc7 10.Ke6 Lf4
= (0.00) Tiefe: 31 00:00:35 554MN
...
1.d6 Lxd6 2.e5 Lfxe5 3.Kb1 Lc7 4.Kc1 Lc3 5.Kc2 Lg7 6.Kd3 Lb2 7.Ke3 Lc3 8.Kd3 Lf6 9.Ke3 Lfe5 10.Ke4 Lcd6 11.Kd5 Lb8 12.Ke6 Lf4 13.Kd7 Lfc7 14.Ke6 Le5 15.Kd7 Lec7
= (0.00) Tiefe: 53 00:02:02 1581MN
1.d6 Lxd6 2.e5
= (0.06 ++) Tiefe: 54 00:04:21 3310MN
1.d6 Lxd6 2.e5
= (0.14 ++) Tiefe: 54 00:06:49 5611MN
1.d6 Lxd6 2.e5
= (0.25 ++) Tiefe: 54 00:08:23 7033MN
1.d6 Lxd6 2.e5
+/= (0.40 ++) Tiefe: 54 00:10:51 9276MN
1.d6 Lxd6 2.e5
+/= (0.61 ++) Tiefe: 54 00:13:29 11517MN

Stopped, best move found, Eval's raising

[mjlef]

Another link getting this very wrong:

http://interestingengineering.com/can-y ... ware-cant/

It mentions the 1997 Beep Blue match with Kasparov, then in the next paragraph says:

"Komodo, a chess engine with an Elo rating of 3304 (450 points higher than Kasparov) was next in line to prove that computers are far superior when it comes to head to head chess matches."

It totally skips a bunch of computer-human results. It also mentions this:

"This is partially due to Moore’s Law, which states that the number of transistors per square inch on integrated circuit board doubles year on year, allowing for greater computational power. This statement was originally made by Intel co-founder Gordon Moore in 1965 and holds up today."

Of course, most of the advancement in chess program strength is due to better software. Hardware is much less of a factor and in fact, Moore's Law keeps getting "amended" since it simply does not hold true now. Computers are just not getting faster very quickly.

Mark

[IanO]

I have modified the original position:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

Awesome! Even better than I was expecting!

[Arpad Rusz]

Another related position:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/3p4/1p3k2/1Pp3p1/BRP1B1P1/KPp3P1/Pp4B1/8 w - - 0 1

Draw

The solution is the following:

1. Bb1! (Thematic try: 1. Bf5? Ke5 2. Bge4 Kd4 3. Bb1 Ke3 4. Bh7 (There is no time to capture the pawn: 4. Bxd7 Kd2 5. Bdf5 c2! 6. Bfxc2 Kc3 7. Bf5 cxb4#) 4... Kd2 5. Bhc2 d6! mutual zugzwang 6. Bf5 c2! 7. Bfxc2 Kc3 8. Bf5 cxb4#) 1... Ke5 2. Bc6!! Kd4 3. Bxd7 Ke3 4. Bdf5 Kd2 5. Bfc2! mutual zugzwang =

[Sergei S. Markoff]

The real question isn't "Which strong engine can solve this", but rather, "Which strong engine can't solve this.

Simple inspection of the pv will show you that the big three all solve this problem immediately.

We could go so far as to argue that the evals are also correct, because there is a huge material advantage.

If the white side were to do something so foolish as to capture one of the rooks with a pawn, he would lose immediately.

Some numbers from one of my lections on this topic:



All slides: http://nooscope.ru/files/ai_more_pictures.pptx (sorry, only Russian, but you can see a lot of pictures here).

[MikeB]

I have modified the original position:

8
7
6
5
4
3
2
1
	a	b	c	d	e	f	g	h

8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1

White wins!

Code: Select all

McBrain v2.1a
so name threads value 12
so name hash value 8192
so name tactical value 8
so name NullMove value 0 
p f 8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1
....    
info depth 34 seldepth 41 multipv 1 score cp -986 nodes 3114611843 nps 27300561 hashfull 793 tbhits 0 time 114086 pv a2b1 e5h8 b1c2 h8c3 c2b1 c3g7 b1c2 g7d4 c2b1 d4c3 b1a2 f4d6 a2b1 d6c7 b1c2 c7h2 c2d3 h2e5 d3c2 e5b8 c2d1 c3e5 d1c1 e5d6 c1d2 d6g3 d2c1 g3h2 c1c2 b8g3 c2c1 g3e5 c1d2 e5a1 d2c1
info depth 35 seldepth 41 multipv 1 score mate 15 nodes 4884094468 nps 28419691 hashfull 926 tbhits 0 time 171856 pv d5d6 e5d6 e4e5 d6c7 a2b2 f4h2 b2c2 c7b8 c2d3 b8c7 e5e6 h2d6 e6e7 d6e7 d3e4 e7f8 e4d5 f8g7 d5e6 g7a1 e6d7 a1b2 b7b8n c7b8 c6c7 b8c7 d7c6 c7e5 c4b5
....
info depth 36 seldepth 45 multipv 1 score mate 13 nodes 7627066389 nps 29050732 hashfull 984 tbhits 0 time 262543 pv d5d6 e5d6 e4e5 f4g3 a2b1 d6c7 b1c2 c7b8 c2d3 g3h2 d3e4 b8c7 e4d5 h2f4 d5e6 f4e3 e6d7 e3d4 b7b8n c7b8 c6c7 b8c7 d7c6 d4e5 c4b5

[MikeB]

with tablebases, find the move d6 and mate score even faster

Code: Select all

McBrain 2.1a 64 POPCNT by M. Byrne, based on Stockfish
so name threads value 12
so name hash value 8192
so name tactical value 8
so name NullMove value 0  
so name SyzygyPath value /applications/tablebases
info string Found 510 tablebases
p f 8/pP6/kpP3p1/brpPb1p1/1pP1PbP1/1P6/K5P1/8 w - - 0 1
info depth 29 seldepth 46 multipv 1 score cp -982 nodes 441014090 nps 25725607 hashfull 132 tbhits 399 time 17143 pv d5d6 e5d6 e4e5 d6e5 a2b1 e5d4 b1c2 f4e5 c2d3 e5b8 d3e4 d4e5 e4d5 e5c7 d5e4 c7d6 e4d5 d6f4 d5e4 f4c1 e4d5 b8f4 d5e4 f4d6 e4d5 d6g3 d5e4 g3f4 e4d5 f4c7 d5e4 c1a3 e4d5 c7g3 b7b8r g3b8 c6c7 a6b7 c7b8q b7b8 d5e6
...
info depth 30 seldepth 49 multipv 1 score cp 10 nodes 766465503 nps 26565420 hashfull 268 tbhits 1376 time 28852 pv d5d6 e5d6 e4e5 d6e5 a2b1 e5d4 b1c2 d4g7 c2d3 f4h2 d3e4 g7d4 e4d3 d4g7
...
info depth 31 seldepth 49 multipv 1 score mate 15 nodes 1257741841 nps 26792387 hashfull 505 tbhits 11257 time 46944 pv d5d6 e5d6 e4e5 d6b8 a2b2 f4g3 e5e6 g3d6 e6e7 d6e7 b2c2 e7d6 c2d3 b8c7 d3e4 d6f4 e4d5 f4c1 d5e6 c1a3 e6d7 a3b2 b7b8n c7b8 c6c7 b8c7 d7c6 c7d6 c4b5
...
although the mate in 13 took about the same