7 steps to heaven. 7 testpositions of variable difficulty!

[peter]

Wow, George, that looks ingenious!

Do you know, what my greatest mistake was?
To think, I'd already know all the studies unsolvable for engines.

I did look at 1.Rxh1 only very shortly, not seeing the main variant with more than the first few moves underestimating the chances and missing the point, then always tried other first moves, which need some length of variants still to proof them wrong.
Thanks a lot for the very fine position.
Would you yet tell about the origin, please

[peter]

And you know what?
I could have solved this easily, using the engines in the right way.

This is, what Houdini shows as its output after a few minutes computing 12 variants MV mode on 12 cores, I just copied the first three best moves only:

1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - - 0 1

Analysis by Houdini 3 Pro x640:

1. -+ (-6.48): 1.Txb4 Ka8 2.Ta4+ Kb7 3.Tb4 Ka6 4.Lc7 g2 5.Tb6+ Ka7 6.Tg6 Sg4 7.Lb6+ Ka6 8.Lg1+ Kb5 9.e6 dxe6 10.Txe6 h4 11.Tb6+ Kc4 12.Td6 Sg3 13.Td4+ Kb5 14.Td3 Se2 15.Td5+ Kc6 16.Tc5+ Kb7 17.Txf5 h3 18.Tb5+ Ka6 19.Tb6+ Ka5 20.Tb8 Sf6 21.Lb6+ Ka6 22.Lg1 Sd5 23.Th8 Sxg1 24.Txh3 Se2 25.Th6+ Kb5 26.Tb6+ Kc4 27.Tb4+ Kd3 28.Td4+ Ke3 29.Te4+ Kf3 30.Te3+ Kf4 31.Te4+ Kg3 32.Tg4+ Kh2 33.Txg2+
2. -+ (-7.42): 1.Tc4 g2 2.Tc1 Sh3 3.Te1 h4 4.Td1 Kb7 5.Lg1 Kc7 6.Tc1+ Kd8 7.e6 dxe6 8.Lb6+ Ke7 9.Tc7+ Kf6 10.Th7 Ke5 11.Txh4 Sf4 12.Th7 Sg3 13.La7 Sge2 14.Tg7 Ke4 15.Tb7 Sd3 16.Tg7 Kf3
3. -+ (-11.05): 1.Txh1 Sxh1 2.e6 dxe6 3.Lc7+ Kb7 4.Lxg3 Kc6 5.Lh4 f4 6.Lg3 f3 7.Le1 e5 8.Lf2 e4 9.Le1 e3 10.Lf2 e2 11.Le1 Kd5 12.Lh4 Kc4 13.Lf2 Kd3 14.Le1 Kc2 15.Lg3 Kd2 16.Le1+ Kd3 17.Lf2 Kc4 18.Le1 Kd4 19.Lf2+ Ke4 20.Le1 Kd3 21.Lf2
...
...

So I simply should have taken the third best variant for real and watch the change of the evals over the moves in forward and backward analysis compared to the other variants.
Of course, the numeric evals all are bogus, but the ones of the solution's variant would have been the only one staying the same for many moves, going up finally, while all the others went worse and worse.

At least I would have seen the point by myself anyway anytime.

Typical beginner's mistake using engines for analysis, and that to an old stager, maybe getting too old now.

[Eelco de Groot]

You probably can''t always rely on the evals going further down or up even if it is clearly winning or losing. That probably depends on the amount of extensions that is going on in the PV and the assumptions the program makes there (and what depth is stored in the PV). For instance, if you do a lot of extensions there, I don't have Houdini myself and not really studied the one Richard re-engineered because I consider that a pirated version but I suspect Houdini 2/3/Strelka 5 etc. is also doing a lot of extensions in the PV. If on a next iteration then the PV is not evaluated differently from the previous line, the program is likely to find (in the hashtable) one of these nodes in the PV that already has sufficient depth for this iteration. It may depend on the program but most programs will not extend further than they have to for depth to be equal to iteration minus distance to the root, not counting any extensions they might encounter going further down (or up, if you like) the branches towards the leaves. If they don't do that, the risk of a search explosion is going up a lot.

(Edit: Well, this is not correct I suppose, if the program does not store the extensions done in a node as added depth for this node, my reasoning is not very accurate, and normally that added depth is not stored, by programs like Stockfish, Fruit and family, Crafty etc. So I am not exactly sure how this works...)

For instance my not so good Stockfish clone only considers Rxb4 and the eval does not clearly go down at the end either:


1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - -

Engine: Stockfish 2.3.1 Hybrid (256 MB)
by Tord Romstad, Marco Costalba and Joona Kiiski

29/77 44:58 -7.67 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd6 6.Rc1 f4 7.Bxf2 Kxe6
8.Bg1 Ng3 9.Re1+ Kf5 10.Rd1 h4
11.Rxd7 Ne2 12.Bf2 h3 13.Rh7 Kg4
14.Bb6 (1.545.352.532) 572

30/77 54:17 -6.34 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd6 6.Bc5+ Kd5 7.Rc1 dxe6
8.Bxf2 f4 9.Rc5+ Ke4 10.Rxh5 e5
11.Rg5 Ng3 12.Bg1 Kd5 13.Bf2 Ke6
14.Rg6+ (1.925.087.816) 590

31/79 80:51 -7.03 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Bxf2 f4
8.Bg1 Kf5 9.Rd1 h4 10.Rxd7 Ng3
11.Rg7 h3 12.Rh7 Kg4 13.Rg7+ Kf5 (3.053.088.190) 629

32/79 98:53 -7.03 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Bxf2 f4
8.Bg1 Kf5 9.Rd1 h4 10.Rxd7 Ng3
11.Rg7 h3 12.Rh7 Kg4 13.Rg7+ (3.798.428.255) 640

33/79 134:35 -7.03 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Bxf2 f4
8.Bg1 Kf5 9.Rd1 h4 10.Rxd7 Ng3
11.Rg7 h3 12.Rh7 Kg4 13.Rg7+ Kf5 (5.296.428.295) 655

best move: Rh4xb4 time: 322:00.172 min n/s: 655.830 nodes: 5.296.428.295

Thanks everybody for the comments on the analysis by Stockfish Hybrid. The program is clearly not functioning very well here and it has to be something in the search but at the moment I have not much of an idea where exactly, but all the comments are very welcome!

Eelco

[Eelco de Groot]

(Re-edit: Well, this is not totally correct I suppose, if the program does not store the extensions done in a node as added depth for this node, my reasoning is not very accurate, and normally that added depth is not stored, by programs like Stockfish, Fruit and family, Crafty etc. But because of an extension, search is now called with a larger depth for a child node and in the child node a larger depth does get stored. So with this mechanism, it still works the way I described, when next time the extension is smaller or in a transposition the extension is smaller.

[George Tsavdaris]

For instance my not so good Stockfish clone only considers Rxb4 and the eval does not clearly go down at the end either:

1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - -

Engine: Stockfish 2.3.1 Hybrid (256 MB)
by Tord Romstad, Marco Costalba and Joona Kiiski


33/79 134:35 -7.03 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Bxf2 f4
8.Bg1 Kf5 9.Rd1 h4 10.Rxd7 Ng3
11.Rg7 h3 12.Rh7 Kg4 13.Rg7+ Kf5 (5.296.428.295) 655

best move: Rh4xb4 time: 322:00.172 min n/s: 655.830 nodes: 5.296.428.295

Thanks everybody for the comments on the analysis by Stockfish Hybrid. The program is clearly not functioning very well here and it has to be something in the search but at the moment I have not much of an idea where exactly, but all the comments are very welcome!

After (the line in its PV) 1.Rxb4? Ka8 2.Ra4+ Kb7 3.Rb4, Stockfish 2.3.1 Hybrid considers 3...Kc6?.
[d]8/3p4/1Bk5/4Pp1p/1R6/1p4p1/pP3n2/K6n w - - 0 4

A bad move and then black enters a very difficult position to win since after(which is the best continuation for both and also shown in the PV):
4.e6 g2 white has a crucial check to give 5.Rc4+
[d]8/3p4/1Bk1P3/5p1p/2R5/1p6/pP3np1/K6n b - - 0 5

That must save the position i think.
So it's no wonder Stockfish Hybrid doesn't have a fail low, since after 3...Kc6 it must be a draw.

But had black played his 3rd move correctly, i.e instead of what Stockfish Hybrid suggest 3...Kc6?, to play 3...Ka6! now white is lost since after e.g:
4.e6 g2 white doesn't have the time to defend the promotion square and loses.

After 3...Ka6 the best defense i guess is 4.Be3! and then after 4...g2 5.Rb6+ Ka6 6.Rg6 Ng4 7.Bb6+ Kb5 and now:
- 8.Bg1 f4 and it's over.
- 8.Ba7 h4 9.e6! dxe6 10.Rxe6 h3 11.Bg1 Nhf2 12.Re7 and now the win is easy with many ways e.g the most elegant 12...h2

[lech]

Avoid 1.Bxc7? that loses as also all other moves that lose too and play 1.c6! that draws.
[d]8/p1pp3p/8/2P5/5B2/p2K4/7P/1k6 w - - 0 1

1.Bxh7! wins! Classic Bxh7 sacrifice, but here the win is more difficult than the classic ones.
[d]r1bq1rk1/1p1nbppp/p3p3/2ppP3/5B1P/2PBP3/PP1N1PP1/R2QK2R w KQ - 0 1

The two positions are dedicated for engines (or for Peter) ?

[zullil]

With the removal of the wrong WAC.230 ...b2 position and the addition of this, as i understand computers are only be capable of solving the first 2(the easy ones) of the 7. That's unfortunate and i hope to see someday a program to solve 2-3 of these 5 tough ones....

My testing Sting SF 3 (bred on Stockfish 2.1.1 - modified null move search) gets it in 50 minutes (2 threads 1056M hash).
[d]1b6/3kB3/8/1KpPp2p/4Pp1P/5P2/8/8 w - - 0 1 bm Bf8;

Code: Select all

info depth 55 seldepth 63 multipv 1 score cp 177 nodes 1295351015 nps 1205485 ti
me 1074547 pv e7c5 b8c7 c5b6 c7b8 b5c4 b8d6 b6f2 d6c7 c4b4 d7d6 f2c5 d6d7 c5g1 c
7d6 b4c4 d6e7 g1f2 e7d6 f2c5 d6c7 d5d6 c7a5 c5b4 a5b6 c4d5 b6d4 b4d2 d4b2 d5c5 b
2d4 c5d5
info depth 56
info currmove e7c5 currmovenumber 1
info nodes 1693686623 nps 1191569 time 1421391
info currmove b5c5 currmovenumber 2
info currmove d5d6 currmovenumber 3
info nodes 1751065480 nps 1192722 time 1468125
info currmove b5c4 currmovenumber 4
info currmove e7d8 currmovenumber 5
info currmove e7g5 currmovenumber 6
info nodes 1752196588 nps 1192578 time 1469250
info currmove e7f6 currmovenumber 7
info nodes 1764634282 nps 1191854 time 1480578
info currmove b5b6 currmovenumber 8
info currmove e7d6 currmovenumber 9
info currmove e7f8 currmovenumber 10
info depth 56 seldepth 0 multipv 1 score cp 185 lowerbound nodes 3627347184 nps
1189172 time 3050313 pv e7f8 b8c7 b5c5 c7d8 f8g7 d8h4 g7e5 h4f2 c5c4 h5h4 c4d3 f
2e3 d3e2 h4h3 e2f1 d7d8 e5d6
info nodes 3627347184 nps 1189172 time 3050313
info currmove e7f8 currmovenumber 1

Critter-1.6a (8 threads, 8GB hash) gets this in about 5 minutes:

Code: Select all

33/78+ 05:01    3267M  10827K  +1.28 Bf8 Bc7 Kxc5 Bd8 Bg7 Bxh4 Bxe5 Bf2+ Kc4 h4 Kd3 Be3 Ke2 h3 Kf1 Kc8 Bc3 Bb6 e5 Kd7 Bd2 Be3 e6+ Kd6 Bb4+ Kc7 Ba3 Bd4 Bf8 Bh8 Kg1 Kd8 Kh2
33/78+ 07:15    4712M  10825K  +1.41 Bf8 Bc7 Kxc5 Bd8 Bg7 Bxh4 Bxe5 Bf2+ Kc4 h4 Kd3 Be3 Ke2 h3 Kf1 Kc8 Bc3 Bb6 e5 Kd7 Bd2 Be3 e6+ Kd6 Bb4+ Kc7 Ba3 Kd8 d6 Ke8 d7+ Kd8 Bd6 Bd4 Bxf4 Bf6 Kf2 Be7 Bh2 Bh4+ Kg1 Ke7 Bc7 Kxe6 d8=Q Bxd8 Bxd8 Kf5 Bh4 Kf4 Kf2

[zullil]

With the removal of the wrong WAC.230 ...b2 position and the addition of this, as i understand computers are only be capable of solving the first 2(the easy ones) of the 7. That's unfortunate and i hope to see someday a program to solve 2-3 of these 5 tough ones....

My testing Sting SF 3 (bred on Stockfish 2.1.1 - modified null move search) gets it in 50 minutes (2 threads 1056M hash).
[d]1b6/3kB3/8/1KpPp2p/4Pp1P/5P2/8/8 w - - 0 1 bm Bf8;

Code: Select all

info depth 55 seldepth 63 multipv 1 score cp 177 nodes 1295351015 nps 1205485 ti
me 1074547 pv e7c5 b8c7 c5b6 c7b8 b5c4 b8d6 b6f2 d6c7 c4b4 d7d6 f2c5 d6d7 c5g1 c
7d6 b4c4 d6e7 g1f2 e7d6 f2c5 d6c7 d5d6 c7a5 c5b4 a5b6 c4d5 b6d4 b4d2 d4b2 d5c5 b
2d4 c5d5
info depth 56
info currmove e7c5 currmovenumber 1
info nodes 1693686623 nps 1191569 time 1421391
info currmove b5c5 currmovenumber 2
info currmove d5d6 currmovenumber 3
info nodes 1751065480 nps 1192722 time 1468125
info currmove b5c4 currmovenumber 4
info currmove e7d8 currmovenumber 5
info currmove e7g5 currmovenumber 6
info nodes 1752196588 nps 1192578 time 1469250
info currmove e7f6 currmovenumber 7
info nodes 1764634282 nps 1191854 time 1480578
info currmove b5b6 currmovenumber 8
info currmove e7d6 currmovenumber 9
info currmove e7f8 currmovenumber 10
info depth 56 seldepth 0 multipv 1 score cp 185 lowerbound nodes 3627347184 nps
1189172 time 3050313 pv e7f8 b8c7 b5c5 c7d8 f8g7 d8h4 g7e5 h4f2 c5c4 h5h4 c4d3 f
2e3 d3e2 h4h3 e2f1 d7d8 e5d6
info nodes 3627347184 nps 1189172 time 3050313
info currmove e7f8 currmovenumber 1

Stockfish gets this in less than 4 minutes (8 threads, 8GB hash):

Code: Select all

info depth 52 seldepth 80 score cp 161 lowerbound nodes 1568059696 nps 7002392 time 223932 multipv 1 pv e7f8 b8c7 b5c5 c7d8 f8g7 d8h4 g7e5 h4g3 e5d4 h5h4 e4e5 h4h3 e5e6 d7e7 c5c6 h3h2 d4c5 e7f6 e6e7 h2h1q e7e8q h1f3 e8e6 f6g7 c5d4 g7f8 e6c8 f8f7 c8f5 f7e7 d4c5

[George Tsavdaris]

Avoid 1.Bxc7? that loses as also all other moves that lose too and play 1.c6! that draws.
[d]8/p1pp3p/8/2P5/5B2/p2K4/7P/1k6 w - - 0 1

1.Bxh7! wins! Classic Bxh7 sacrifice, but here the win is more difficult than the classic ones.
[d]r1bq1rk1/1p1nbppp/p3p3/2ppP3/5B1P/2PBP3/PP1N1PP1/R2QK2R w KQ - 0 1

The two positions are dedicated for engines (or for Peter) ?

For engines of course.
The Bxh7+ sacrifice is particularly interesting since it is a normal position that could happen in a game and it shows the ability of the engine to attack(calculate correctly the attack).

[Eelco de Groot]

For instance my not so good Stockfish clone only considers Rxb4 and the eval does not clearly go down at the end either:

1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - -

Engine: Stockfish 2.3.1 Hybrid (256 MB)
by Tord Romstad, Marco Costalba and Joona Kiiski


33/79 134:35 -7.03 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Bxf2 f4
8.Bg1 Kf5 9.Rd1 h4 10.Rxd7 Ng3
11.Rg7 h3 12.Rh7 Kg4 13.Rg7+ Kf5 (5.296.428.295) 655

best move: Rh4xb4 time: 322:00.172 min n/s: 655.830 nodes: 5.296.428.295

Thanks everybody for the comments on the analysis by Stockfish Hybrid. The program is clearly not functioning very well here and it has to be something in the search but at the moment I have not much of an idea where exactly, but all the comments are very welcome!

After (the line in its PV) 1.Rxb4? Ka8 2.Ra4+ Kb7 3.Rb4, Stockfish 2.3.1 Hybrid considers 3...Kc6?.
[d]8/3p4/1Bk5/4Pp1p/1R6/1p4p1/pP3n2/K6n w - - 0 4

A bad move and then black enters a very difficult position to win since after(which is the best continuation for both and also shown in the PV):
4.e6 g2 white has a crucial check to give 5.Rc4+
[d]8/3p4/1Bk1P3/5p1p/2R5/1p6/pP3np1/K6n b - - 0 5

That must save the position i think.
So it's no wonder Stockfish Hybrid doesn't have a fail low, since after 3...Kc6 it must be a draw.

But had black played his 3rd move correctly, i.e instead of what Stockfish Hybrid suggest 3...Kc6?, to play 3...Ka6! now white is lost since after e.g:
4.e6 g2 white doesn't have the time to defend the promotion square and loses.

After 3...Ka6 the best defense i guess is 4.Be3! and then after 4...g2 5.Rb6+ Ka6 6.Rg6 Ng4 7.Bb6+ Kb5 and now:
- 8.Bg1 f4 and it's over.
- 8.Ba7 h4 9.e6! dxe6 10.Rxe6 h3 11.Bg1 Nhf2 12.Re7 and now the win is easy with many ways e.g the most elegant 12...h2

Thanks George!

A new version I made can find your 3...Ka6! But it still has trouble I think with finding a further decrease in the score. Since this version is pruning even heavier than the one I had before I do like the change in the code, for now:

27/80 14:54 -6.94 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Re1+ Kd5
8.Bxf2 f4 9.Rd1+ Ke5 10.Bg1 h4
11.Rd3 Ng3 12.Rxd7 h3 13.Rh7 Ke4
14.Rxh3 (659.938.415) 737

28/80 18:47 -6.94 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Re1+ Kd5
8.Bxf2 f4 9.Rd1+ Ke5 10.Bg1 h4
11.Rd3 Ng3 12.Rxd7 (822.312.697) 729

29/80 22:43 -6.94 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Kc6 4.e6 g2
5.Rc4+ Kd5 6.Rc1 Kxe6 7.Re1+ Kd5
8.Bxf2 f4 9.Rd1+ Ke5 10.Bg1 h4 (990.828.139) 726

30/80 40:41 -8.16-- 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6
4.Rxb3 h4 5.Bxf2 Nxf2 6.Re3 h3 7.b4 h2 (1.744.908.554) 714

30/81 91:47 -8.24-- 1.Rxb4 Ka8 (3.918.200.610) 711

30/82 115:54 -8.36-- 1.Rxb4 Ka8 (4.948.271.659) 711

30/87 235:41 -8.55-- 1.Rxb4 Ka8 (10.093.863.064) 713

30/87 275:53 -8.60 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6
4.Rxb3 h4 5.Bc5 g2 6.Rb6+ Ka5 7.Rg6 h3
8.Kxa2 Kb5 9.b4 Nd3 10.Bg1 f4 11.Rg5 Kxb4
12.Rh5 Nhf2 13.Rh7 Kc4 14.Rxd7 (11.785.631.486) 711

31/87 298:17 -8.48 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6
4.Rxb3 h4 5.Bd4 g2 6.Rb6+ Ka5 7.Rg6 h3
8.Kxa2 Kb4 9.b3 Nd3 10.Bg1 Nhf2
11.Rg7 Ng4 12.Rg8 Ngxe5 13.Rg3 f4
14.Rxh3 (12.725.809.288) 711

32/87 348:01 -8.48 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6
4.Rxb3 h4 5.Bd4 g2 6.Rb6+ Ka5 7.Rg6 h3
8.Kxa2 Kb4 9.b3 Nd3 10.Bg1 Nhf2
11.Rg7 Ng4 12.Rg8 Ngxe5 13.Rg3 f4
14.Rxh3 (15.060.294.541) 721

33/95 511:34 -8.68 1.Rxb4 Ka8 2.Ra4+ Kb7 3.Rb4 Ka6
4.Rxb3 h4 5.Bd4 g2 6.Rb6+ Ka5 7.Rg6 h3
8.Kxa2 Kb4 9.b3 Nd3 10.Bg1 Nhf2
11.Rh6 f4 12.Rh7 f3 13.Rxd7 Nxe5
14.Rb7+ (22.439.621.288) 731

Eelco