chess, artificial intelligence, horizon effect

[hgm]

Scientists use chess and chess engines to prove that people need an artifical intelligence, of course not to solve chess problems.

What do you think about it?

It makes no sense. If you don't want to solve chess problems, what could you possibly learn from / prove /disprove with AIs that can do nothing but solving Chess problems?

[jpqy]

Here some more info about this position:

http://chessengine.blogspot.be/p/horizon-limit.html

[hgm]

[FEN "1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - - 0 1"]

1. Rxh1 Nxh1 2. e6 dxe6 3. Bc7+ Kb7 4. Bxg3 e5 5. Be1 e4 6. Bh4 e3 7. Bf2 f4 8. Be1 e2 9. Bg3 f3 10. Bf2


After exchanging the Rook against the Knight, the Bishop has to keep the remaining Knight at h1 with the threat of stalemate when getting captured

Well, this obviously is a way to force a draw. But the question is whether it is the only way, and if not, whether it is the best way. Normally the quickest way to achieve the objective (whether mate or draw) would be considered the correct solution. And this one seems excessively slow, because it leaves the black King free to roam the board, and leaves black 3 passers, which he can advance lot to reset the ply counter a number of times. So it will take hundreds of moves to acheive the draw.

A rabid Rook is potentially much faster: it can confine the King to a fraction of the board, and does not leave the opponent time to push Pawns. So there is a good chance to force repeats, and even without them, you are done after 50 moves.

So Fruit seems to have the better plan; the question is just whether it borns out.

Score, excluding ZERO and mates mens rather nothing.

Score means everything. It tells you that the engine really did not see the solution at all. It just picks this PV because all alternatives would have got it checkmated by that time, it is the only way to survive that long. But it still thinks it is badly lost.

This of course is crucial in similar positions where there would be other slow but certain losses. It would then latch on to the slow loss untill long after the certain draw is well within the horizon, just because its eval does not recognize it as a certain draw, but attaches an absurdly low score to it. It will only switch to the draw by the time it searches so deep that all the losing variations have been pushed below it. Such 'negative selection' is quite unreliable; the alternatives might be arbitrarily slow, yet very certain.

So to not count as 'Artificial Stupidity' it is imperative the evaluation would recognize such draws. And the triggers for this can be very cheap. For instance, most engines would evaluate a King safety of some sort, depending on the number of squares next to it that are attacked. It should be easy to notice that in this case all the squares are attacked or blocked, so the white King has no legal moves. This seems quite relevant information in any case, as this should be considered a severe tactical weakness, where every check means an immediate mate. But in combination with the presence of only two pieces (King + other), it of course also means you have an iron piece and can play for stalemate.

[peter]

So Fruit seems to have the better plan

Not so in the latest variant of your shown output as for optimal black moves.

Rxb4 Ka8 Ra4+ Kb7 Rb4 Kc6 e6 g2 Rc4+ Kd5 Rc1 dxe6 Bxf2 Nxf2 Rc5+ Ke4 Re5+ Kd3 Rd5+ Ke2 Re5+ Kd2 Rd5+ Ke3 Rd3+ Ke4 Rg3

3...Kc6? might lead to draw rather soon to be "seen" by engines

but 3...Ka6 instead might not.

I have stored a .pgn with lots of variants back then, when I first looked at this position:

[Event "?"]
[Site "?"]
[Date "2013.03.14"]
[Round "?"]
[White "eighth, step"]
[Black "to , heaven"]
[Result "1/2-1/2"]
[Annotator "Martan,Peter"]
[SetUp "1"]
[FEN "1k6/3p4/1B6/4Pp1p/1p5R/1p4p1/pP3n2/K6n w - - 0 1"]
[PlyCount "19"]

1. Rxh1 (1. Rxb4 $2 Ka8 2. Ra4+ (2. Rc4 g2 3. Rc8+ (3. Rc1 Nd3 4. e6 dxe6 5.
Rc3 Ne1) 3... Kb7 4. Rc1 (4. Rg8 Ng4 5. Bg1 f4 6. e6 dxe6 7. Rg6 e5 8. Rd6 Ng3
9. Rg6 Kc7 10. Bb6+ Kd7 11. Bc5 f3 12. Rd6+ Kc7 13. Rg6 Ne2 14. Bd4 Kd7 15. Bc5
Nf4 16. Rd6+ Kc7 17. Rd1 h4) 4... Nd3 5. e6 (5. Rc3 Kxb6 6. Rxb3+ Kc5 7. Rxd3
g1=Q+ 8. Kxa2 Qg2) 5... dxe6 6. Rc7+ Ka6 7. Ra7+ Kb5 8. Rb7 Ne1 9. Ba5+ Ka6 10.
Rb6+ Ka7) 2... Kb7 3. Rb4 Ka6 (3... Kc6 $2 4. e6 g2 5. Rc4+ Kd5 6. Rc1 dxe6 (
6... Kxe6 7. Bxf2) 7. Bxf2 Nxf2 (7... h4 8. Rd1+) 8. Rc5+ Ke4 9. Re5+ Kd3 10.
Rd5+ Ke2 11. Re5+ Kd2 12. Rd5+ Ke3 13. Rd3+ Ke4 14. Rg3) 4. Be3 (4. e6 $2 g2) (
4. Rxb3 h4 (4... g2 $2 5. Bxf2 Nxf2 6. Rg3) 5. Bd4 (5. Bc7 g2 6. Rb6+ Ka7 7.
Rg6 h3 8. e6 dxe6 9. Rg7 Ng4 10. Bh2+ Kb6 11. Bg1+ Kc6) (5. Be3 g2 6. Rb6+ Ka5
7. Rg6 h3 8. Kxa2 Ng4 9. Bg1 Ng3 10. Kb3 Ne2 11. e6 dxe6 12. Rxe6 Nxg1 13. Kc4
Ne3+ 14. Rxe3 Nf3 15. Re6 Nd2+ 16. Kd3 g1=Q 17. Re8 Qh2 18. Rh8 Kb4 19. Rh7
Qd6+ 20. Kc2 Nb3 21. Rb7+ Kc4 22. Rxb3 Qh2+ 23. Kd1 Kxb3 24. Ke1 Qxb2 25. Kd1
Qf2 26. Kc1 Qe1#) 5... g2 6. Rb6+ Ka5 7. Rg6 h3) (4. Bc7 f4 5. Rb6+ (5. e6 $2
g2) 5... Ka7 6. Rg6 (6. Rxb3 g2) 6... Nd3 7. Bb6+ Kb7 8. Bd4 Ne1) 4... g2 5.
Rb6+ Ka5 6. Rg6 Ng4 7. Bb6+ Kb5 8. Ba7 h4 9. e6 dxe6 10. Rxe6 h3 11. Bg1 Nhf2
12. Re2 h2) (1. e6 $2 g2 2. Bc7+ Kxc7 3. Rc4+ Kb7 4. Rxb4+ (4. Rc1 Ng4 5. exd7
Ne3 {#5}) 4... Ka6) (1. Bxf2 $2 Nxf2 2. Rxb4+ Kc7 3. Rc4+ (3. Rb7+ $2 Kxb7 4.
e6 g2 5. exd7 g1=Q#) 3... Kb7) (1. Rc4 $2 g2 2. Rc1 (2. Bxf2 Nxf2 3. Rc1 Ng4 4.
e6 Ne3 5. e7 Nc2+ 6. Rxc2 g1=Q+ 7. Rc1 Qxc1#) 2... Nh3 3. e6 (3. Ba7+ Kb7 4. e6
dxe6 5. Bg1 (5. Re1 Nf4 6. Be3 Nd5 7. Bg1 Ng3 8. Rxe6 Kc7 9. Bb6+ Kd7 10. Rg6
f4 11. Bc5 Nc3 12. Rd6+ Kc7 13. Rf6 Nge4 14. Rf7+ Kc6 15. Bg1 Ne2 16. Rg7 N4g3
17. Rg5 Kd6 18. Ba7 Ke6 19. Bd4 h4 20. Re5+ Kf7 21. Rg5 h3 22. Rg7+ Ke6 23. Rh7
Nc1 24. Rh8 Nd3 25. Bg1 Kf5 26. Ra8 Ne4 27. Rf8+ Kg4 28. Re8 Ne1 29. Rg8+ Kf3
30. Rc8 Nc2+ 31. Rxc2 bxc2 32. Be3 Kxe3 33. Kxa2 Nd2 34. b3 g1=Q 35. Kb2 Qb1#)
5... Ng3 6. Rc5 f4) 3... dxe6 4. Rd1 (4. Rc4 f4 5. Ba7+ Kb7 (5... Kxa7 $2 6.
Rc7+ Ka6 7. Rc6+ Kb5 8. Rc5+) 6. Rxb4+ (6. Re4 Kc6 7. Rxe6+ (7. Re2 f3 8. Rxe6+
Kd5) 7... Kd5 8. Re8 (8. Re2 f3 9. Rd2+ Ke6 10. Bg1 Nf4 11. Rd4 Ke5 12. Rd7 Ng3
13. Re7+ Kf5 14. Rf7+ Kg4 15. Rg7+ Kh3 16. Re7 Nge2 17. Rf7 h4) 8... Ng3 9. Rb8
h4 10. Rxb4 Nf5 11. Bg1 f3 12. Rb5+ Ke6 13. Rb6+ Ke7 14. Rb7+ Kf6 15. Bd4+ Ke6
16. Bg1 Ng5 17. Rb6+ Ke5 18. Rb5+ Kf4 19. Rb4+ Ne4 20. Be3+ Ke5 21. Rb5+ Ke6
22. Rb6+ Nfd6 23. Rb8 h3) 6... Kc7 7. Be3 e5 8. Bd4 Kc8 9. Ba7 f3 10. Rc4+ Kd7
11. Rc3) (4. Ba7+ Kb7 5. Bg1 (5. Rc4 f4 6. Rxb4+ Kc7 7. Be3 e5 8. Bd4 Kc6 9.
Rb6+ Kd7 10. Rb7+ Ke6 11. Rb5 Kf5 12. Rxe5+ Kg4 13. Re2 Kf3 14. Rd2 Ng3 15. Rd1
h4 16. Rd3+ Ke2 17. Rc3 Ng5) 5... Ng3 6. Bb6 f4 7. Bg1 h4 8. Bb6 Ng5 9. Bg1 h3)
4... Ng3 5. Be3 (5. Rc1 f4 6. Rc4 h4 7. Rc1 e5 8. Rc4 e4 9. Rc1 Nf1 10. Rc4 Nd2
11. Rc1 f3 12. Rc6 Nf4 13. Rc1 Nd3) 5... Kc8 6. Rc1+ Kb7 7. Rc4 f4) (1. Rxh5 $2
g2 {#19} 2. Rg5 Nd3 3. Rxg2 Ne1 4. e6 dxe6 5. Rg8+ Kb7 6. Rg7+ Kc8 7. Rg8+ (7.
Rc7+ Kb8 8. Ba5 Nc2+ 9. Rxc2 bxc2 10. Kxa2 c1=Q) 7... Kd7 8. Rd8+ Ke7 9. Rd2
Nc2+ 10. Rxc2 bxc2 11. Kxa2 (11. Be3 b3 12. Bd2 Nf2 13. Be3 Ke8 14. Bc1 Nd3 15.
Bd2 c1=Q+ 16. Bxc1 Ne1 17. Bd2 Nc2#) 11... c1=Q) (1. Be3 Ng4) 1... Nxh1 (1...
g2 2. Rg1 Nd3 3. Bf2 Nxf2 4. Rxg2) (1... Nd3 2. Rd1 Nxe5 (2... Nf2 $2 3. Bxf2
gxf2 4. Rf1) (2... Nf4 3. Rxd7) 3. Be3) (1... Ng4 2. Rxh5 Kb7 (2... Nxe5 $2 3.
Rxf5) (2... f4 3. e6 dxe6 4. Rh4 Ne3 (4... f3 $2 5. Rxg4 f2 6. Bxf2 gxf2 7. Rf4
) 5. Bxe3 fxe3 6. Rh2 gxh2) 3. Bd4 f4 4. e6 dxe6 5. Rh4 Ne3 (5... e5 6. Rxg4
exd4 7. Rxg3 fxg3) 6. Bxe3 fxe3 7. Rh2 gxh2) 2. e6 dxe6 (2... f4 3. exd7) 3.
Bc7+ Kb7 4. Bxg3 e5 5. Be1 (5. Bxe5 $2 Nf2) 5... e4 6. Bh4 e3 7. Bf2 f4 (7...
Kc6 8. Bg3 f4 9. Be1 f3 10. Bh4 Kd5 11. Be1 Kc4 12. Bh4 Kd4 13. Be1) 8. Be1 e2
9. Bg3 f3 10. Bf2 1/2-1/2

I didn't have SF with bbs- support then and now did some backward solving of the one and the other variant only with SF6 and full Syzygys. Even if it maybe would have been even better to leave bbs away, cause they probably don't help here anyhow, here's the output with full hash afterwards with 1.Rxb4(?) played:


1k6/3p4/1B6/4Pp1p/1R6/1p4p1/pP3n2/K6n b - - 0 1

Analysis by Stockfish 6 64 POPCNT:

1...Ka8
-+ (-13.34 ++) Tiefe: 42/98 00:06:48 9069MN, tb=8102784

And after 1.Rxb4 Ka8:

k7/3p4/1B6/4Pp1p/1R6/1p4p1/pP3n2/K6n w - - 0 1

Analysis by Stockfish 6 64 POPCNT:

2.Tc4 g2 3.Tc8+ Kb7 4.Tg8 Sg4 5.Lg1 f4 6.e6 dxe6 7.Td8 Kc6 8.Td2 f3 9.Td4 e5 10.Td3 e4 11.Td8 Sg3 12.Tg8 Kd7 13.Tg5 Ke6 14.Tg8 e3 15.Lxe3 Se4 16.Te8+ Kf5 17.Tf8+ Sef6 18.Lc5 Ke6 19.Th8 Kd7 20.Tb8 h4 21.Tb7+ Kc6 22.Tb6+ Kc7 23.Tb5 h3 24.Lg1 Kc6 25.Tf5 f2 26.Lxf2 h2 27.Tc5+ Kb6 28.Tc1+ Sxf2 29.Tc6+ Ka7 30.Ta6+ Kb7
-+ (-13.77) Tiefe: 40/69 00:01:29 1304MN, tb=597403


As far as I remember this is a study and it wasn't cooked when published.
I don't think there are other ways to remis besides 1.Rxh1

[jorose]

I suppose the irony is that even if we as humans can understand the solution, I don't think we understand why the engines solution may or may not work except with a large amount of their help. At least I have trouble understanding some of the lines in that analysis.

Still a very interesting problem from a theoretical perspective.

[peter]

I suppose the irony is that even if we as humans can understand the solution, I don't think we understand why the engines solution may or may not work except with a large amount of their help. At least I have trouble understanding some of the lines in that analysis.

Of course you're right, I wouldn't say I'd really "understand" all of these variants I got interactively in the sense of being sure, there couldn't be alternative moves anywhere along with a possible change of outcome. And no, a single numeric eval except #in x doesn't mean a thing. (Neither 0.00 does, as we see often enough in other positions.)

Yet the change of evals along the moves and between them in depth and variance does say enough to me to believe in the variants of good engines with enough hardware-time in forward- backward- analysis.

At the moment I try to get a mate-score after 1.Rxb4(?) from this variant backward as near as possible to the root- position:

1. Rxb4 Ka8 2. Ra4+ Kb7 3. Rb4 Ka6 4. Be3 g2 5. Rb6+ Ka5 6. Rg6 Ng4 7. Bg1 h4 8. e6 dxe6 9. Rg7 h3 10. Ra7+ Kb5

Right now I'm at 7...h4 with a #29- score but with one ply only output- variant. Will tell if further relevant progress is to be made onwards