A chess problem solvable by intuition but not by computers

**Lee Hendon** · Tuesday, 14th March, 2017, 12:14 AM

Re: A chess problem solvable by intuition but not by computers

Draw just capture the 3 B's
Win promote to a B or Q

**Peter McKillop** · Tuesday, 14th March, 2017, 12:29 AM

Re: A chess problem solvable by intuition but not by computers

White only moves his king and draws via 50-move rule.

**Mathieu Cloutier** · Tuesday, 14th March, 2017, 12:34 AM

Re: A chess problem solvable by intuition but not by computers

Well, yeah, just move the king on the white squares.

As a side note, this position, even if completely ridiculous compared to practical chess, is still of some use in the context of computer analysis. Let me explain.

I enter the position and fire up the latest version of Komodo. What is the output? A steady -25 (huge advantage for black). But I insist on the 'steady' part. The number stays the same whatever the depth of analysis is.

Now, some might say the computer doesn't understand the position, but I partly disagree. The computer doesn't see a mate, so it's not mate in X. And there's too many pieces for a clear evaluation. So a ridiculous number comes out, BUT, the computer doesn't see how to progress. Which immediately tells me it's a draw. I don't care what is the number in the computer's evaluation. What I do care about is the fact that the number stays the same, whether it's at 12 plys or 30. It does tell me that the computer can't find a way to progress, so it's still some valuable insight into the position.

**Wayne Komer** · Tuesday, 14th March, 2017, 12:35 AM

Re: A chess problem solvable by intuition but not by computers

A chess problem solvable by intuition but not by computers

March 14, 2017

How can you take a bishop when you have two other black bishops guarding it?

If you advance the white pawn and it is taken, then the black king is going to come out of the blocked position with the queen just behind it.

Where can I buy a quantum computer?

**Kerry Liles** · Tuesday, 14th March, 2017, 10:18 AM

Re: A chess problem solvable by intuition but not by computers

Originally posted by Peter McKillop View Post

White only moves his king and draws via 50-move rule.

I think you should submit that solution!

I realized that by only moving the King around, Black was paralyzed of course. I also have looked at posting the white K on d7 and then sacrificing the pawn to a Bishop on c7 then moving the White King to c6 to somehow take advantage of the pawn captures that may follow, but I didn't see a lot of opportunity for NOT losing with that idea... :)

**Paul Bonham** · Wednesday, 15th March, 2017, 03:26 AM

Re: A chess problem solvable by intuition but not by computers

Originally posted by Kerry Liles View Post

I think you should submit that solution!

I realized that by only moving the King around, Black was paralyzed of course. I also have looked at posting the white K on d7 and then sacrificing the pawn to a Bishop on c7 then moving the White King to c6 to somehow take advantage of the pawn captures that may follow, but I didn't see a lot of opportunity for NOT losing with that idea... :)

In Wayne's post, he mentions there may even be a way for White to win. Obviously, if Black took all 3 Bs off of the b8-h2 diagonal and it were White to move, the c6 Pawn can Queen and mate.

Thanks for this thread, Wayne. Really interesting to see how computer brute force search can become a hindrance rather than a help!!!

A heuristic that would detect this, if programmed in to the engine, would be that:

(1) if I (the engine) am losing materially in a big way, and
(2) if my opponent can only move non-mating material that does not include Pawns and can only attack my King, and
(3) if I can only move my King, any other move would end condition (2)

then two things hold true:

(a) any opponent move is not going to change conditions (1), (2), or (3), so the heuristic still applies, and
(b) I the engine should not resign, but must move my King and the game will result in draw by 50 move rule.

The problem with such a heuristic is that calculating conditions (2) and (3) would be hugely expensive in number of calculations -- especially condition (3), because for every non-King move for the engine, the algorithm would have to revalidate condition (2).

Now here's the thing: if the engine is losing by large material, and you the author of the engine want it to keep playing because this heuristic may at any time be found true, then you have to keep checking for it after each opponent move. Only when it is found true can you stop checking for it (conclusion (a) above) and start playing only your King. So this hugely expensive calculation must be repeated over and over until it is found to be true.

Yet we humans can figure this out in very little time. That's because we humans have pattern recognition that doesn't go away when we fall asleep at night. But once a computer process is terminated, there is no memory kept of what it "learned". The next startup of the same process starts with a blank slate.

We could try and load a process with memory of previous learnings by use of databases, but these databases would very quickly grow to unimaginable proportions. Proof if this is the size of Nalimov tablebases of 7-piece chess endgame positions. 8-piece tablebases may never be seen in our lifetimes. 9-piece tablebases: LOL!

The greatest mysteries of the human brain have to do with memory and how we can retain so much data over our entire lifetime. Unless you are into computer science, you can't fathom just how "non-accidental" that is. Could it be evolved over eons of time? I very, very, VERY much doubt so. Even if it could, to combine that accident of evolution with all the other incredible accidents of not only life, but even of the conditions that had to be created for life to be able to exist..... it all combined together just cannot be accidental.

I think this is my favorite chess related thread ever on this forum!

**Kerry Liles** · Wednesday, 15th March, 2017, 09:21 AM

Re: A chess problem solvable by intuition but not by computers

Similar issues have been shown when engines are faced with blockade positions where a human player can easily see there is no possible breakthrough (except perhaps a very clearly suicidal breakthrough) and the outcome is clear to the human player. Modifying chess engines to deal with such rare situations is not as big a payoff as tweaking the engine so that the opponent gets crushed long before that position may occur (lol). I am sure a lot of people who are not aware of how chess-playing programs work might be astonished that any position could cause the 'engine' to be so impotent.

Clearly the diagram could lead to a win for White - given absolutely stupid play by Black (which *is* allowed of course) but other than Peter's suggestion of the 50 move rule, I currently cannot see another way for White to force a draw... As I said, Peter's suggestion is legal and the best plan I can see at this point.

**Egidijus Zeromskis** · Wednesday, 15th March, 2017, 09:59 AM

Re: A chess problem solvable by intuition but not by computers

Though, which computer will generate a 50-moves rule so quick as humans?

I don't know how these days a blockade is programmed but it's quite obvious that locked pieces have zero moves. If White does not take any of rooks and no move with a pawn on c6, those locked pieces will stay forever in the zero-move state. Thus we left with White king and three Black bishops to dance around for a 50 moves rule. That's in a principle 4 piece tablebase. Should be solve-able for a decent computer in a blink (with proper programming) :)

**Mathieu Cloutier** · Wednesday, 15th March, 2017, 12:26 PM

Re: A chess problem solvable by intuition but not by computers

I don't understand why people use that kind of position to state that chess engines are 'stupid' or that they don't understand the game.

Give that position to an engine to play as white and it will draw effortlessly. And after 30-40 moves, the 50 moves rules will come within the horizon of the engine and the evaluation will drop to 0.00.

If the computer is still able to find all the right moves, does it matter that the evalution might be off for a while?

**Wayne Komer** · Wednesday, 15th March, 2017, 01:25 PM

Re: A chess problem solvable by intuition but not by computers

A chess problem solvable by intuition but not by computers

March 15, 2017

Day Two

This thread has been more popular than ever I could imagine – getting over a thousand hits in two days.

My expectation was that some bright person would solve the problem in the first week of it being set, send the solution off to the Penrose Institute and bask in the fame such a feat would produce.

The position is legal. A trivial solution is just to move your king back and forth until the 50-move rule kicks in with a draw.

My intuition tells me that there is a forced draw for white in twelve moves or less. Last night I marched the king to c8 while having black keep his bishops on the diagonal and block the pawn advance c6 to c7. I got one surprising stalemate but then found I had made a weak move for black. At the moment I have no solution and am questioning both my intuition and analytical ability.

When they first wrote algorithms for chess analytical engines, I believed they tried to have an “intuitive” recognition of positions. Was this Botvinnik’s approach? Anyway, now, with faster computers being able to evaluate thousands of positions a second, they have strayed from that first approach and Sir Roger is hoping to go back to it, starting with this problem. Indeed the article says, “the new chess puzzle is one of several which will be released in the coming weeks by the Institute in an attempt to crack the code of human ingenuity”

I will count the days until the first solution is released and give the other problems as they come out.

The best thing to do is to set up the position and see if you can think your way to a suitable outcome.

Here are some of the comments online about the first problem:

- I have been looking at this problem for most of the day now and it’s nice to see computers failing. I would also play for the draw if this was my game, Yet it’s still my hope that since the article is new and I just posted it here I am sure someone will figure out a viable win for white. So far I cant see it on my own board and as we all know putting it through a computer is a waste...lol.....but I will post back if I do find a solution. Hope to hear from you guys soon. Of course if you do find a viable win for white, send it into Penrose first for the contest before everyone else does!

- yeah easy draw, white king stays on white squares, black can only move bishops to dark squares...games goes hundreds if not thousands+ of moves maybe but eventual draw was obvious to me....maybe because it goes so many moves machine can't see it since they deal in specific solutions.

- scientists at the newly-formed Penrose Institute say it’s not only possible, but that human players see the solution almost instantly, while chess computers consistently fail to find the right move

- All of blacks pieces are blocked except for its 3 bishops. So maneuver the king up to c8. Then your pawn at c6 captures black pawn en passant. The black king cannot take the pawn so white pawn once again captures black pawn en passant and queens at a8 checkmate in 8 moves.

- I'm not sure that Roger Penrose's position is really that profound - most chess payers understand that there are positions that computers just do not get.

I remember a game by ex-World Champion GM Kramnik from a couple of years ago (at the London Grandmaster tournament?) where he played a sacrifice which all the chess engines considered a losing move, but in fact produced for him a positional win.

I have often thought there should be an annual composition tournament to create legal chess positions which fool chess engines the most - chess engines score positions: 0 to 0.5 equal; 0.5 to 0.99 White is better; 1 and above White is winning. (negative scores mean lack is in control).

However the interesting thing about Penrose's position - I posit - is that (to any moderately competent human chess player) the position is pretty obviously a draw simply by inspection - apart from the three (black squared) bishops, Black has no moves and even with them no moves on the white squares! For that to change White has to move the c-pawn and Black cannot compel that move. So White doesn't touch the c-pawn and just shuttles the king on white squares.

**Wayne Komer** · Wednesday, 15th March, 2017, 01:54 PM

Re: A chess problem solvable by intuition but not by computers

A chess problem solvable by intuition but not by computers

March 15, 2017

Day Two (continued)

I was wondering what would happen when the chess problem hit the big chess sites.

Peter Doggers has written it up at:

https://www.chess.com/news/view/will...ciousness-4298

In the Comments section, a Norwegian with the nom of PerdusOfficial managed to win for white against a computer:

1. Kf3 Bc3 2. Kg2 Bce5 3. Kh3 Bb8 4. Kg4 Bbc7 5. Kf5 Bb8 6. Ke6 Bbe5 7. Kd7 Bc7 8. Ke6 Bce5 9. Kd5 Ba1 10. Ke4 Bd4 11. Kd3 Bc3 12. Kc2 Ba1 13. Kb1 Bb2 14. Kc2 Ba1 15. Kb1 Bc3 16. Kc2 Bd6 17. Kd3 Bgf4 18. Ke4 Bde5 19. Kf5 Bd6 20. Ke4 Bde5 21. Kf3 Bc1 22. Ke4 Bc7 23. Kd3 Ba1 24. Kc2 Bab2 25. Kb1 Be3 26. Kc2 Bed4 27. Kd3 Bc1 28. Ke2 Bdb2 29. Kd1 B1f4 30. Ke2 Bg3 31. Kf3 Bcd6 32. Ke3 Bf6 33. Ke4 Bc3 34. Kf5 Bb2 35. Ke6 Bg7 36. Kd5 Bc7 37. Ke6 Bb2 38. Kd7 Bc3 39. Ke6 Bge5 40. Kd5 Bf4 41. Ke6 B3e5 42. Kf5 Ba1 43. Ke4 Bh2 44. Kd5 Bb2 45. Ke6 Bd8 46. Kd7 Bdc7 47. Kc8 Bh8 48. Kd7 Bg1 49. Kxc7 Be5+ 50. Kd7 Bgh2 51. Ke6 Bhf4 52. Kf5 Bc7 53. Ke4 Bfd6 54. Kd5 Bh2 55. Ke6 Bg1 56. Kd7 Bgh2 57. Kc8 Bhd6 58. Kd7 Bh2 59. Kc8 Bce5 60. Kd7 Bf6 61. Ke6 Bfe5 62. Kd5 Bc7 63. Ke6 Bcd6 64. Kd7 Bde5 65. Ke6 Bhg3 66. Kf5 Bc7 67. Ke4 Bge5 68. Kd5 Bc3 69. Ke6 Ba1 70. Kd7 Bae5 71. Ke6 Ba1 72. Kd7 Bh2 73. Ke6 Bg3 74. Kd7 Bb2 75. Ke6 Ba1 76. Kd7 Bb2 77. Ke6 Bge5 78. Kd5 Ba1 79. Ke4 Bab2 80. Kf5 Bc7 81. Ke6 Bce5 82. Kf5 Bd6 83. Ke6 Bc7 84. Kd7 Bce5 85. Ke7 Bbc3 86. Ke6 Bcd4 87. Kd7 Ba1 88. Ke6 Bf4 89. Kf5 Bae5 90. Ke4 Bc7 91. Kf5 Bc1 92. Ke6 B7f4 93. Kd7 Bce3 94. Kc8 Bh2 95. Kd7 Bd6 96. Kxd6 Bd2 97. Kd7 Bf4 98. Ke6 Bh6 99. c7 Bd2
(99... Kb7 100. Kd7 a6 101. c8=Q+ Ka7 102. Kc6 Bf4 103. Qb7#)
100. c8=Q#

An explanation as to what happened above:

- If you take a look at PerdusOfficial's playthrough, you'll see why White can actually win this position. The premise is due to the 50-move rule; a computer evaluates the position as overwhelmingly dominant, and refuses to let White draw, so sacrifices a bishop to keep the game going. This happens again, close to the 100 move mark (well beyond the search depth of any computer), so black sacrifices yet another bishop. Now, if the black bishop left does not control the c7 diagonal, white can play c7 and then promote to c8, winning; this doesn't always happen (and the position is thus usually a draw, because the comp won't sacrifice the 3rd bishop, seeing that it will lose soon after)

Thank Heavens that is not the solution!
__________

The website for the Penrose Institute is:

https://penroseinstitute.com/#introduction

and there are many videos of Sir Roger in conversation and delivering lectures on YouTube.

He is the brother of Jonathan Penrose, well-known to chess players. The Wikipedia entry:

Jonathan Penrose, OBE (born 7 October 1933) is an English chess Grandmaster and International Correspondence Chess Grandmaster (1983) who won the British Chess Championship ten times between 1958 and 1969. He is the son of Lionel Penrose, a world-famous professor of genetics, the grandson of the physiologist John Beresford Leathes, and brother of Roger Penrose and Oliver Penrose. He is a psychologist and university lecturer by profession, with a PhD.

Sir Roger was born in 1931.

**Kerry Liles** · Wednesday, 15th March, 2017, 02:05 PM

Re: A chess problem solvable by intuition but not by computers

Originally posted by Wayne Komer View Post

- All of blacks pieces are blocked except for its 3 bishops. So maneuver the king up to c8. Then your pawn at c6 captures black pawn en passant. The black king cannot take the pawn so white pawn once again captures black pawn en passant and queens at a8 checkmate in 8 moves.

I don't follow this part at all... capture "en passant" is not possible in this situation... or am I missing something??

**Kerry Liles** · Wednesday, 15th March, 2017, 02:08 PM

Re: A chess problem solvable by intuition but not by computers

That was very interesting (the Black "help mate" idea - to keep sac'ing Bishops to prevent the 50 move rule and then eventually losing (White has to be careful to avoid allowing a stalemate but that is easily done in that scenario. If an engine (playing Black) adopted that technique in the misguided analysis that the material advantage is so huge and therefore the 50-move draw must be avoided... wow LOL

**Wayne Komer** · Wednesday, 15th March, 2017, 02:34 PM

Re: A chess problem solvable by intuition but not by computers

A chess problem solvable by intuition but not by computers

March 15, 2017

Very interesting indeed, Kerry. No, no en passant. Just one of the odd comments that the problem has generated.