
A chess position to defeat computers? - balsam
http://www.telegraph.co.uk/science/2017/03/14/can-solve-chess-problem-holds-key-human-consciousness/
======
nippples
> The institute is also hoping to develop new technology to improve the
> treatment of brain disease and anesthetics, develop a new type of telescope
> to detect dark matter and even __resolve the Schrodinger’s Cat paradox,
> which suggests a cat in a box could be alive and dead at the same time __.

This is why I dislike most science reporters.

~~~
pvitz
The article starts already with the "World prize". The reporter obviously
didn't think or check anything before publishing.

~~~
scrumper
It should have said "Wolf Prize." Not vastly off (while being of course
completely wrong.)

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waisbrot
The claim here isn't that computers _couldn 't_ solve this, just that they
currently _don 't_. In general, computers and humans play the beginning and
ending of chess games with some strong heuristics -- there are too many
possible moves to enumerate, but there's a very limited number of worthwhile
moves to consider.

In this puzzle, we have an extremely weird end-game. Humans can come up with a
new heuristic on the fly, but current chess programs find all their existing
heuristics fail and have to resort to brute-force search or really dumb
heuristics and neither is helpful.

Obviously, it would be a matter of minutes to code up a new heuristic to
detect this case. The interested question is what the humans are doing that
lets us solve the problem so rapidly.

~~~
kirse
_The interested question is what the humans are doing that lets us solve the
problem so rapidly._

The need for strategy is eliminated with tactically perfect play... Since
computers are not yet to the point of having "solved" chess to tactical
perfection, there will always be scenarios where strategy wins.

IMO this is the maximum win for human-machine interaction... humans define the
strategy, and computers aid in the tactical execution of that strategy. I'm
not really a big believer that AI is anywhere close to beating humans at being
human, especially when you step outside the bounds of a simplistic game with a
narrowed rule-set.

Like with cars and planes, you won't ever see an autonomous vehicle winning a
World Rally Championship, and you won't ever see a computer figuring out how
to make a Hudson river emergency landing. But computers can greatly assist
with the braking, shifting, adjusting flaps, engine management, etc...

~~~
jasonwatkinspdx
> you won't ever see an autonomous vehicle winning a World Rally Championship

Autonomous vehicles will surpass human rally teams. I've competed in rally
here in the US.

The vision problems involved are difficult but don't underestimate how much
humans struggle with sun and dust as well. With everything else the computer
has the advantage.

WRC as an org may not ever run an autonomous class, but I would expect to see
a robo rally event of some sort to show up, perhaps first as a spectacle at
Pikes Peak or Isle of Man.

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yaakov34
The position nearly plays itself - none of the black pieces except the bishops
have any legal moves, so if white moves his king around, without capturing
anything, a draw will result by the 50 move rule (the bishops can't mate the
king, since they won't control any light squares). For black, the play is even
more automatic, since moving the bishops back and forth on the dark squares is
the only legal option.

I do think that a computer will play this correctly for both black and white;
for white, a capture will result in a checkmate within a few moves, which the
computer will be able to see. So this may result in incorrect computer
evaluation, but not in incorrect play.

~~~
dsp1234
_none of the black pieces except the bishops have any legal moves,_

Why couldn't black move the topmost pawn forward?

~~~
yaakov34
Forward for black pawns is down, in a standard chess diagram; white's side of
the board is at the bottom.

So black pawns have no legal moves, while the white pawns could move (the
topmost pawn) or capture either of the black rooks, although this would be
disastrous for white, as the black pieces would then be able to leave their
position and would checkmate white in a few moves.

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CalChris
_Rybka v Nakamura_ is this sort of anti-computer strategy where the computer
clearly doesn't understand the position. 270 moves of Naka calmly moving back
and forth behind a blockade, the exchange down. Rybka eventually tries to _do_
something since it's up on material. And then it just gets slaughtered.

[http://www.chessgames.com/perl/chessgame?gid=1497429](http://www.chessgames.com/perl/chessgame?gid=1497429)

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zwischenzug
'The chess problem - originally drawn by Sir Roger - has been devised to
defeat an artificially intelligent (AI) computer but be solvable for humans.'

I take issue with that statement. All chess engines I'm aware of will
correctly play out the draw, so it doesn't defeat them. The engines will
_evaluate_ a material advantage for black.

Frankly, this isn't really a surprise.

Incidentally I once won money on Betfair (a P2P betting site) by evaluating a
position in a Kasparov vs computer game that looked like a win to computers
for the computer, but that I knew Kasparov would prevail in. My fellow
gamblers were trusting the computer evaluations :)

~~~
ouid
will a chess engine, as white, enter this position from any of the possible
preceding positions?

~~~
zwischenzug
Why does that matter?

~~~
ouid
[https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q...](https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0)

stockfish loses here, but could easily draw.

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overlordalex
If anyone wants to play with this, here is the board in lichess:
[https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/pP4b...](https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/pP4b1/P3K3/8_w_-_-)

~~~
ifdefdebug
Constantly valuating at about -30...

Crazy enough, every chess player in the world can see immediately it's a draw
from the very beginning, unless white concedes a helpmate, yet stockfish
doesn't get it...

~~~
yaakov34
True, but the engine does see that a pawn move by white results in checkmate
in a few moves, so it would actually play this position correctly and get a
draw, despite the huge negative evaluation.

~~~
ajennings
I played it out on lichess.org. After 47 moves, Stockfish sacrifices a bishop
to keep the game going.

I was wondering if it would repeat that 47 moves later, but it didn't. Settled
for the draw.

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TorKlingberg
The claim that computers cannot solve this problem is never really clarified.
Which chess AI's exactly? That it involves Roger Penrose and claims about
special abilities of the human brain only makes me more suspicious.

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selfsimilar
I don't play chess regularly but the stalemate was obvious to me immediately
and the mate after about 3 minutes. Kinda clever but I'd be surprised if a
chess AI couldn't see this. Penrose is notorious for thinking that
consciousness depends on some spooky quantum effects that machines cannot
capture (See Emperor's New Mind).

~~~
ythn
Isn't it already a stalemate? As long as the king never leaves white squares,
he will never be in danger, and thus the game will be a draw by the 50 move
rule.

I don't see how mate is possible. In order to mate, you need to advance the
white pawn to promotion, but it's impossible to advance the white pawn without
one of the 3 bishops killing it.

~~~
klodolph
Technically, a stalemate is a draw and the 50 move rule is a different way to
get a draw.

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iainmerrick
Okay, here's my answer: all of black's pieces are blocked except for the
bishops. The black king can't move without being checked by a pawn. All the
black bishops are on black squares (meaning two must be promoted pawns --
unlikely but possible)

So the white king just needs to stay on a white square to stay safe.

The so-called "aha!" moment was remembering that bishops always stay on the
same color. I can't claim any great insight, it's just something I read
somewhere (so it could certainly be programmed into a computer).

I had to check that there was no way for the other pieces to escape. I'm not
good at chess, so I just did a very quick check and then assumed it was
probably fine -- given the nature of the puzzle it's unlikely there'd be a
tricky edge case to cover there.

The thesis seems to be that a computer could never develop and use general
theorems that let you short-circuit the search process. That's probably true
for chess engines (and also mostly irrelevant to real chess matches, rather
than puzzles). Definitely an interesting question to explore. My guess would
be that real computer creativity is possible, but may require some new
techniques.

~~~
thaumasiotes
> All the black bishops are on black squares (meaning two must be promoted
> pawns -- unlikely but possible)

Is this possible outside the context of purposely making bad moves to
humiliate your opponent? I thought you got to choose whatever officer you
wanted, which would mean bishops are strictly dominated by queens.

~~~
pjungwir
Underpromotion is real thing and has its (very rare) uses. Even underpromoting
to a bishop can turn a draw into a win:

[https://en.wikipedia.org/wiki/Promotion_(chess)#Bishop_under...](https://en.wikipedia.org/wiki/Promotion_\(chess\)#Bishop_underpromotion)

~~~
curun1r
It kinda sucks that they changed to rule to require you to promote a pawn to a
piece of your own color. The mate-in-1 puzzle on that promotion page that
requires promoting a pawn to an opponent's knight is pretty neat and I can't
see that rule having a practical impact on any real chess game.

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ouid
Here's a position derived from the one shown in which stockfish plays white
incorrectly.

[https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q...](https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0)

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ChuckMcM
Interesting, it took me reading the comments to realize the board orientation
vs the piece movement. Like many people the fact that the black bishops are
basically unable to attack anything stands out, and given the orientation that
none of blacks other pieces can move. Once you see those two things, the
solution does just pop out.

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ranprieur
This is a terrible puzzle. I'm glad I didn't rack my brain for hours looking
for the "flash of insight" when all I had to do was be reminded of the 50 move
rule.

~~~
umanwizard
The 50-move rule is a hack and the wrong way to think about it. What's really
going on is "black can never force a win, therefore the position is drawn".

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buzzy_hacker
The draw is fairly easy but the author mentions a win. Any ideas?

~~~
edko
White cannot force a win. However, if it manages to move the king to D7, and
the black bishops leave the B8-H2 diagonal (a huge blunder), then white can
move its pawn to C7, and checkmate in the next move, by crowning the pawn into
a queen.

~~~
irixusr
Why not?

Once you're on D7 the pawn can be captured or kept. If black moves to capture
the pawn with a bishop, you move the king into pawn's old spot. You capture
the black rook with the other pawn for the win.

If there are no more bishops on the diagonal, or if they move their king to
the B column, then you get a Queen and finish them off.

Am I missing something (I'm a _very_ bad player)?

~~~
Liquid_Fire
> If black moves to capture the pawn with a bishop, you move the king into
> pawn's old spot. You capture the black rook with the other pawn for the win.

If you capture the black rook, black will capture your pawn with the queen
(and proceed to mate you now that their queen can move).

------
mark_l_watson
I remember coming home from the 1982 AAAI AI conference with my "AI, it is for
real!" and thinking of how little skepticism about AI that I heard at the
conference. Years later I bought Penrose's book "The Emperor's New Mind:
Concerning Computers, Minds and The Laws of Physics" to 'know the enemy', but
over the years I have started to agree more with Penrose's position on AI.

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GuB-42
An important thing to consider is that this puzzle is designed by a human for
humans.

The way we solve this problem is not by thinking in term of pure chess logic.
We solve it by thinking "what did the puzzle creator thought". So we recall
from memory what kind of patterns are suitable for such a problem and start a
tree search. It is similar the what a chess AI does but nodes are abstract
patterns rather than just chess moves.

This puzzle follows a mental pathway that is common for most humans. We could
also design problems that can easily be solved by specific chess AIs but not
by humans or other chess AIs : just make it so that the AI naturally moves in
the right direction, for example by making specific heuristics always right.

So while this problem is interesting for getting insight into the way humans
solve puzzles, it doesn't make the human brain special.

~~~
samiru
This is not a "hard" problem. It is just a problem you can't solve with brute
force.

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tunesmith
I think you just push the king around on white squares, hope _all three_
bishops eventually blunder off the same diagonal (come on), and promote that
c6 pawn to a queen. That's not a very satisfying "mate" solution but I don't
see anything more clever.

Reading other comments, I see you'd also need to use the white king to guard
the white pawn at c7 - I missed that - but even with that, you'd still need to
hope that _all three_ black bishops would go off that diagonal.

Anyway, this seemed mostly about visual pattern recognition and thinking
geometrically, visualizing vectors, seeing unblocked pathways. That's not how
computers do it.

~~~
twinkletwinkle
There's sort of a silly argument as to how you could get mate. If a computer
is playing black, it reads the board as greatly to its advantage. So when it's
coming up on the 50-move draw, it might offer you a bishop to take to prolong
the game. It has such a material advantage, a draw "feels like" a bad outcome,
so it's worth giving up some material to continue the game and go for the win.
Which is a very computer way of "thinking". Once you take all 3 bishops in
this manner, you promote the pawn and get checkmate.

~~~
tyilo
Once you take all 3 bishops it is a draw as black can't move any pieces.

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JamilD
I have a hard time believing that a chess computer wouldn't draw this game…
the main issue is in the centipawn evaluation function which would show black
ahead. This doesn't seem like a difficult thing to correct, and it might not
even be a bad idea to have an evaluation function show black ahead in that
position.

Practically, this isn't really an issue. In fact, running the position through
the GarboChess JS engine
([http://analysis.cpuchess.com](http://analysis.cpuchess.com)), playing as
white, it just moves the king around — exactly what a human would do to draw
the game.

~~~
gweinberg
The heuristic would probably show black as ahead, but it would also show that
black can make no progress. So it's an obvious draw.

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mjhoy
This reminds me somewhat of an interesting recent video from GM Simon Williams
[1], analyzing a queen sac from a real game. He disagreed with the computer's
favoring black, and my very uneducated guess about this is that the position
is odd enough -- white is down a queen and an exchange, but all of black's
pieces are tied up in defense -- that a GM can better understand the
implications.

[1]:
[https://www.youtube.com/watch?v=-YX17fljs4E](https://www.youtube.com/watch?v=-YX17fljs4E)

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UweSchmidt
Can anyone with a chess engine handy confirm the claims in the article and
explain what your engine is trying to do? I wouldn't be surprised if at least
some engines have some kind of conservative heuristics built in, like "If I
can't find something good after x cycles, let's play something safe." and "If
the opponent isn't gaining any ground after several turns of me buying time,
it is likely going to be a draw even though I don't know why."

~~~
CJefferson
If you actually play this state in a chess engine they play it "correctly",
they just can't tell what the final outcome is going to be.

~~~
ouid
[https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q...](https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0)

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aaron695
All this might prove is that humans are less intelligent.

We are we wasting brain and heuristics solving problems that would never exist
in real chess play? Seems like an inefficiency to me.

An artifact from our lack of ability to play chess as intelligently as
machines.

Just like an inferior machine might be able to do something like burn outs
because it doesn't have antilock braking. (I don't get cars insert real
example here)

------
erelde
I'm more interested in how the board got this way.

~~~
vinchuco
[https://en.wikipedia.org/wiki/Retrograde_analysis](https://en.wikipedia.org/wiki/Retrograde_analysis)

------
ingmarheinrich
White King goes to a8, only using white squares and b8. Black has to make the
mistake to leave b8 unguarded for one move. Then white pawn to c7. Black King
cannot b7 because of the white King on a8. Black bishop has to take the pawn,
or pawn c8Q will be mate. Black bishop on c7 however is forced stale, since
the white King cannot move.

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Overtonwindow
As long as the King stays on white squares it will result in a draw in 30
moves... -shrugs- I think the computer could see this. It would revert to the
rules that it knows. It would know +1, +2, +3.. and so forth moves down that
it is growing closer to the draw line. It will wait for a pawn move from
White. Without a pawn move... draw.

------
robertlagrant
This just seems like an odd edge case on the 50 move stalemate rule, because
it's such an unusual thing to shoot for to achieve a draw that a chess program
doesn't normally bother to look for it.

Doesn't seem that useful a demonstration, except for people who don't know
much about computers. Is this a bit like Hawking on AI?

~~~
umanwizard
You mean draw, not stalemate. A stalemate is one particular type of draw that
has nothing to do with the 50 move rule.

------
toolslive
I bet machines will have a hard time with Blathy's mate in 290 too.

[https://www.chess.com/forum/view/more-puzzles/longest-
checkm...](https://www.chess.com/forum/view/more-puzzles/longest-checkmate-
problem-290-move)

------
mrfusion
I can't tell which way the board is oriented? Where did white start?

~~~
umanwizard
By convention, chess diagrams are presented with White's home rank on the
bottom and Black's on the top.

------
umanwizard
I must be missing something... isn't it impossible for black to win no matter
what white does with her king (as long as she doesn't move her pawn)?

~~~
iainmerrick
That's the answer they're looking for. (White could still lose by making
really bad moves, but so could black.)

~~~
umanwizard
I thought it would be more complicated than that, as they really play up the
"puzzle" aspect of the article (even offering a prize!)

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dmichulke
Assuming the bishops stay on their bottom-left to top-right diagonal, you
could move the king to b1 and then

white b3xa4

black Qa4 (queen is forced because otherwise a4xb5 mate)

~~~
yaakov34
That would lose - it would not be a stalemate, no matter where the bishops
are, since white has pawn moves; and starting with the next move, black would
begin checking white and will quickly checkmate.

~~~
dmichulke
Yes, not sure how I could overlook that pawns, just assumed them all blocked

------
vcdimension
Can white get a stalemate in 7 moves instead of 50 by just moving its king
next to the black king? or is that not allowed?

~~~
sushid
No you can't move a king adjacent to another king. There must be at least a
square between the kings for the move to be valid.

------
gweinberg
I think the claim that this position would defeat a computer is nonsense. Any
decent program would draw as white.

------
tommymachine
This chess position doesn't defeat computers. A decent engine will draw this
every time. But the disparity in the efficiency of line of reasoning (a
humans' being much more efficient than a computers for this problem)
illustrates the value add of a programmer to a computer, and what the job of
computer programming really is.

Computers basically know nothing--which is good and bad. It's good because
they don't require much convincing before performing boring, repetitive tasks.
They simply don't know or care that a given task is repetitive or boring, or
even useful or not useful, so they will keep chugging along until they can
return their output. The downside of this is that if they are to know anything
at all, they must be programmed to know it.

They can also learn through evolutionary iterations once programmed
conceptively. One could conceive of a computer program that would spit out
random logical relationships to describe a large set of data, (what humans
might refer to as "life experiences") and prune the logical statements until
they eventually returned accurate logic describing the data. But this would
require large quantities of generations for pruning, and careful programming
of heuristics for logical evaluation at inception.

We can observe that our brains are born out of a system of evolution that has
already undergone such processes. We have had a powerful survival heuristic on
our genetic program for developing a broad set of skills, including logical
reasoning, and it has been running for billions of years, pruning countless
generations to give rise to our inherent level of intelligence that can
discover logical shorcuts like the one in this problem. The evolutionary
process also gives rise to possibly illogical but robust sets of skills, since
survival and procreation are hueristically more valuable than being logically
perfect in reasoning.

Sure, theoretically, and given sufficient computing resources and time, a man
made computer system could approximately match and even exceed the human
capacity for discovering logical shortcuts. But when paired with a competent
human programmer, or team of programmers, the programmers can vastly reduce
the time and resources required to achieve this process of intelligent
evolution, and produce intelligent programs much more quickly than a computer
program left to simply evolve it's intelligence on its own.

It took us humans quite a while to get here. Why would we assume that a
computer could evolve faster than us, autonomously, without being programmed
by us to do so? It is possible I suppose, but it's even more unlikely than the
evolution of human intelligence, which sure, it happened autonomously, but
over a course of billions of years.

~~~
zuluxray
Which 'decent engines' will draw this every time?

------
geuis
I'm just an amateur chess player. How does black have 3 bishops on the board?

~~~
DuoSRX
Black promoted 2 of his pawns to bishops.

------
c3534l
I must be pretty dumb because the solution to the problem isn't "obvious" at
all, nor do I see how this proves quantum intelligence.

------
hoagiefest
could this info, once cracked, simply be fed to the machine?

~~~
ars
Obviously. The question is why can't the machine figure it out itself.

------
anonymousiam
King to bishop 3.

------
jlebrech
so it's the halting problem?
[https://en.wikipedia.org/wiki/Halting_problem](https://en.wikipedia.org/wiki/Halting_problem)

~~~
umanwizard
How is this related to the halting problem? I'm not seeing it.

~~~
jlebrech
unless you catch 50 moves it's a runaway algorithm

~~~
umanwizard
The fact that a particular algorithm never halts is only tangentially related
to the halting problem.

It's even possible to write non-halting algorithms in non-Turing-complete
systems for which the Halting problem doesn't hold.

