I think it must involve playing ...g4, at the right moment. At a point when the black knight will get to g5. (eg. when the knight is on e6/f7, or when the white king is on h1 and the knight has access to e6/f7).Ray Sayers wrote:That was pretty much my thinking too; win the g2 pawn. I'll be blowed if I can see how to force it there though. I gave up, figuring I must be a) missing something obvious or b) barking up the wrong tree.IM Jack Rudd wrote:I want to get that knight to g2 somehow. Can we use corresponding squares, or something like that?
If I get the knight to e3 or e1, I win the pawn and the game. Therefore, white must stop me getting the knight to c4, c2, d3 or d1. Thus:
Nd4: bishop must be on a4, b1, d1, d3
Na3: bishop must be on b3, d3
Nc3: bishop must be on b3, c2
Nb4: bishop must be on b1
Nb2: ....
So b2 is a winning square for the knight - which means a4 is as well. Thus:
Nc5: bishop must be on b5, c2
Nb6: bishop must be on b5, b3
Hmmm. Is this getting us anywhere? (I can quite clearly see that it would be beyond the Event Horizon.)
I would be grateful for the solution!
Evil endings that embarrass engines
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Re: Evil endings that embarrass engines
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Re: Evil endings that embarrass engines
I like the idea of Jack Rudd of the corresponding squares. Even though the bishop is bad (having all own pawns on it's own color) it can still prevent a lot of knight maneuvers.Ray Sayers wrote:That was pretty much my thinking too; win the g2 pawn. I'll be blowed if I can see how to force it there though. I gave up, figuring I must be a) missing something obvious or b) barking up the wrong tree.IM Jack Rudd wrote:I want to get that knight to g2 somehow. Can we use corresponding squares, or something like that?
If I get the knight to e3 or e1, I win the pawn and the game. Therefore, white must stop me getting the knight to c4, c2, d3 or d1. Thus:
Nd4: bishop must be on a4, b1, d1, d3
Na3: bishop must be on b3, d3
Nc3: bishop must be on b3, c2
Nb4: bishop must be on b1
Nb2: ....
So b2 is a winning square for the knight - which means a4 is as well. Thus:
Nc5: bishop must be on b5, c2
Nb6: bishop must be on b5, b3
Hmmm. Is this getting us anywhere? (I can quite clearly see that it would be beyond the Event Horizon.)
It will hit right in after 3.Bb5?? Nc3 followed by Nd1 an Ne3. Easy win. But it can't be forced as you mention. After 3.Bb3 Nd4 4.Ba4 Ne6 Black actually threatens g4, hxg4, Ng5 followed by h3, gxh3, Nxf3+,Kh1,Kg3 and probably Nh4 (or Nxh4) and f3 and the f3-pawn is very dangerous. I always believed this should be avoided, so on 4...Ne6 5.Bb3 would be correct. Now 5...Nc5 6.Bc2 Na6 7.Bd3 Nb4 8.Bb1 Ke1! and Black shows a new theme - run to capture the bishop on b1! How will that play out? Over to you guys ...
Not so fast, you have to put up some work for it tooRay Sayers wrote:I would be grateful for the solution!
Indeed, spot on!Richard Bates wrote:I think it must involve playing ...g4, at the right moment. At a point when the black knight will get to g5. (eg. when the knight is on e6/f7, or when the white king is on h1 and the knight has access to e6/f7).
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Re: Evil endings that embarrass engines
Trying first to sit the N on d2:-IM Jack Rudd wrote:I want to get that knight to g2 somehow. Can we use corresponding squares, or something like that?
If I get the knight to e3 or e1, I win the pawn and the game. Therefore, white must stop me getting the knight to c4, c2, d3 or d1. Thus:
Nd4: bishop must be on a4, b1, d1, d3
Na3: bishop must be on b3, d3
Nc3: bishop must be on b3, c2
Nb4: bishop must be on b1
Nb2: ....
So b2 is a winning square for the knight - which means a4 is as well. Thus:
Nc5: bishop must be on b5, c2
Nb6: bishop must be on b5, b3
Hmmm. Is this getting us anywhere? (I can quite clearly see that it would be beyond the Event Horizon.)
if the WK is on h1, WB on d3 , BK on f2, BN on d2 the Black g4 push, giving up the g and h if nec, breaks through.
the additional threat of trapping the WB on b1 with a BN on b4 wins a pawn if W prevents the Nd2 line
So 3. ... Nc3
Jack has done the rest.
Re: Evil endings that embarrass engines
OH Ok, I get it.
I tried the g4 idea too, but in a slightly different move order and it didn't work
I tried the g4 idea too, but in a slightly different move order and it didn't work
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Re: Evil endings that embarrass engines
3...Nc3 is an interesting try, and the drawbacks with 4.Kh1 is shown in the lines you give. I believe though that 4.Bc2 is a better defense. That allows 4...Na2 5.Bd3 Nb4 6.Bb1 Ke1 but I would like to know how to win that position? (My question was posted above).E Michael White wrote: Trying first to sit the N on d2:-
if the WK is on h1, WB on d3 , BK on f2, BN on d2 the Black g4 push, giving up the g and h if nec, breaks through.
the additional threat of trapping the WB on b1 with a BN on b4 wins a pawn if W prevents the Nd2 line
So 3. ... Nc3
Jack has done the rest.
Note that the 6-man tablebases are called "Nalimov" and are not particularly useful here because there are too many pawns on the board in most variations. Note also that the Nd2 idea was not part of my solution at all, quite possibly you have found something very useful, if 4.Bc2 is forced then Black can get the Nb4 idea in without first returning the knight to e6, then bring it over c5 to a6 and then to b4. So my congratulations for finding a different move order that quite possibly enriches this "study". It isn't really a study in the classic sense, because it wasn't composed as such, and just happened in one of my games (that ended up in a draw).
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Re: Evil endings that embarrass engines
One of the secrets of this ending is that winning the e-pawn by running for the bishop through e5 and fxe5 is just a draw:
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Re: Evil endings that embarrass engines
I agree that if Black sits, it's hard for White to make progress, but if Black tries to push for a win, I reckon White has the better winning chances. Once Black pushes his central pawns with king supporting, the queenside pawns become horribly vulnerable to attack, particularly after Black has played b5. He has to keep denying the White king and bishop entry squares/diagonals.Ray Sayers wrote: I think if Black just didn't want to lose he can play b5, f6, K to d6 and sit. Play e5+ if Kd4.
So Black seems to have at least a draw, so I would rather be Black! ('2 results').
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Re: Evil endings that embarrass engines
Another of the secrets of this ending is that Black can still make use of the trapped in bishop on b1, through "gaining the opposition" so to say, pushing the king back to h1 (which avoids the possibility of h3 being answered by Kxh3):
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Re: Evil endings that embarrass engines
The other branch is what happens with fxg4. I found that Black can win without giving up any more pawns, and the variations also looks "safe" to the human eye, e.g. it is unlikely that a defense will be found in these variations. The engines all prefer fxg4, perhaps because the bad effects of having the king entrapped in h1 appear outside their horizon:
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Re: Evil endings that embarrass engines
The last piece of evidence is whether the three healthy pawns can be used for any purpose in the hxg4 variation. Since e5 or g5 strengthen the black pawns (after fxe5 or fxg5) the most logical is to push h4 and then try to run with the king: