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Hot Topic (More than 10 Replies) very interesting endgame K+2N vs K+p (Read 8647 times)
IMJohnCox
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Re: very interesting endgame K+2N vs K+p
Reply #15 - 08/28/17 at 22:12:20
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Jonathan, I can answer your question (why isn't it a draw once the a-pawn crosses the Trotsky line?) to a certain extent. Trotsky himself wrote (p.246 of Chess Studies) that a pawn on a6 only draws if the king makes it to the 'no-mate zone', being h1-h3, h3-f5, f5-c5, c5-c3, c3-e1. Why that should be so I've no idea, but there it is. Somebody called Bolton contributed to this discovery in 1840 with a position showing the king getting mated if it was trapped near enough to the knight.

I never let the ending of 2N -v- P pass without repeating the wise words of a team-mate who reached it in a blitz finish and handled it quite impressively to get within a few moves of mating before losing on time thanks to the pawn he had been too proud to capture. When I offered my congratulations he replied along the lines of, 'It's not hard to play. You just play it positionally and don't get involved in the tactics.'

And who was the old-timer who thought for 45 minutes after the position arose and then raised his head from the board with the words, 'No, thankee. I'll take a draw.'? Another wise man - Seitz, was it, perhaps?
  
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Jonathan Tait
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Re: very interesting endgame K+2N vs K+p
Reply #14 - 10/29/16 at 09:32:01
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brabo wrote on 10/25/16 at 10:56:10:
The Lomonosov tablebases don't take the 50 moves rule into account. It is well possible to play a quicker losing move and get the 50 moves rule kick in.
I explained this in my article http://chess-brabo.blogspot.com/2013/10/iccf.html
Only a limited set of tablebases do consider the 50 moves rule. A summary you can find at http://chess.jaet.org/cgi-bin/compstatus

So the line given by Jonathan Tait does not give any guarantee that the startposition is a theoretical win for OTB.


Good point.

And given that the Troitsky Line is all about blockading the pawn, it'd be quite ironic if the only way to save the game is not to move it, even when released. Smiley
  

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Re: very interesting endgame K+2N vs K+p
Reply #13 - 10/25/16 at 20:44:00
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Ah, I see that Jonathan Tait and RdC already made that point. My apologies for piling on.
  
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Re: very interesting endgame K+2N vs K+p
Reply #12 - 10/25/16 at 20:42:06
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Some of you seem to be forgetting that the 50 move rule resets every time a pawn is pushed.

The tablebase may have a mate in 102, but that may be completely within the rules of the game for OTB chess.
  
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Re: very interesting endgame K+2N vs K+p
Reply #11 - 10/25/16 at 10:56:10
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The Lomonosov tablebases don't take the 50 moves rule into account. It is well possible to play a quicker losing move and get the 50 moves rule kick in.
I explained this in my article http://chess-brabo.blogspot.com/2013/10/iccf.html
Only a limited set of tablebases do consider the 50 moves rule. A summary you can find at http://chess.jaet.org/cgi-bin/compstatus

So the line given by Jonathan Tait does not give any guarantee that the startposition is a theoretical win for OTB.
  
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Re: very interesting endgame K+2N vs K+p
Reply #10 - 10/25/16 at 07:19:58
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Actually not, because White advanced the a-pawn at move 55.

So with a pawn move also at 100 and mate at move 102, a win even under OTB rules with exact tablebase play.


Entrapment is then exactly what happens and at the right time the pawn blocking knight hops in to deliver mate.

That's the standard method. I had to defend the ending of pawn against two Knights in the 4NCL once against Eddie Dearing. That was a straightforward example because the pawn started off being blockaded on e5 by Knights on e4 and e3. I can recall my King being forced to march down the h file to its demise on h1. A spectator described the h file as the valley of death.
« Last Edit: 10/25/16 at 14:13:40 by RdC »  
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Re: very interesting endgame K+2N vs K+p
Reply #9 - 10/24/16 at 23:16:26
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Hello.

Jonathan Tait wrote on 10/20/16 at 09:49:13:
On this theme, I recently had an endgame with king and two knights vs. king and three pawns.

Would be fun to play K+2N vs. K+3P over the board. With such non-natural technique there is much advantage in being abe to work things out in the peace of the home.

RdC wrote on 10/20/16 at 17:40:58:
Where does the defending King head to make the mate as long as possible?

So... I'm thinking... ummm... away from the knight blocking the pawn while not getting trapped on the rim.

For games where the strong side has managed to capture all pawns but a knight-blocked h-pawn or a-pawn (like in reply #4) what seems to happen is that with amazing king-knight teamplay the strong side eventually flanks the weak side king and forces him towards the knight blocking the rim pawn. When the weak side king reaches the general area where the strong side pawn blocking knight starts taking away squares from the weak side king there is little real choice but to dash for freedom. Alas the only route is via the rim of the board where the weak side king is in danger of being trapped. Entrapment is then exactly what happens and at the right time the pawn blocking knight hops in to deliver mate.

RdC wrote on 10/20/16 at 17:40:58:
Is there any hope of a fifty moves sequence without a pawn move or capture?

The endgame is complex so there will always be hope for dragging most endgames of this type past 50 (pawn move or capture free) moves in otb games. In correspondence chess the fifty move rule is, as mentioned, not relevant.

Jonathan Tait wrote on 10/21/16 at 06:54:17:
And in all that it lets the a-pawn beyond the Troitsky Line halfway through. Why isn't it a draw then? Huh

The king is trapped on the rim so there appears to be an effective herding technique because of this (see move 55-78 in reply 4).



Semi-topical:

Can't recall if this has been mentioned on chespub before but Kotronias actually recommended going into the following related endgame in His second Mar del Plata book (p.272):

It took not long for someone to check it with a 7-man tablebase and post the result on the QC blog.

Interestingly (at least how I saw it) was that the mating sequence posted on the QC-blog would have been fouled out due to the 50 move rule like a move or two before mate (as I recall). So there is a chance the line would have held in otb chess but not correspondence Roll Eyes.

Have a nice day.
  
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Re: very interesting endgame K+2N vs K+p
Reply #8 - 10/24/16 at 11:30:23
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RdC wrote on 10/22/16 at 08:08:17:
The end of that line has the King mated on a1. If that's the corner to avoid, the longest defence would be to avoid that corner.


Yes, that makes sense here, given that the a6-knight has three moves to mate before the new queen spoils it all.

RdC wrote on 10/22/16 at 08:08:17:
Whilst noting that different rules may apply in correspondence chess, it would have been claimable as a draw from move 62 under over the board (FIDE) rules.


Actually not, because White advanced the a-pawn at move 55.
  

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Re: very interesting endgame K+2N vs K+p
Reply #7 - 10/22/16 at 08:08:17
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Jonathan Tait wrote on 10/21/16 at 06:54:17:
I don't really understand why it gets trapped in some cases and not others. It looks totally random to me.


The end of that line has the King mated on a1. If that's the corner to avoid, the longest defence would be to avoid that corner. Whilst noting that different rules may apply in correspondence chess, it would have been claimable as a draw from move 62 under over the board (FIDE) rules. If neither player claimed, a watching arbiter, assuming there was one, could step in around move 87 under the more recent 75 move rule.

The more modern models of DGT will count the number of times they have been pressed, but you have to press a button to get it displayed. That's relevant with an increasing number of weekend tournaments and evening leagues using 10 or 15 second increments, when no score need be maintained once the time remaining runs under 5 minutes for the first time.
  
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Re: very interesting endgame K+2N vs K+p
Reply #6 - 10/22/16 at 06:40:25
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okay, thanks Smiley
  

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Re: very interesting endgame K+2N vs K+p
Reply #5 - 10/21/16 at 07:01:50
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Jonathan Tait wrote on 10/21/16 at 06:54:17:
I think FIDE changed the laws because of the Troitsky Line, but I don't know whether they're still in effect.

See https://en.wikipedia.org/wiki/Fifty-move_rule
" in 1992 FIDE abolished all such exceptions and reinstated the strict 50-move rule"
"A game is not automatically declared a draw under the fifty-move rule – the draw must be claimed by a player on his turn to move. Therefore a game can continue beyond a point where a draw could be claimed under the rule. Theoretically, a game could continue indefinitely this way, but in practice, when a draw under the fifty-move rule can be claimed, one of the players is usually happy to claim it (Hooper & Whyld 1992:134). In 2014 FIDE amended the rules to eliminate the possibility that a game could continue without end. Rule 9.6b states that if 75 consecutive moves have been made without movement of any pawn or any capture, the game is drawn unless the last move was checkmate."
  
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Re: very interesting endgame K+2N vs K+p
Reply #4 - 10/21/16 at 06:54:17
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RdC wrote on 10/20/16 at 17:40:58:
Where does the defending King head to make the mate as long as possible?


Playing through the longest lines, it seems the king just rushes about. I don't really understand why it gets trapped in some cases and not others. It looks totally random to me.



And in all that it lets the a-pawn beyond the Troitsky Line halfway through. Why isn't it a draw then? Huh

RdC wrote on 10/20/16 at 17:40:58:
Is there any hope of a fifty moves sequence without a pawn move or capture?


I think FIDE changed the laws because of the Troitsky Line, but I don't know whether they're still in effect.
  

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Re: very interesting endgame K+2N vs K+p
Reply #3 - 10/21/16 at 06:36:28
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RdC wrote on 10/20/16 at 17:40:58:
Jonathan Tait wrote on 10/20/16 at 09:49:13:
The endgame tablebase declares mate in 102 after 57...Kf3


Where does the defending King head to make the mate as long as possible? Is there any hope of a fifty moves sequence without a pawn move or capture?

The ICCF congress of 2013 decided that the 50-move rule is suspended when the TB are entered see https://www.iccf.com/Message.aspx?message=557

As I wrote in my article http://chess-brabo.blogspot.com/2013/10/iccf.html I am not pleased about that decision.
  
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Re: very interesting endgame K+2N vs K+p
Reply #2 - 10/20/16 at 17:40:58
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Jonathan Tait wrote on 10/20/16 at 09:49:13:
The endgame tablebase declares mate in 102 after 57...Kf3


Where does the defending King head to make the mate as long as possible? Is there any hope of a fifty moves sequence without a pawn move or capture?
  
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Re: very interesting endgame K+2N vs K+p
Reply #1 - 10/20/16 at 09:49:13
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On this theme, I recently had an endgame with king and two knights vs. king and three pawns.
The endgame tablebase declares mate in 102 after 57...Kf3, but we continued just because it was so unusual.



And I've blogged about it here:
http://200opengames.blogspot.co.uk/2016/10/002-skirting-troitsky-line.html
  

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very interesting endgame K+2N vs K+p
09/08/07 at 13:22:34
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Hello everybody!

I wanna to share with You this endgame which I first saw in "Fundamental Chess Endings"by Muller and Lamprecht.
  At first sight it's a bit surprising but King and two knights vs king+pawn could mate a king by force in some examples.When defender hasa pawn it can provide the desired tempi.The Russian theoretician Troitsky made a detailed study of this endgame and discovered the following rule:


Troitsky said:"If the pawn is securely blockaded by a white knights no further down than the line,then Black loses,no matter where the kinkg are."If the pawn has advanced beyond the line there is usually a drawing and losing zone for defending king.

Example:


The pawn has advanced beyond Troitsky's line(with the pawn on g6 and the knights on g5 and h3,the position would be lost no matter where the kings are),but Black's king is inside the losing zone.Before White can release the blockading knight he has to impose the black king on a1 and b1.

So:
1.Kc3! Kb1
1...Ka1 2.Kb3! Kb1 3.Nb2! Kc1 4.Kc3! Kb1 5.Nd3! Ka1 6.Kb4 Ka2 7.Ka4! Ka1 8.Ka3! Kb1 9.Kb3! +-
2.Kd2! Ka1 3.Kc1 Ka2 4.Kc2! Ka1 5.Kb3! Kb1 6.Nb2! Kc1 7.Kc3! Kb1 8.Nd3! Ka1 9.Kb4 Ka2 10.Ka4! Ka1 11.Ka3! Kb1 12.Kb3! Ka1 13.Ne3 g2 14.Nc2!+ Kb1 15.Na3!+ Ka1 16.Ne1!!(or 16.Nb4!)
Without the pawn Black would be stelmated,but now he can and must move.
16...g1Q 17.Nec2#!

This is an amazing chess problem(K+2N vs.K+p), I think it is one of the best,if someone is interested in this topic I may recommended following articles by Karsten Muller.
http://www.chesscafe.com/text/mueller35.pdf
http://www.chesscafe.com/text/mueller36.pdf
http://www.chesscafe.com/text/mueller37.pdf

Reference works:
Fundamental chess endings-Muller,Lamprecht
« Last Edit: 09/08/07 at 16:55:43 by Chwileulotne85 »  
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