Endgame riddle: The eternal duel - bishop vs knight

by Karsten Müller
4/15/2021 – The International Master Ole Jakobsen (19 October 1942 - 30 June 2010) from Denmark is not particularly well-known but from 1960 to 1980 he was one of the best players of his country and in 1969, 1971 and 1980 he won the Danish Championship. In 1973 he finished fourth in the IBM-B Tournament in Amsterdam, where he defeated Eugenio Torre, who was soon to become one of the world's best players, in an interesting endgame bishop versus knight. Karsten Müller has taken a closer look at this endgame and invites you to help analysing it.

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The eternal duel: bishop vs knight

Endgames in which the bishop fights against the knight – and vice versa – are often full of surprising subtleties. Often they are also complicated and not easy to understand. The following endgame, in which Black performs long manoeuvres with king and knight to win in the end, is a typical example. Was this win indeed forced or could White have saved himself, perhaps with the help of the 50-move rule?

The reader is invited to search for the truth about this endgame – could White have saved himself, and if so, when and how?

 

Share your analyses and findings in the comments!

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Karsten Müller, born 1970, has a world-wide reputation as one of the greatest endgame experts. He has, together with Frank Lamprecht, written a book on the subject: “Fundamental Chess Endgames” in addition to other contributions such as his column on the website ChessCafe as well as in ChessBase Magazine. Müller's ChessBase-DVDs about endgames in Fritztrainer-Format are bestsellers. The PhD in mathematics lives in Hamburg, where he has also been hunting down points for the HSK in the Bundesliga for many years.
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Karsten Müller Karsten Müller 4/20/2021 09:14
Charles Sullivan and malfa: Many thanks for your great work! I have sent Charles' solution to ChessBase for publication. A really amazing riddle with a very nice solution winning just in time!
malfa malfa 4/20/2021 02:32
Charles: Aaah! OK, now I understand the misunderstanding. I supposed we were still talking about the winning lines stemming from 70...Nh7, where only the Nc3-a2 manouvre appears and precisely at move 101. My reference to Na4 "as in the game" was actually confusing, but I didn't notice that in the game this very move was played precisely at move 102. Thanks for the corrections, so Jakobsen's planned manoeuvre against 103.Bc4, the improvement over the losing 103.Bb5? of the game, would have been as good as the other path above, with correct play by both sides. I mean: both insufficient after 80...Ka5? but both winning after the correct 80...Kc6 and both winning after 67...c5 and 70...Nh7.

The perspective of seeing "many many many more variations" somewhat terrifies me: rather than tons of moves, I largely prefer ideas, together with the minimum of calculations necessary to support them, but I am curious to see if further ideas will appear in addition to the many ones, hidden in this fascinating endgame, that I have already been acquainted with during the discussion ;-)
CharlesSullivan CharlesSullivan 4/20/2021 01:43
malfa:
By playing 80...Ka5, Black has lost two tempi, and that is enough to allow White to achieve a draw.
Here is your variation, with my added notes:
80...Kc6 81. Kd3 Kb5 82. Kc3+ Kc5 83. Kd3 Kb4 84. Be2 Ka3 85. Bd1 Kb2 86. Kd2 Ka1
87. Ke1 Ka2 88. Kd2 Kb2 89. Ke1 Kc3 90. Ba4 Kc4 91. Bd1 Kd3 92. Kf1 Kc3 93. Ke1
Nb5 94. Ke2 Na3 95. Kf1 Nc4 96. Ba4 Ne3+ 97. Kg1 Kd2 98. Bb5 Ke1 99. Bd3 Nd1
100. Bf1 Nc3 101. Bd3 Na4 102. Bc4 Nb6 103. Ba6 Na8 104. Bb5 Nc7
105. Bc4 (2 tempi better is 105. Bd7)
105... Ne8 106. Bb5 Nd6 107. Ba6 Nf7 108. Bb7 Ng5 109. Bc8 Ke2 110. Bg4 Nf7
111. Bc8 (2 tempi better are both 111. Bd7 and 111.Be6)
111... Nd6 (4 tempi better is 111... Nd8)
112.Ba6+ Ke1 113. Bd3 Nb7 114. Bb5 Na5 115. Ba4 Nc4 116. Bb5 Nd2 117. Ba6 Nb3 118.
Bc4 Nd4 119. Ba6 Kd2 120. Bc8 Ke3 (Here is where it gets tricky because
FinalGen does not consider the 50-moves rule. FinalGen considers 120...Ke3 a
co-optimal move, but when considering the 50-moves rule, a better move is
120... Ke2! 121. Bg4 Ke1! 122. Bh3 Ne2+ 123. Kh1 Kf2 124. Bc8 Nd4 125. Bg4
Nc2 126. Bc8 Ne1 127. Bh3 Nxf3-+) 121. Bg4 Ke2 122. Bh5 Ke1 123. Be8 Ne2+
124. Kh1 Kf2 125. Bd7 Nd4 126. Bg4 Nc2 127. Bh3 Ne1 128. Bg4 Nxg2-+.

So, as far as I can tell, 101...Na4 and 101...Na2 both allow Black to beat the clock on move 127. I believe the solution to our puzzle will be published shortly and then you will see many many many more variations!
CharlesSullivan CharlesSullivan 4/20/2021 12:52
malfa: You have confused me (it's easy to do). When you said "it is critical that the knight ... choose to start from a2 instead of a4 ***AS IN THE GAME** ..." -- emphasis added by me. So I found the position in the game where the knight landed on a4, which was move 102. Hence, I gave you that variation starting from 102...Na2. Having said that, I will now look at the variations you have just given me and give feedback in a few minutes (I hope!).
malfa malfa 4/20/2021 12:36
Charles: I notice that in this last variation the numbering of moves is increased by 1 with respect to the lines we have been discussing until now. I suppose it is because you have inserted 74.b8=D+ Kxb8 instead of having White directly play 74.Ba4-d1, haven't you? I ask this before providing my lines, in order to avoid confusion.

Under this hypothesis, this line is identical to the one you provided earlier and I see nothing wrong with it. If FinalGen considers 102...Na4 and 102...Na2 of equal value with respect to the 50-move rule, then there should be a mistake in what follows.

Here is what I analyzed when considering 80...Kc6 in lieu of the wrong 80...Ka5 played in the game. In the following lines the numbering of moves is again decreased by 1:

A) 101...Na4 102.Bc4 Nb6 103.Ba6 Na8 104.Bb5 Nc7 105.Bc4 Ne8 106.Bb5 Nd6 107.Ba6 Nf7 108.Bb7 Ng5 109.Bc8 Ke2 110.Bg4 Nf7 111.Bc8 Nd6 112.Ba6+ Ke1 113.Bd3 Nb7 114.Bb5 Na5 115.Ba4 Nc4 116.Bb5 Nd2 117.Ba6 Nb3 118.Bc4 Nd4 119.Ba6 Kd2 120.Bc8 Ke3 121.Bg4 Ke2 122.Bh5 Ke1 123.Be8 Ne2+ 124.Kh1 Kf2 125.Bd7 Nd4 126.Bg4 Nc2 127.Bh3 Ne1 128.Bg4 Nxg2

B) 101...Na2 102.Bb5 Nb4 103.Ba4 Na6 104.Bc6 Nc7 105.Bd7 Ke2 106.Bc8 Ne8 107.Ba6+ Ke1 108.Bf1 Nd6 109.Ba6 Nf7 110.Bb7 Ng5 111.Bc8 Ke2 112.Bg4 Nf7 113.Bd7 Nd6 114.Be6 Ke1 115.Bd7 Nc4 116.Bc8 Nd2 117.Ba6 Nb3 118.Bf1 Nd4
119.Ba6 Kd2 120.Bc8 Ke2 121.Bg4 Ke1 122.Bd7 Ne2+ 123.Kh1 Kf2 124.Bg4
Nd4 125.Bh5 Nc2 126.Bg4 Ne1 127.Bh3 ( 127.Bh5 Nxg2 )

Numbering apart, variation B should be exactly identical to yours. Following the evaluation of FinalGen, variation A should contain a mistake and be longer than necessary. If instead it is correct then it is enough to win after 80...Kc6 (instead of 80...Ka5? as in the game), since the last capture was made on move 78 by Black, but it is not after 70...Nh7, since there the last capture is made on move 78 by White.
CharlesSullivan CharlesSullivan 4/19/2021 11:13
malfa: FinalGen considers 102...Na4 and 102...Na2 as co-optimal and both are barely good enough to win:
102... Na2
103. Bb5 Nb4 104. Ba4 Na6 105. Bc6 Nc7 106. Bd7 Ke2 107. Bc8 Ne8 108. Ba6+ Ke1
109. Bb5 Nd6 110. Ba6 Nf7 111. Bb7 Ng5 112. Bc8 Ke2 113. Bg4 Nf7 114. Bd7 Nd6
115. Be6 Ke1 116. Bd7 Nc4 117. Bb5 Nd2 118. Ba6 Nb3 119. Bc4 Nd4 120. Ba6 Kd2
121. Bc8 Ke2 122. Bg4 Ke1 123. Bf5 Ne2+ 124. Kh1 Kf2 125. Bg4 Nd4 126. Bh5 Nc2
127. Bg4 Ne1 128. Bh5 (128. Bh3 Nxf3-+) 128... Nxg2-+
I'm curious -- do you see an improvement?
malfa malfa 4/19/2021 10:43
Charles: thanks again! Among the so many interesting points of this endgame, apparently it is critical that the knight, upon embarking on its long journey to the kingside and back, choose to start from a2 instead of a4 as in the game: according to my analysis, against the best defence it seems quicker by one decisive tempo!
CharlesSullivan CharlesSullivan 4/19/2021 10:11
malfa: Your analysis is correct(!), according to FinalGen.
malfa malfa 4/19/2021 09:35
No, wait! He can! I already noticed that after 113.Bc8 now Black plays 113...Nd8! instead of 113...Nd6 as after 113.Bd7, but if now White replies with 114.Bd7 (controlling both c6 and e6) I overlooked the simple waiting move 114...Ke1! after which the black knight will reach the key square d4 even quicker than after 113.Bd7. So I feel to confirm that 70...Nh7! is winning after all :-)
malfa malfa 4/19/2021 08:16
Karsten: 113.Bc8 appears to win at least two tempi over 113.Bd7, so Black cannot make it... Or he can?
Karsten Müller Karsten Müller 4/19/2021 08:08
malfa: We never could have enough of endgame analysis...
I have just mailed Charles.
malfa malfa 4/19/2021 07:53
Charles: thanks, but this is exactly the line I have problems with: what if White plays 113.Bc8 instead of 113.Bd7?
CharlesSullivan CharlesSullivan 4/19/2021 07:32
malfa: The winning line (starting with move 90) is: 90. Ba4 Kc4 91. Bd1 Kd3 92. Kf1 Kc3 93.
Ke1 Nb5 94. Ke2 Na3 95. Kf1 Nc4 96. Ba4 Ne3+ 97. Kg1 Kd2 98. Bb5 Ke1 99. Bd3
Nd1 100. Bf1 Nc3 101. Bd3 Na2 102. Bb5 Nb4 103. Ba4 Na6 104. Bc6 Nc7 105. Bd7
Ke2 106. Bc8 Ne8 107. Ba6+ Ke1 108. Bf1 Nd6 109. Ba6 Nf7 110. Bb7 Ng5 111. Bc8
Ke2 112. Bg4 Nf7 113. Bd7 Nd6 114. Ba4 Ke1 115. Bd7 Nc4 116. Ba4 Nd2 117. Bb5
Nb3 118. Bf1 Nd4 119. Ba6 Kd2 120. Bc8 Ke2 121. Bg4 Ke1 122. Bh3 Ne2+ 123. Kh1
Kf2 124. Bg4 Nd4 125. Bh5 Nc2 126. Bg4 Ne1 127. Bh5 Nxg2
malfa malfa 4/19/2021 05:52
It's been a pleasure and a challenge, but to me it is not over, as yet!
The good news is that finally I too have apparently been able to find a win after 80...Kc6, exactly at move 128 :-)
But, as we have established, White should have drawn around moves 73-74, so 67...c5 with 70...Nh7 was the really critical line for the evaluation of the whole B vs N endgame.
The bad news (for Black, of course) is that here I am apparently unable to find the win at move 127 by Black as in Charles's line on 4/18/2021 08:58, so am I still missing something? I manage one move later but, if I don't misunderstand the 50-move rule, by then White would have claimed the draw by the 50-move rule exactly at move 128, because the last capture was his (78.Bxc4), wouldn't he? Unless you two have had enough of it, I would post my evidence ;-)
Karsten Müller Karsten Müller 4/19/2021 09:29
Charles Sullivan and malfa: Many thanks for all the hard work day and night. So fortunately it looks very good for my conjecture...
malfa malfa 4/18/2021 10:29
Charles: many thanks! I suspect that the position I mentioned is so pivotal to any winning attempt that I would call it the Main Critical Position (or MCP for brevity) and I am trying to understand at which stage Black's play needs to be enforced, whether between the last capture (LC again for brevity) and this position, or from the latter to the end:

1. In this line it occurs 12 moves after the last capture and so Black is left with 38 more at his disposal to force the issue.

2. In my analysis of 67...c5 with 70...c4 (LC=72), the MCP occurs after 90.Ba4 i.e. no less than 18 moves after the LC, so Black is left with only 32 residual moves to win.

3. In my analysis of 80...Kc6 (instead of 80...Ka5? as in the game, see my post on 4/16/2021 01:05) the MCP occurs after 90.Ba4 (i.e. again 12 moves after LC, as in your line) so Black can count on exactly the same number of residual moves as in your line. Therefore it is sufficient that from the appearance of the MCP onwards Black play like in your line to prove that 80...Kc6 is also winning as Karsten says, isn't it? Anyway I still need to find out where exactly I went wrong in that stage of my analysis.
CharlesSullivan CharlesSullivan 4/18/2021 08:58
malfa: One variation I examined after 67...c5 and 70...Nh7 was 71.Be8 Ng5 72.Ba4 c4 73.b7 Kc7 74.Bd1 Kxb7 75.Kd2 Kb6 76.Kc3 Kc5 77.Be2 Ne6 78.Bxc4 Nd4 79.Bf1 Kb6 (transposes to game [see 79...Kb6]) 80.Kd2 Kc6 81.Kd3 Kb5 82.Kc3+ Kc5 83.Kd3 Kb4 84.Be2 Ka3 85.Bd1 Kb2 86.Kd2 Ka1 87.Ke1 Ka2 88.Kd2 Kb2 89.Ke1 Kc3 90.Ba4 [your requested position]. [So, move 90 & last capture at White's move 78, to answer your question.] Black requires all 50 moves to win: his 127th move is ...Nxg2. Hope that helps.
malfa malfa 4/18/2021 07:50
Charles: at present I can try an answer on purely positional grounds. Generally speaking, to break the enemy's pair of knights is not a bad idea, but here of course it directly plunges White into the (in)famous "bad bishop vs. good knight" scenario, whereas, as the saying goes, bishops are made to be exchanged with knights at the right moment ;-) Therefore I would intuitively blame such a decision, but frankly as yet I did not pay much attention to the previous phase of the game.

Regarding 70...Nh7, I have another question. Please consider the following position:

W. Ke1, Ba4, Pp. e4, f3, g2 - B. Kc3, Nd4, Pp. e5, f4, g3 (Black to move)

In the game it occurred after 88.Ba4. Following 70...Nh7, could you please indicate at which stage it arises in your winning line, and how far from the last capture?
Karsten Müller Karsten Müller 4/18/2021 07:34
Charles Sullivan: Many thanks! If this is true then I strongly conjecture that amazingly 66.Nc4+? is a losing mistake even within the limits of the 50 move rule. Chess really is a very deep game...
CharlesSullivan CharlesSullivan 4/18/2021 07:19
Karsten & malfa: After 67...c5 and 70...Nh7, I spent quite a bit of time trying to make a draw for White with 71.Ke1, but malfa is correct that 71.Ke1 eventually transposes to other losing variations. So my opinion today is that 67...c5 and 70...Nh7 leads to a win for Black. Next question: was White's 66.Nc4+ a mistake? Perhaps 66.Kd3 was more prudent?
Karsten Müller Karsten Müller 4/18/2021 03:59
Charles Sullivan: So it was a good choice as riddle. If everything is known by tablebase in advance the readers' ideas are not needed of course....
CharlesSullivan CharlesSullivan 4/18/2021 03:54
malfa (and others): Just a note: I generated a FinalGen endgame tablebase to help with analysis. Because of time & storage limitations, I generated a tablebase that includes only the kingside pawns -- so it was most useful after move number 78 (when the queenside pawns came off). It took 5 hours and 600 gigabytes to generate the tablebase. (Creating a tablebase that included the queenside pawns would have taken several days and and too many *terabytes*!) So, as we have found out, there is still room for discoveries between moves 66 and 78.
Karsten Müller Karsten Müller 4/18/2021 01:55
malfa: Yes. 80...Kc6 wins within the limits of the 50 move rule. This is still to be found.
And of course I am very curious if 70...Nh7 wins within the limits of the 50 move rule.
A really very deep example. Many thanks to Charles for suggesting it!
malfa malfa 4/18/2021 01:21
There is another question which remains unanswered, as far as I am concerned: Karsten claimed that after all Black had a "legal" win also in the game continuation if he had played 80...Kc6, whereas my (apparently) winning path starts much earlier. So Karsten's continuation is still to be found, at least by me, isn't it?
malfa malfa 4/18/2021 12:35
Charles: thanks again! As far as I understand, with FinalGen the difficulty lies in supplementing its own calculations with extra info connected with a change in the material situation, does it? If it is, then it is critical to decide when to push c4 in order to have the program start taking the 50-move rule into account.
CharlesSullivan CharlesSullivan 4/18/2021 02:46
malfa: You may be absolutely right about 71.Ke1. Perhaps your 67...c5 is a winner! (Still checking...)
malfa malfa 4/18/2021 01:19
Charles: thanks, but crossposting again! :-) As I wrote, after a deeper look I understood why FinalGem prefers 90...Kc4, but as you can see now I have another much bigger problem, I hope it will let me sleep tonight ;-)
malfa malfa 4/18/2021 01:16
Well, one last contribution for tonight, before falling asleep: after this incredible 71.Ke1 why should Black immediately play 71...c4? What's wrong with 71...Ng5, keeping one of the white pieces tied to the defense of the kingside? Now if 72.Ba4 Ne6 73.Kd2 Nd4 74.Bd1 Kc6 75.Kd3 Kxb6 76.Kc4 Kc6 didn't we transpose to the lines we evaluated as losing for White after my 71.Ba4? 72.Be2 Kc6 looks even worse. Basically White looks one full tempo down with respect to those lines, since he wasted time by retreating his king to e1. What am I missing?
CharlesSullivan CharlesSullivan 4/18/2021 12:56
malfa: In the 70...c4 variation you reference, FinalGen determines that 90...Kd3 is one move *less* optimal than 90...Kc4. After 90...Kd3, these optimal moves (according to FinalGen) 91.Bd1 Ke3 92.Kf1 Nb5 93.Ke1 Na3 94.Kf1 Kd3 95.Ke1 Kc3 96.Kf1 arrive at the same position (1 move later) as the 90...Kc4 ... 95.Kf1 variation. Of course, there are positions in most variations for which co-optimal moves exist. So far, I have found that FinalGen does an excellent job differentiating between 2 different moves. However, it is necessary to supplement FinalGen with computer computation about 40 moves into the 50-moves rule because of possible sacrificial combinations.
malfa malfa 4/18/2021 12:39
CharlesSullivan: GOSH! Our messages crossed each other again! Not exactly the good news I had just hoped for, but thanks again... As a meager consolation, you confirm a conclusion I reached on my own when analyzing 71.Be8: I reverted my attention to 71.Ba4 precisely because I evaluated the former as losing. Now I need to give another fresh look to the position, since 71.Ke1 didn't even cross my mind. But I leave it for tomorrow ;-)
malfa malfa 4/18/2021 12:30
OK, I had a bit deeper look and now I understand the program's "point of view" on 70...c4. After his 101.Bd3 the position is identical to the one after 102.Bd3 in the game, but FinalGen at that stage has only 21 moves left to avoid the 50-move rule, while Jakobsen had 26. The difference lies in the path they followed to reach the position after 79.Bf1 and, respectively, 79.Kc3: the program took 7 moves to get there after the last capture (72...Kxb7), while the human only 1 after 78...Kxc5, so I am afraid that this is a very solid reason why 70...c4 cannot be an improvement over Jakobsen's way of dealing with the 50-move rule. Roughly speaking, this is consistent with the common-sense practice of keeping in reserve as much pawn pushes as possible in a superior endgame. Under this respect, Charles's follow-up to 70...Nh7 looks indeed promising, given that the last pawn push is needed not earlier than at move 90. Waiting for further news about 70...Nh7, hopefully good ones...
CharlesSullivan CharlesSullivan 4/18/2021 12:15
After 67...c5 68.b5 Ne8 69.b6 Nf6 70.Bb5 (suggested by malfa") 70...Nh7 (suggested by Karsten), we have seen in an earlier post that
[A] malfa's 71.Ba4 Ng5 72.Bd1 Kc6 73.Kd3 Kxb6 74.Kc4 Kc6 75.Ba4+ Kd6 76.Bd1 Ne6 seems to lose.
Zoran Petronijevic suggested [B] 71.Be8 Ng5 72.Ba4 c4 73.b7 Kc7 74.b8=Q+ Kxb8 75.Bd1 Kc7 76.Kd2 Kc6 77.Kc3 Kb5 78.Be2 Kc5 79.Bf1 Ne6 80.Bxc4 Nd4 81.Bf1. The problem with this position is that we have transposed back to the game [see 79.Kc3]. In the game, Black fell into a draw position by losing 2 tempi with 80...Ka5(?). From this position (after 81.Bf1), Black wins if he avoids mistakes.
[C] 71.Ke1 -- fantastically?!!? -- seems to draw. If you cannot improve upon 71...c4 72.b7 Kc7 73.b8=Q+ Kxb8 74.Bxc4, then FinalGen says: 74...Kc7 75.Bg8 Ng5 76.Ba2 Kd6 77.Bg8 Kc5 78.Ke2 Kd4 79.Ba2 Kc3 80.Bg8 Kc2 81.Bc4 Nh7 82.Ba6 Kb2 83.Bc4 Kc3 84.Ba6 Ng5 85.Bc8 Kc2 86.Ke1 Kd3 87.Bg4 Nf7 88.Bc8 Ke3 89.Kf1 Nd6 90.Ba6 Kd2 91.Be2 Nb7 92.Ba6 Nc5 93.Bc4 Na4 94.Ba6 Nc3 95.Be2 Kc2 (95...Nxe2= STALEMATE) 96.Ke1 Kc1 97.Bd3 Nd1 98.Kf1 Ne3+ 99.Kg1 Kd2 100.Ba6 Ke1 101.Bd3 Nd1 102.Bf1 Nc3 103.Bd3 Na4 104.Bc4 Nb6 105.Ba6 Na8 106.Bb5 Nc7 107.Bd7 Ke2 108.Bc8 Ne8 109.Ba6+ Ke1 110.Bb5 Nd6 111.Ba6 Nf7 112.Bb7 Ng5 113.Bc8 Ke2 114.Bg4 Nf7 115.Bd7 Nd6 116.Be6 Ke1 117.Bd7 Nc4 118.Bc8 Ne3 119.Bh3 Nf1 120.Bd7 Nh2 121.Bh3 Ke2 122.Bg4 Kd2 123.Bh5 Ke3 124.Bg6=. White claims a draw because of the 50-moves rule, even though Black is ready to play 124...Nxf3+ [which would have been a win for Black].
Summary: No win for Black at move 67 (pending further discoveries, of course!).
malfa malfa 4/17/2021 11:26
CharlesSullivan: thanks for your input. Going back to FinalGen's line after 70...c4, one thing which strikes me is why the program plays 90...Kc4 instead of the direct 90...Kd3. Isn't this a whole tempo lost? If it is, I would go on carefully checking all the rest.
CharlesSullivan CharlesSullivan 4/17/2021 10:03
malfa: I agree that after 67...c5 and 70...Nh7, your variation 71.Ba4 Ng5 72.Bd1 Kc6 73.Kd3 Kxb6 74.Kc4 Kc6 75.Ba4+ Kd6 76.Bd1 does seem to lose after 76...Ne6. My computer then continues (3 hours 23 minutes, depth=58, -14.02) with 77.Kd3 Kc6 78.Kc3 Nd4 79.Kc4 Kd6 80.Kd3 Nb5 81.Bb3 Na3 82.Kc3 Kc6 83.Ba4+ Kb6 84.Kb3 Nb1 85.Kc2 Ka5 86.Bd7 Na3+ 87.Kb3 Nb5 88.Kc4 Nd4 89.Bg4 Kb6 90.Kd5 c4 91.Kxc4. This is the same position that you reached in your analysis after 92.Kxc4. FinalGen then says 91...Kc6 and mate in 49.
(I will post more 70...Nh7 analysis shortly...)
malfa malfa 4/17/2021 07:36
CharlesSullivan: sorry, I posted my previous message before noticing yours! Checking your analysis of 70...c4 developments...
malfa malfa 4/17/2021 07:27
KM: OK, meanwhile maybe I have found a way also here: after 76.Bd1 Ne6 77.Bc2 Nd4 78.Bd1 Black may win an important tempo with 78...Kc6 79.Ba4+ Kc7! and then exploit it in the next moves by means of an acrobatic knight tour: 80.Bd1 Kd6 81.Kd3 Nb5 82.Bb3 (82.Kc4 Na3+! 83. Kb3 c4+!! 84.Kxa3 Kc5-+ is the tactical point: Black after all manages to evict the enemy king from the c4 square and combines a king penetration on the kingside with the threat to push his 'c' pawn) Na3! 83.Kc3 Kc6 84.Ba4+ Kb6! 85.Kb3 Nb1 86.Kc2 Ka5! 87.Bd7 Na3+ 88.Kb3 Nb5 89.Kc4 Nd4 90.Bg4 Kb6 91.Kd5 c4! 92.Kxc4 Kc6 93.Kd3 Kc5 94.Kc3 Nb5+ 95.Kd3 Kb4 96.Kd2 Nd4 97.Bh3 Kb3 98.Kd3 Nc2 and eventually the black pieces infiltrate into the enemy lines. In short, if this line holds, after 67...c5 both 70...c4 and 70...Nh7 should win for Black.
Karsten Müller Karsten Müller 4/17/2021 07:27
Many thanks Charles! I am already very curious, if 70...Nh7 wins...
CharlesSullivan CharlesSullivan 4/17/2021 07:01
malfa: So many interesting ideas! However, it looks like 70...c4 (after 67...c5!) does not win, according to FinalGen. Here is a "best play" line:
67...c5 68.b5 Ne8 69.b6 Nf6 70.Bb5 c4 71.Bxc4 Kc6 72.b7 Kxb7
(Now move 122 is key for the 50-moves rule.) 73.Bd3 Kc6 74.Kd2 Kc5
75.Kc3 Nh7 76.Bc2 Ng5 77.Bd1 Ne6 78.Be2 Nd4 79.Bf1 Kb6 80.Kd2 Kc6 81.Kd3 Kb5
82.Kc3+ Kc5 83 Kd3 Kb4 84.Be2 Kb3 85.Bd1+ Kb2 86.Kd2 Kb1 87.Be2 Ka2
88.Bd1 Kb2 89.Ke1 Kc3 90.Ba4 Kc4 91.Bd1 Kd3 92.Kf1 Kc3 93.Ke1 Nb5 94.Ke2 Na3
95.Kf1 Nc4 96.Ba4 Ne3+ 97.Kg1 Kd2 98.Bb5 Ke1 99.Bd3 Nd1 100.Bf1 Nc3
101.Bd3 Na2 102.Bb5 Nb4 103.Ba4 Na6 104.Bc6 Nc7 105.Bd7 Ke2 106.Bc8 Ne8
107.Ba6+ Ke1 108.Bf1 Nd6 109.Ba6 Nf7 110.Bb7 Ng5 111.Bc8 Ke2 112.Bg4 Nf7
113.Bd7 Nd6 114.Be6 Ke1 115.Bd7 Nc4 116. Bc8 Nd2 117.Ba6 Nb3 118.Bf1 Nd4
119.Ba6 Kd2 120.Bc8 Ke2 121.Bg4 (not 121.Ba6+?? Ke3 122.Bc8 Nxf3+-+) 121...Ke1
122.Bd7 (Now Black's last chance under the 50-moves rule is) 122...Nxf3+
123.gxf3 Ke2 124.Kg2= DRAW.
But 67...c5 and later 70...Nh7 has great promise. I am currently looking at your idea of 71.Ba4 to see if White can hold. I will post analysis as soon as I can....
Karsten Müller Karsten Müller 4/17/2021 04:35
malfa: Many thanks! I will have a look and have also asked Charles Sullivan and Zoran Petronijevic.
malfa malfa 4/17/2021 04:29
KM: well, 70...Nh7 is natural and actually was my first try, but the difference is that it allows White an amazing opportunity to activate his king, though at the cost of his golden passed pawn: namely 71. Ba4! Ng5 72.Bd1! Kc6 73.Kd3 Kxb6 74.Kc4 Kc6 75.Ba4+ Kd6 76.Bd1, when the black king is constantly tied to the defence of the Pc5 and of the invasion square on d5, and I see no way to remove the white king from his blockading square. Instead after 70...c4!! White cannot transfer his king so readily: 71.Kd2 Ng4!! when 72.Bxc4 Ne3 73.Bd5 Nxg2 is hopeless. And on 71.b7 (or directly 71.Bxc4 for what it matters) there follows 71...Kc7 72.Bxc4 (or 72.Bc6 Nh7 73.Bd5 Ng5 74.Bxc4 Kxb7 75.Bg8 Kc6 and though Black's knight cannot move, Zugzwang allows his king to penetrate after 76.Ke1 Kc5 77.Ke2 Kd4-+) 72...Kxb7 73.Kd2 Kc6 74.Kc3 Kc5 75.Be2 Nh7 76.Bd1 Ng5 77.Be2 Ne6 78.Bd1 Nd4 79.Kd3 Kb4 80.Kd2 Kc4 81.Be2+ Kb3 reaching the same position which occurred in the game after 85...Kb3, but no less than 4 moves earlier.