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Mar0917
  KEG: <beatgiant> Your line seems the most promising for Black, but I still don't see anything approaching a win. If 42. Bd5 Rdc8 43. Bb3 Rc1 44. Rd2 Rg1 (maybe 44...Rf1 is a good alternative) White still seems fine after 45. Kf4 (or perhaps 45. Kf3) and if 45...Rcc1 then 46. Kg3 appears to hold everything for White. A tough position to be sure, butat least in theoryBird might have been able to hold the game. 

Mar0917
  beatgiant: <KEG>
Continuing from your suggested line, it might go 42. Bd5 Rdc8 43. Bb3 Rc1 44. Rd2 Rg1 45. Kf4 Rcc1 43. Kg3 Rce1 44. Bd5 (because 44. Rd4 Re2) Kd6. Now Black is planning to maneuver ...Ke5, ...Re3+, ...Rge1 eventually ...Kf4. After that, White's king is in a box and the gpawn is hard to defend. How does White prevent that plan while also avoiding a rook trade? click for larger view 

Mar0917
  KEG: <beatgiant> Continuing your line, after 42. Bd5 Rdc8 43. Bb3 Rc1 44. Rd2 Rg1 45. Kg3 Rce1 White seems to have a draw with 46. Ba4 and if 46...Rxe4 47. Bc6 with perpetual check. Am I missing something?
I'm not sure that 46. Bd5 loses, but it appears definitely inferior to 46. Ba4. That may be the move that gets White in trouble in your line. As you say, this is a fascinating ending, and you have identified Black's best chance of seeking a win. As of now, however, I still think White can save the game with best play. 

Mar1017
  beatgiant: <KFG>
I'm not seeing the perpetual check after 42. Bd5 Rdc8 43. Bb3 Rc1 44. Rd2 Rg1 45. Kg3 Rce1 46. Ba4 Rxe4 47. Bc6 Re3+ 48. Kf2 Rge1 49. Rd7+ Kf8 and now the checks end after 50. Rd8+ <Kf7> 51. Rd7+ Re7 52. Bd5+ Ke8, etc.But it's true White could simply grab the apawn in this line with <50. Rxa7>. It's hard to imagine Black could still win the ending after that. So this whole ending requires further investigation. 

Mar1017
  Straclonoor: Fast look on position after 41 moves by Stockfish gives:
Stockfish 090317 64 BMI2 0.58 (depth 30) 42.Bd5 Kd6 43.Kf4 Rc1 44.Rd2 Kc5 45.a3 Rd7 46.Kf3 Kb6 47.Ke3 Re1+ 48.Kf3 Rf1+ 49.Ke3 Rc1 50.Kf3 a5 51.Rd3 Rc2 52.Rb3+ Kc5 53.Rb8 Rc7 54.Be6 a4 55.g3 Kd6 56.Rb4 

Mar1117
  KEG: <beatgiant> Thank you for your correction to my analysis. You are correct that there is no perpetual, but I still think White has a draw in your line. Giving the line again (we both omitted a move) after 42. Bd5 Rdc8 43. Bb3 Rc1 44. Rd2 Rg1 45. Kf4 Rcc1 46. Kg3 Rce1 47. Ba4 Rxe4 48. Bc6 Re3+ 49. Kf2 Rge1 50. Rd7+ Kf8 I think White is just fine after 51. Rd8+ Kf7 52. Bb5 (though, as you rightly point out, there is no perpetual). I am not so sure about your suggestion that White could also survive by grabbing the apawn with 51. Rxa7. since Black's Rooks may now be able to make serious trouble for White with 51...R1e2+. White may indeed be able to survive in this line as well, but I would want to play either 51. Rd8+ and then 52. Bb5 to stop the check on e2 (or perhaps 51. Bb5 immediately). Your final assessment definitely seems correct. This ending requires (and well warrants) further investigation. Thank you for your thoughts on this fascinating endgame! 

Mar1117
  KEG: <Straclonoor> Your line beginning with 42...Kd6 looks to be about as promising a line for Black to seek a win as the immediate 42...Rc1 beatgiant and I have been considering. In both lines, it seems clear that Black has the only real winning chances but I have (at least provisionally) concluded that White can survive with careful play. I don't have Stockfish, so I would be interested in any deeper analysis you are able to provide. beatgiant and I agree that this ending needs further analysis to determine whether Bird could have saved the ending. 

Mar1717
  beatgiant: <KFG>
Perhaps an easier question is whether, as you suggested above, <Bird could probably have held the position with 44. e5>To me, it looks pretty grim after 44. e5 Rf1+ 46. Ke4 Rg3. The g4 pawn will fall, and soon one or two other kingside pawns, and I do not find sufficient counterplay with the passed epawn after <47. e6>. What am I missing? 

Mar2017
  beatgiant: <KFG>
Also, you suggested <Bird would have been fine with 43. Kf2.> After 43. Kf2 <Rd4>, Black threatens to advance his king with ...Kd6, ...Ke5. After 43. Kf2 Rd4 44. Ke3 Rb4, now 45. Rd2 would be answered by ...Re1+ picking up the epawn, but otherwise I don't see how to prevent Black from advancing his king. What did you see there to believe <Bird would have been fine>? 

Mar2117
  KEG: <beatgiant> ,Perhaps an easier question is whether, as you suggested above, <Bird could probably have held the position with 44. e5>
To me, it looks pretty grim after 44. e5 Rf1+ 45. Ke4 Rg3. The g4 pawn will fall, and soon one or two other kingside pawns, and I do not find sufficient counterplay with the passed epawn after <46. e6>. What am I missing?> I certainly agree that in your line 46. e6 is hopeless. The question is whether Bird could have survived with the better 46. exf6+ Kxf6 47. Kd5 Rxg4 48. Bc2. But the more I look at this, it looks as if Lasker would have been able to win with 48...Rb4 49. b3 Rb5+ While I am not certain, it does indeed seem that 44. e5 would probably not have saved the game for Bird. Thank you for your excellent analysis! 

Mar2117
  KEG: <beatgiant> I still do not see a winning line for Lasker after 43. Kf2. If 43...Rd4 44. Ke3 Rb4 45. Bb5 seems to hold since now Re1+ will not pick up the e pawn. How would Lasker have made headway here? 

Mar2117
  beatgiant: <KFG>
43. Kf2 Rd4 43. Ke3 Rb4 <45. Bb5>I assume this is a misprint for <45. Bd5> since the bishop can't reach b5 and anyway would get captured there. Here's a diagram:
43. Kf2 Rd4 43. Ke3 Rb4 44. Bd5
click for larger viewBlack's strategic threat is to advance the king to e5 leading to situations such as described in my posts above on Mar917. But it's true White has a lot of resources against the simple and obvious approaches. For example 44...Kd6 <45. Rd2> prevents 45...Ke5?? 46. Bc4. Or if Black prepares with 44...Rd1, White jumps to the cfile <45. Rc2> with annoying counterplay. So Black has to do a lot of preparatory maneuvering first, and the resulting situations are similar to those occurring after <42. Bd5> as we discussed above. I haven't found a definite win yet, but at least Lasker could torture White's position for quite a while. 

Mar2117
  KEG: <beatgiant> Yes, I meant to say 45. Bd5 as you correctly surmised. Sorry for the misprint. I agree with your final assessment. This is indeed similar to the positions occurring after 42. Bd5. Lasker could certainly have made life tough for Bird butlike youI have found no win. Interesting endgame. Thank you so much for your thoughts. PS I am "KEG" not "KFD." 

Mar2217
  Straclonoor: Here two lines on 43 move
Stockfish 180317 64 BMI2 0.75 (depth 32) 43.Bd5 Rdc8 44.Bb3 Rf1 45.Rd2 Rcc1 46.Rd4 a5 47.Ra4 Rc5 48.Rd4 Rb1 49.Be6 Rc7 50.Rd2 Rf1 51.Rd5 Re1+ 52.Kf3 Rb1 53.Rd2 a4 54.Ke2 Rg1 55.Kd3 Rf1 56.b3 a3 57.Bc40.93 (depth 32) 43.Kf2 Rd3 44.Bc2 Rd4 45.Ke3 Rb4 46.Bb3 Rb1 47.Kf3 a5 48.e5 a4 49.exf6+ Kxf6 50.Re6+ Kf7 51.Bd5 Kf8 52.Ra6 R1xb2 53.Be6 Rc2 54.Kg3 Rc7 55.Kh4 Ke7 56.Kh5 Rc2 57.g5 As seen, in first line position at the end closed and anclear, in second  more favorable for black 

Mar2217
  Straclonoor: After 45 moves no chances to escape for white.
Stockfish 180317 64 BMI2 2.22 (depth 37) 45.Ba4 Rde3 46.Bb5 Rxe4+ 47.Kg3 R4e3+ 48.Kh2 Re5 49.a4 R1e4 50.Kh3 Rd4 51.Rc2 Kd8 52.b3 a5 53.Bc4 Ree4 54.Be6 Rxg4 55.Rc3 Rg5 56.Rc5 Rd3+ 57.Kh2 Rdg3 58.Bd5 R3g42.75 (depth 37) 45.Bd5 Red1 46.Rf3 R3d2 47.g3 Rd3 48.Rxd3 Rxd3 49.b3 Kd6 50.a4 Rd2 51.Kf3 Rc2 52.Bf7 Ke5 53.Bd5 Rc3+ 54.Kg2 Kd4 55.Kf2 Rd3 56.Kg2 Ke3 57.Kh3 Rd1 58.Kg2 Rc1 2.77 (depth 37) 45.Bc4 Rd4 46.Bd5 Red1 47.Rf3 R4d2 48.g3 Rd3 49.Rxd3 Rxd3 50.b3 Kd6 51.a4 Rd2 52.Kf3 Rc2 53.Bf7 Kc5 54.Bc4 Rc3+ 55.Kg2 Kd4 56.Bd5 Rd3 57.Bc4 Re3 58.Bd5 Rc3 2.77 (depth 36) 45.Bg8 Rd4 46.Bd5 Red1 47.Rf3 R4d2 48.g3 Rd3 49.Rxd3 Rxd3 50.b3 Rd2 51.a3 Kd6 52.Ke3 Ra2 53.a4 Rg2 54.Kf4 Re2 55.Be6 Kc5 56.g5 hxg5+ 57.Kf3 Rc2 58.Bd5 Kd4 

Mar2217
  KEG: <Straclonoor> Thank you for this superb analysis. I think you have answered the question beatgiant and I have been pondering. 

Mar2317
  Straclonoor: <KEG> You are welcome!
I took a look on the game one more time and find one interesting point.
Why Lasker on 28th move exchanged bishop on knight? I gave this position to Stockfish here is result Stockfish 180317 64 BMI2
0.34 (depth 28) 28...Qe5 29.b3 Rd7 30.a4 Bxd5 31.Bxd5 Rc8 32.Bc4 Rd4 33.g4 Re8 34.Kf3 Re7 35.g3 a5 36.g5 hxg5 37.Qxg5 Rxe4 38.Qxe7 Qxe7 39.Rxe4 Qf6 40.Rf4 Kf8 41.g4 Qc3+ 42.Ke2 Qg3 0.31 (depth 28) 28...Rd7 29.Re2 a5 30.Qb6 Bxd5 31.Qxd6 Rxd6 32.Bxd5 Rc8 33.Kf3 Kf8 34.Re3 Rb6 35.Re2 Ke7 36.g4 Rb4 37.Rd2 a4 38.Kf4 Kf6 39.a3 Rb5 40.g3 Rcc5 41.e5+ Ke7 42.Ke4 Rc1) 0.27 (depth 28) 28...a5 29.Rd1 Qe5 30.b3 Bxd5 31.Bxd5 Rc8 32.Bc4 Red8 33.Rxd8+ Rxd8 34.Kf3 Qa1 35.Qe2 Rd4 36.Qe3 Qd1+ 37.Be2 Qd2 38.Bc4 Rd8 39.a3 Qc2 40.a4 h5 41.Bd5 Qd1+ 42.Qe2 Qxe2+ 0.15 (depth 27) 28...Ba8 29.Rd1 Rc8 30.b3 Qa3 31.Nc3 Red8 32.Re1 Qd6 33.g4 Qe5 34.Nd5 Re8 35.Nc3 Rcd8 36.Bd5 Bxd5 37.exd5 Qxe3+ 38.Rxe3 Kf8 39.Rxe8+ Kxe8 40.Ke3 Rb8 41.Ne4 Kd7 42.Kd4 Rb4+ There are no suggestions on 28....Bxd5 in four (!) lines. Bird doesn't used this weak move for avoid lost. Also I find interesting 'antianalogy'  Lasker vs Bird, 1890  were Bird had real chances to win but skipped its. 

Mar2617
  KEG: <Straclonoor> Thank you for this additional analysis. 28...BxN or 28...Qe5 seem best for Lasker. As Stockfish has confirmed, Lasker did not have anything approaching a win at this stage. As you have shown, Lasker didn't have anything approaching a win before Bird's 43. Kf4, and Bird was probably not lost until his weak 44. Rf2. Thank you for your valuable contribution to the discussion with beatgiant concerning this fascinating game. 

Mar2617
  beatgiant: <Straclonoor>
Here's a diagram for the end of the Stockfish line you posted above and assessed as <closed and unclear>(after 43.Bd5 Rdc8 44.Bb3 Rf1 45.Rd2 Rcc1 46.Rd4 a5 47.Ra4 Rc5 48.Rd4 Rb1 49.Be6 Rc7 50.Rd2 Rf1 51.Rd5 Re1+ 52.Kf3 Rb1 53.Rd2 a4 54.Ke2 Rg1 55.Kd3 Rf1 56.b3 a3 57.Bc4) click for larger viewIt's a long line, but plausible enough so let's start from here. I think Black has strong winning chances. Besides the old strong point at e5, Black has a new one on b2. Let's say Black now tries ...57. Rd7+ 58. Bd5 Rc1 59. Ke3 Rb1 60. Kd3 Kd6. How does White manage to cover both Black's strategic threats (advance king to e5 and beyond, play ...Rb2) while also avoiding an exchange of rooks? 

Aug0617
  offramp: <KEG: <Straclonoor> ...I think you have answered the question beatgiant and I have been pondering.> Are you pondering what I'm pondering? 

Aug0917
  KEG: <beatgiant> Thank you for your further analysis. Sorry for my delay in responding but I only just saw your March 26 post yesterday. I see no win for Black in the extended line you give. After 60...Kd6, White seems to hold on with 61. Kc2 Rb2+ 62. Kc3 and now if: A) 62...RxR 63. KxR Ke5 64. Ke3 (with g3 to follow) B) 62...Rc7+ 63. Bc4+ RxR 64. KxR Ke5 65. Ke3
But there may be a problem earlier in Straclonoor's line that I had overlooked before. After 55. Kd3 Rcc1 looks deadly. The saving move for White may therefore be 55. Ke3 (since 55...Rcc1 can now be answered with 56. Rd7+. In all these lines, White is holding on by a thread. But I still can't find a winning plan for Black. 

Aug0917   Boomie: <offramp: Are you pondering what I'm pondering?> I'm guessing he's a quarter ponder with cheese. 

Aug1017
  Straclonoor: <beatgiant> I take position from your post as initial for analysis.
Here is results
Stockfish 060817 64 BMI2
A. 1.31 (depth 33) 57...Rf4 58.g5 hxg5 59.Ke3 Rh4 60.Rd1 Rc8 61.Rc1 Rhh8 62.Rd1 Rhd8 63.Rc1 Kd6 64.Kd4 Rc7 65.Rh1 Kc6+ 66.Ke3 Kc5 67.Rc1 Kb4 68.Ke2 Rh8 69.Ke3 Kc5 70.Bd5+ Kd6 71.Bc4 Ke7B. 1.30 (depth 33) 57...Rd7+ 58.Bd5 Rc7 59.Bc4 Rf4 60.g5 hxg5 61.Ke3 Rh4 62.Rd1 Rc8 63.Kf3 Rh2 64.Re1 Rc5 65.Rd1 Rh8 66.Ke3 Rcc8 67.Re1 Rhd8 68.Rc1 Kd6 69.Kd4 Rc7 70.Rh1 Kc6+ 71.Kc3 Kc5 It's easy to see that final positions in both variations are closer to initial:))) 

Jul0820   iron john: what if 28 e5 ? 

Jul0820   sneaky pete: If 28.e5 Bxd5 wins. 


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