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1. d5!, exd5 (white's pawn can't be taken by black King, only by black pawn, which then blocks the diagonal h1-a8 - important later) 2. a6, Kc6 3. a7, Kb7 4. Ke3, h5 5. Kd4, h4 6. Kc5! (leaving black pawn on the same spot, thus blocking the diagonal h1-a8 - important later), h3 7. Kd6, h2 8. a8Q+, Kxa8 9. Kc7, h1Q 10. b7+ (effect of white's moves 1 and 6 - the pawn on b7 can't be taken by black Queen on h1), Ka7 11. b8Q+, Ka6 12. Qb6#
a6 Kc6a7 Kb7Kf3 h5Ke4 h4d5 d5Ke5 h3Kd6 h2A8=Q Ka8Kc7 h1=Qb7 Ka7b8=Q Ka6Qb6
It seem that the correct winning line is 1. a6, Kc6 2. a7, Kb7 3. Kf3, h5 4. Ke4, g4 (4. - , h4 5. d5, exd5+ 5. Ke5, h3 6. Kd6, h2 7. a8+, Kxa8 8. Kc7, h1Q 9. b7+, Ka7 10. b8+, Ka6 11. Qb6#) 5. Ke5, g3 6. Kd6, g2 7. a8Q+, Kxa8 8. Kc7, g1Q 9. b7+, Ka7 10. b8Q+, Ka6 11. Qb6#
This is hard.
Instantly this looks like dead draw, since white can't sweep up g+h pawns but his king must go there and immobilize them if they move, black can't sweep up a+b pawns but his king must go there and immobilize them if they move, neither d or e pawn will be mobile, and both kings will have 2 or 3 fields to frequent, no zugzwang occurs.The trick here must be very well hidden....
My instincts told me that the first move should be a6 to be followed a7 tying the black king to b7/a8 permanently (as far away from the center as white can push black's king). However, I really didn't seem the main theme until I had played through some the variations we will see below. However, let's digress from that plan to see why the seemingly similar plan of b7 and a6 fails to win:1. b7 Kc7 (forced)2. a6 h5I think in this position, black probably has a lot of drawing moves, but this one is by far the clearest in my head and aligns with the same instincts that tell me 1.a6 was the correct first move. Basically, black is going to push his own advanced connected passers tying down the white king permanently to preventing a black queen forming at h1 or, even, g1. Continuing:3. Kf3 h4 (Kb8 ok too, I think)4. Kg4 Kb8And neither player can afford to push the center pawns since doing so creates the decisive passer. So the kings end just guarding against the other's pawns and we will eventually get a draw by repetition. Now, white might think to go gather up the center black pawn by playing 4.Ke4 instead of 4.Kg4, and then marching the king over to the queen side and threatening some sort of push, but there is just isn't time:4. Ke4 h35. Kf3 or lose.Now, let's see why a6 might be better:1. a6 Kc6 (forced)2. a7 Kb7 (forced)3. Kd3White's plan is going to put the king on d6 and then push a8Q with check followed by b7 with check and b8Q. For example:3. .....h5 (too slow)4. Kc4! h4 (or g4 now)5. d5! ed5 (h3 is too slow, too)6. Kc5!Important to note that white will lose if he retakes the pawn: [6.Kd5?? h3 7.Kd6 h2 8.a8Q+ Ka8 9.Kc7 h1Q covers b7 now]. White needs black to retain the d5 pawn so that newborn h1 queen will not have cover on b7 at the critical moment, and if black takes the time to push d4, he loses the tempo needed to queen the h-pawn in time:6. .....h3 (or d4 loses too)7. Kd6 Kb6Or get mated [7. ...h2 8.a8Q Ka8 9.Kc7 h1Q 10.b7 Ka7 11.b8Q Ka6 12.Qb6#]. Continuing:8. a8Q h2 (lost anyway)9. Qc6 with mate to follow in another 2 moves.So, back at move 3 in the line above, can black muck up white's plan by pushing the more advanced g-pawn? Let's see. Taken from the top:1. a6 Kc62. a7 Kb73. Kd3 g44. Ke4! g35. Kf3Clearly, white has no time for either Ke5 or d5 here, so he must retreat to stop the g-pawn. However, this creates another problem for black- he can no longer protect the g-pawn with the h-pawn, and now both must be lost, along with the game.This was very, very pretty endgame problem. Props to anyone who could see the blocking theme of black's d5 pawn in the main line from the start, or who at least had some idea like it mind. I didn't spot it until I was literally on top of it.
PreambleA nice study based on an old setting (De la Bourdonnais, 1839) and anticipated for one of the ideas (Davies, 1937) but with a paradoxical effect... anticipated also by Srazil, 1940. The position is more natural, but it is by no means original.Huge hintIt's hard to expect a pawn sac in a pawn ending, especially when this sacrifice is not for a breakthrough!Sources and FENSDe La Bourdonnais, Le Palamède, 1839:8/3ppk1p/7P/5P2/6P1/3p4/3P4/K7 w - - 0 1 winDavies, Chess, 1937:8/Pk6/1P6/3p4/5K1p/8/8/8 w - - 0 1 winSrazil, Sach, 19408/6kP/3p2P1/6p1/Pp2P1K1/p7/P7/8 w - - 0 1 win (warning: the key move of Afek's study doesn't appear in the main line but in a short variation)
Nice job, Yancey. I had an inkling that d5 was the key move (if only because I expect such studies to bring something unexpected), but try as I might, I couldn't make it work.Not to find fault with your analysis, but you were perhaps quick to explain away 4) Kc4; g4 as an option for black. It's not so much that it's too slow, but that white's d4 pawn (which should't move in this variation) blocks the g1-a7 diagonal, thus allowing the mate on b6 even after g1=Q.Anyhow, like I said : nice job.S.P.
SP,The truth is that I didn't even notice that blocking theme. By that time I was just counting moves. Nice catch.
Some lose ends that I meant to address yesterday, but are now more relevant:1. a6 Kc62. a7 Kb73. Kf3?As suggested by a couple of commenters is inaccurate:3. .....h5! (the only move)4. Ke4 h4! (the only move)5. d5?? h3!This is also an only move, but now it is a winning move for black. It easy to assume that black must capture the d-pawn, but it is also easy to miss the fact that the white king is standing on that long white-square diagonal that terminates at h1. Continuing:6. de6 h27. e7 h1Q+8. Ke5 Kb6 Is the simplest win. However, it won't matter if white puts the king on the f-file at move 8 removing the skewer threat of Qe1+- black just plays 8. ...Qh8 instead, blocks the e-pawn with Qe8, then pushes the g-pawn to deflect the white king long enough to gobble up e7 and the queenside pawns.Now, at move 6 in this line, white can do no better by by not capturing at e6:6. Ke5 h27. Kd6 h1Q And white is one move too late to play a8Q-Kc7-b7-b8Q. Continuing:8. de6 Qc69. Ke7 g4 wins pretty easily.I am pretty sure white can only win with 3.Kd3. He must be able to bring the king up the c-file in time in a key line in my previous comment to avoid an untimely check from h1.
There's another loose end, Yancey.1. a6 Kc62. a7 Kb73. Kd3 h54. Kc4 h45. d5 h36. d6 ... and not 6. pxp6. ... h27. d7 h1(Q)8. a8(Q)ch KxQ9. d8(Q)ch Kb710. Q-c7ch K-a611. Q-a7mate another reason for having the king on the c file!
Davey,I left that one loose on purpose when I wrote the first comment. However, nicely analyzed, and you are correct, white must not play 6.de6. He can transpose, however, and play 6.a8Q immediately followed by d6, but it is slightly less accurate overall as black will gobble up b6, too, and escape an immediate mating net.
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