The Subtlest of Differences

by admin on February 5, 2016

One of these positions is a win for White. The other is a draw. Can you tell which is which?

Position 1:

subtlest 1Position after 51. … Kd4. White to move.

FEN: 8/1p3p2/8/p2p2p1/P2k2Pp/1P1B3P/6K1/8 w – – 0 52

Position 2:

subtlest 2Position after 51. … Kd4 (alternate reality). White to move.

FEN: 8/5p2/1p6/p2p2p1/P2k2Pp/1P1B3P/6K1/8 w – – 0 52

While you’re thinking about it, here’s the story. Last night I was playing another training game against Shredder (set at a rating of 2275). I played a really good game up through about move 38, won a pawn and had complete control over the position. But the thing about computers is that they never get discouraged. Where a human might have given up, it was constantly looking for a way to keep the battle going. It spotted a chance to sac a piece for three pawns, and we got to Position 1, where I suddenly realized it was going to be very hard to win. In fact, I wasn’t sure I could win at all.

I decided to take my time-out here and see if I could figure out what to do. My initial inclination was to play 52. Bb5, but I couldn’t see a clear win after 52. … Ke3! If White plays 53. Kf1 to block the d-pawn, then 53. … Kf3! switches the attack over to the h-pawn. If White just waits, Black will push his pawn to d3 and then play … Kd2 and … Kc2, with a draw at least.

Then I saw that I could play 52. Be2!, which I think is the only winning move. The point is that now 52. … Ke3 can be met by 53. Bf3 d4 54. Bxb7! The win of the b-pawn is just enough to tip the balance in White’s favor, for example 54. … d3 55. Bf3 Kd2 56.Kf2 Kc2 57. Ke3 d2 58. Be2 f6 59. Kd4 d1Q+ 60. Bxd1 Kxd1 61. b4! ab 62. a5 Kc2 (if 62. … f5 White just ignores the f-pawn and lets it take on g4 and h3 if it wants) 63. a6 b3 64. a7 b2 65. a8Q b1Q 66. Qe4+ (diagram)

subtlest 3Position after 66. Qe4+ (analysis). Black to move.

FEN:8/8/5p2/6p1/3KQ1Pp/7P/2k5/1q6 b – – 0 66

White wins by trading queens and marching his king over to the kingside. Black’s king is too late to defend any of his pawns.

I actually didn’t work this all out during my time-out; it’s Rybka analysis. But I had the feeling that the position was winning if I could take the b-pawn, and Rybka confirms that.

So we can see that the position of the b-pawn mattered a great deal! In Position 2, the Be2-f3 trick doesn’t work, and in fact Rybka confirms that the endgame is a draw. I was really lucky here, because the position of the b-pawn on b7 or b6 was completely irrelevant up to this point and Shredder could easily have played … b6 earlier in the game. If it had, I’d be showing this game to you as an example of a blown win; instead it was a lucky save of an almost-blown win.

But that’s not all! The endgame continued to be quite interesting, and in fact I did blow the win just one move later! In position 1, after I played 52. Be2! Shredder moved its king in the opposite direction: 52. … Kc3! During my time-out I had not sufficiently thought about the difference between the two moves … Ke3 and … Kc3, and I mistakenly thought that the same plan worked in both cases. I played 53. Bf3??, which only draws! 53. Kf3! was correct, and this time I’ll leave the details to you (or Rybka) to work out. Play continued 53. … d4 54. Bxb7 d3 55. Bf3 Kxb3 56. Kf2 and now it was Shredder’s turn to blunder.

subtlest 4Position after 56. … Kf2. Black to move.

FEN: 8/5p2/8/p5p1/P5Pp/1k1p1B1P/5K2/8 b – – 0 56

Black has two natural-looking moves, 56. … Kc2 and 56 … d2. One draws and one loses. Can you tell which is which?

(space inserted in case you want to think about it)

Shredder played 56. … Kc2??, which loses! This is when playing a computer opponent is less satisfying than playing a human opponent. If it were a human, we could talk about why it made this mistake. Normally I have a rule: control the squares in front of the passed pawn first, then push the pawn. So 56. … Kc2 would seem to be the right choice. But this position is an exception to the rule! I played 57. Be4!, which paralyzes the pawn and allows White to blockade successfully on d1… with the king.

After 56. … d2! White has to blockade with the bishop, and that makes all the difference! For example, 57. Bd1+ Kb2 58. Ke3 Kc1 59. Ke2 f6! and White is done in by the lack of mobility of his bishop. He has nothing better than repeating the position with 60. Bb3 Kb2 61. Bd1, etc. White would be winning if we took the pawns at a4 and a5 off the board.

Alternatively, if White tries for a pawn race with 56. … d2 57. Ke3 Kc2 58. Ke4 d1Q 59. Bxd1+ Kxd1 60. Kf5, both sides queen and White doesn’t have any neat trick at the end as he did in diagram 3.

Why didn’t Shredder play 56. … d2!? Well, here is where playing against a computer is less satisfying than playing against a human. If it were a human, we could talk about it being misled by the general rule. But being a computer, it doesn’t think in terms of rules. It just computes. Remember that I had its strength set at 2275. When its strength is set to less than the maximum, it must be programmed to make a mistake now and then. So it didn’t make a conceptual error, it just had some random number generator coming up snake-eyes. “Time to make a mistake!” Boo.

Even so, the game still continued to be interesting and poised on a knife edge between a win and a draw. I have one more “Subtle Differences” position to show you. We’ve already seen subtle differences between a pawn on b7 or b6, between a king moving to c3 or e3, between blockading with a bishop and a king, and between having the a-pawns on the board and not having them there.

After 56. … Kc2?? the game continued 57. Be4! Kc2 58. Ke1 Kd4 59. Bf5 Ke3 60. Bh7 d2+ 61. Kd1 (success!) Kf4 62. Kxd2 Kg3 63. Ke3 Kxh3. I swear, playing the computer is like battling the Hydra. I cut off one passed pawn (the d-pawn), now a new and dangerous passed pawn appears on the h-file.

Moving on: 64. Kf3 Kh2 65. Kf2 Kh3 66. Bf5 f6 67. Be6 Kh2 68. Bd5 f5. The computer seizes its last chance to muddy the waters. 69. gf g4 and let’s pause for a diagram.

subtlest 5Position after 69. … g4. White to move.

FEN: 8/8/8/p2B1P2/P5pp/8/5K1k/8 w – – 0 70

White to play and win. Oh, that’s too easy. Let me make a change.

subtlest 6Position after 69. … g4 (alternate universe). White to move.

FEN: 8/8/8/3B1P2/6pp/8/5K1k/8 w – – 0 70

Now White to play and win. Do you see the trick?

In the real game, I looked at 70. Bg2 and discovered, to my horror, that 70. … h3 71. Bxh3 gh 72. f6 Kh1 73. f7 h2 74. f8Q was stalemate! So I looked around for other possibilities and found 70. Ke2 g3 71. f6 h3 72. f7 g2 73. f8Q! g1Q and now not 74. Qf2+?? Qxf2+ 75. Kxf2, which would again be stalemate, but 74. Qf4+! Qg3 75. Qxg3+ Kxg3 76. Kd3 and I won in a few more moves.

However, this line only worked because I still had an a-pawn that I could queen. What if we were in an alternate universe where the a4 and a5 pawns weren’t there?

Well, in the alternate universe White is still winning, because after the line in blue above (70. Bg2 h3 71. Bxh3 gh 72. f6 Kh1 73. f7 h2) instead of queening the pawn like a sucker, White instead plays 74. Kg3! letting Black’s king out of captivity. Now 74. … Kg1 75. f8Q h1Q 76. Qf2 mate! Black could of course avoid the mate by promoting to a knight instead (75. … h1N+), but the knight is no match for a queen.

To be honest, I completely missed this idea when I was playing the game, so I’m lucky that the a-pawns were still there to give me an alternative winning method. The reason for my oversight is psychologically interesting. I have definitely seen this trick before (letting him queen and then checkmating him, with the newly promoted queen taking away the king’s only flight square). It comes up in a Q vs. RP endgame when the stronger side’s king is sufficiently close to the queening square. But I wasn’t prepared to see this theme emerge out of a bishop-and-pawn endgame.

I wish I could tie this post all up in a nice little bow for you, but what I think it shows is that in some types of endgames, every little detail matters. You can’t just go on general rules and principles. The evaluation of the position and the optimal plan can change if you just move one pawn from b7 to b6, or move your king left instead of right. Which is, of course, quite discouraging if you’re trying to learn how to play endgames!

Oh yes, and one other practical piece of advice, which came up in both diagrams 3 and 6: When analyzing a pawn race, do not stop your analysis when both pawns promote. There’s a tendency to assume that if they both promote, the race is a tie. But you should always make sure to look at least one move farther ahead, to see if there are any surprising checks (or checkmates!).

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{ 1 comment… read it below or add one }

Todd Bryant February 6, 2016 at 10:27 pm

Nice post. This is a fascinating endgame.

I think that just positionally, you could say that Black is much happier with the pawn on b6, because it’s not a target there. So that was my strong feeling. But the details are not easy to work out.

I also found it hard to analyze because I would reach far-off positions that were difficult to evaluate. For example this position: Black pawns a5, b6, f6 ,g5, h4, Kc5. White pawns h3, g4, Bd7, Kc3. What is going on here??



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