Okay, here’s this position. How do you evaluate it? Is there any way to parse the possibilities in a sanely human kind of way, to reach judgments in a reasonable amount of (over the board) time?
It’s ominous that Black has to give up either a pawn or a knight in order to queen. That pretty much means he has to mate or die.
In the main post, I examine a line where Black promotes his a-pawn at this point. There’s also 63...Nd2+ 64.Kc2 b1/Q+ 65.Kxd2 Qb2+ 66.Ke3 Qc3+, which looks promising when you see 67.Ke4 Qd3+ 68.Kf4 Ne2+ and Black will either win the queen with a queen check on the f-file or by playing 69.Kg4 Qxg3+ 70.Kh5 Nf4+. However the king can simply go 67.Kf4 (a move earlier), or to f2 here. Black may have a perpetual, but it will be difficult. And if White gets the queens off, he has a clear win: 67.Kf4 Qd4 68.Kg5 Qxe5+ 69.Qf5+ Qxf5 70.Kxf5 Nb3 71.Rh2 Nc1 72.Rc2 and after White wins the a-pawn he should be able to queen the g-pawn.
Leon answers his own question. To evaluate this position as +/=/-, it is only necessary to follow the checks for black, which means white is always moving his king and black usually only has one or two choices.
ReplyDeleteFrom a practical point of view, one has to choose among draws, or consider lines where the conclusion isn't completely foreseen.
Difficulties arise when one misses possibilities, e.g., 63...Nd2+ 64 Kc1 b1=Q+ 65 Kxd2 Qb2+ 66 Kd1 which immediately resolves the situation. It's more efficient to look first at short lines and then long forcing lines before considering long lines even if there are only a couple choices along the way.
For instance, it seems that black's practical chances lie in the 63...a2+, which is also the most realistic thing to do, queen the pawn and take an active role in ensuring at least a draw.
I am attracted to 64 Kxb2 a1+ 65 Kc2 Qa2+ 66 Kc3 Qa5+, because it seems that there is trap for white after 67 Kc4 Qc7+ 68 Kd5 Qb7+ 69 Ke6 Nd4+ followed by winning the queen 70 Kf6 Qf3+ or 70 Kd6 Qb4+. I don't think black can win because I see any fantasy variations except for WKc3 B Qd4+ which leads to mate.
Upon reflection, that trap I gave is not really a trap because white can safely play 70 Kf6 Qf3+ 71 Ke7.
ReplyDeleteIn practice, how to recognize one's intuition about a position like this, or that one has no intuition, and what decisions are based on that are interesting.
Over the board, white can be confident of a draw because black's king is not involved, assuming he cannot see any concrete danger. I would guess the chances that there is danger for white is balanced by the possibility that white's king can escape checks. If the players see a concrete perpetual for black, then that guess changes to black's favor.
One critical line is 63...a2+ 64 Kxb2 a1Q+ 65 Kc2 Nd4+. Not sure how hard it is to see that this is critical in advance, but from d4 the knight indirectly covers Kf4, Kc5 due to Ne6+. Then 66 Kd2 is forced, but I have not found a forced win for black. After 66...Qb2+ 67 Ke3 Qc3+ white has two choices. Turns out that 68 Kf2 Qd2+ 69 Kg1 Nce2+ wins quickly (with the knight on b3, e.g., 66...Ncb3+, the K->g1 seems drawn). So there is 68 Ke4 Qd3+ 69 Kd5, which seems to lead to perpetual. With seven or so choices at move 69, analyzing this position is difficult. Black at least can draw with a trap, 69...Qb3+ 70 Ke4 Qd3+ draw since 70 Kxd4 Qd3+ 71 Kc5 Qa3+ wins the queen.