Saturday, September 17, 2016

Practical Rook Endgames 15: Vancura Caveats

Isaac Asimov's short story collection "I, Robot" was made into a 2004 movie starring Will Smith as Detective Spooner. I love the writing in spots and wish to highlight two segments: 1. Dr. Alfred Lanning's soliloquy in the middle of the movie which I have quoted in brief before:

There have always been ghosts in the machine. Random segments of code, that have grouped together to form unexpected protocols. Unanticipated, these free radicals engender questions of free will, creativity, and even the nature of what we might call the soul. Why is it that when some robots are left in darkness, they will seek out the light? Why is it that when robots are stored in an empty space, they will group together, rather than stand alone? How do we explain this behavior? Random segments of code? Or is it something more? When does a perceptual schematic become consciousness? When does a difference engine become the search for truth? When does a personality simulation become the bitter mote... of a soul?

The second passage is near the beginning when Detective Spooner compares his task to Hansel and Gretel:

SUSAN CALVIN: I don't understand. Alfred wrote the Three Laws. Why would he build a robot that could break them?
DETECTIVE SPOONER: Hansel and Gretel.
SUSAN CALVIN: What?
DETECTIVE SPOONER: Two kids, lost in the forest. Leave behind a trail of bread crumbs.
SUSAN CALVIN: Why?
DETECTIVE SPOONER: To find their way home. How the hell did you grow up without reading Hansel and Gretel?

It's obvious to me that I really have a lot to learn about rook endings. The more I learn, the less I know. I didn't give any variations in my previous post because I thought that the Vancura was a shortcut to understanding how to draw the ending like an automaton. "Put your king on g7 and your rook on f6 and check, check, check your way to a draw." My one active reader commented and gave me a Vancura variation to chew on:

Black to move and draw. Since I am too lazy to work all the secrets out myself, I went straight to my favorite 6-man tablebase robot at the Shredder site and plugged in this position. I was surprised to find out that the path to a draw, far from a mindless template, was a bit more complicated. Actually, there are only two bread crumb trails that draw: A) Ra5 and B) Rc1. A) 1...Ra5 2.Ke4:

Here again, only two moves draw, but the pathways are convergent: C) 2...Rb5 3.Kd4 Rb6! (only move) and Black can look forward to moving his rook to f6 and checking until the draw comes home. D) 2...Rc5 3.Kd4 Rc6! (only move) with a similar Vancura pattern.

Going back to the previous diagram, here is the alternate way to draw: B) 1...Rc1 2.Ke5 Rc6! (only move) and we're back to familiar territory. Staying with the first diagram, I began the search for hypotheticals. Why doesn't 1...Rf1+ work?:

White to move and win. 2.Ke5! keeps White's winning path alive. Why can't Black just force the Vancura? It's tactically unsound here: 2...Rf6? 3.Rg8+! Kf7 4.Rf8+! The rooks come off and the a-pawn waltzes in. After Kf4-e5, if only Black could play Rf1-b6 or Rf1-c6, he would be on the true Vancura path. Let's try 2...Rf7.

White can still win. Shredder shows 5 moves to victory. The simplest is the pawn advance 3.a7. Black's rook is misplaced at f7. For the rook pawn on the seventh, the defender should be behind the pawn to prevent the attacker from just sacrificing his rook e.g. 3...Re7+ 4.Rd6 Rf7 5.Rg8+ Kxg8 6.a8=Q+. Continuing this White win variation, what if after 1...Rf1+? 2.Ke5 Black tries to draw with a spate of spite checks? White makes his way to sanctuary at a7 3...Re1+ 4.Kd5 Rd1+ 5.Kc5 Rc1+ 6.Kb6 Rb1+ 7.Ka7. With the defending king so far away, White reshuffles his rook to b8, king to a8, pawn to a7, then the White king moves out through b7, chases down the checking rook, and queens the pawn.

Going back to the beginning, I now asked Shredder, why does 1...Rb1? lose? Can't Black force Rb6 and find the way home?:

White to move and win. Shredder points out an unintuitive variation starting with 2.Ra7+!. White easily wins if Black goes to the eighth rank e.g. 2...Kg8 3.Rb7 Ra1 4.a7 followed by Rb8+ and a8=Q. 2...Kf6 is more testing. Now White has to avoid the drawing 3.Rb7? Ra1 4.Rb6+ Ke7!= but instead find 3.Ke4! Ke6 4.Ra8! It looks like White is going back to a previous position, but with the Black king away from his safe base of g7, more tactical checks come into play for White. I just realized that doing the shuffle is not always straightforward either and I'll probably have to devote a short post to the a6 pawn win.

Why didn't this Ra7+ win work against B) 1...Rc1!=?:

Black to move and draw. Now Black has to find three narrow bread crumb trails E) 2...Kg6!= 3.Ra8 Kg7!= and F) 2...Kg6!= 3.Ke5 Rc6!= and G) 2...Kg6!= 3.Rb7 Rc5!= angling back toward the classic Vancura with Kg7 and Rf6. As you can see, the path with A) 1...Ra5 is much safer than B) 1...Rc1. Here is one more argument in A)'s favor:

Black to move and draw. This diagram has one subtle difference with the first one. The White king is now at f5. Black cannot draw now with 1...Rc1? because 2.Ra7+! Kh6 leaves his king just too far away to prevent the brute force plan of White moving his king to b8 and escorting the pawn in. 3.Rd7 Rc5+ 4.Ke6 Rc6+ 5.Rd6 Rc5 6.Kd7+. Instead, Plan A) still works against Kf5: 1...Ra5+! 2.Ke6 Rh5!. I know that I warned in the last post not to put the Black rook behind the Black king, but here it is necessary. 3.Ra7+ Kg8!=. 3...Kh8? and 3...Kf8 both lose to 4.Rf7! blocking the Rh6+ skewer. Black also has to know that after 3.Kd7 there's still time to get back to Vancura with 3...Rh6! 4.Kc7 Rf6! and Black is ready with checks even if 5.a7 Rf7+!=. 5.a7 Ra6? loses to 6.Kb7! Ra1 7.Rb8.

From the attacker's point of view, getting the king to e4 or e5 while the Black rook is on a1 wins even if Black is on move. With White on move from the last diagram, 1.Ke4 or 1.Ke5 lead to wins. Surprisingly, 1.Ke6? only draws if Black can find .1...Rh1!=. From the defender's point of view, his rook must be on a5 prior to White getting from the kingside to Ke4 or Ke5. From Shredder, I see now that if White can get Kd4 and Black has not gotten his rook to b6 or f6 (e.g. he still has his rook on a1 or a5), then Black is lost. So the speed at which Black can get the ideal setup with rook on f6 or b6 is crucial.

Whew! As my reader commented "The theory of rook + a-pawn versus rook is actually surprisingly deep, with lots of different techniques."

1 comment:

Todd Bryant said...

Nice post! Some of these variations were new to me. The position I suggested appears in Dvoretsky's book right after Vancura. He attributes it to Peter Romanovsky, and refers to it as the "Romanovsky position." He also puts it in blue, meaning he thinks you should have it memorized!

Romanovsky studied this ending in more detail, and found that in the original position Black draws only if White's king falls in a weirdly shaped zone of squares:

http://2.bp.blogspot.com/-zNB31RnW0Mw/UVfnrXCxd7I/AAAAAAAAAnE/e-HXKKKQR_k/s1600/Drawing+zone.bmp

Your analysis already clears up two cases:

If White's king is on e6, we go 1...Rh1! I remember this was so surprising when I first found it.
If White's king is on f5, we go 1...Ra5+!
I think like your preference to go 1...Ra5 for simplicity if the king is on f4.

I've been meaning to learn the full Romanovsky drawing zone for some time now, but I've been putting it off, as it seems REALLY pointless, even compared to some of my other adventures, like memorizing key positions in KQ vs KR.