KQ versus KR, part two

In my last post, I looked at the K and Q versus K and R endgames, one of the four endgames of the Apocalypse, which occurred in both of the semifinal matches of the World Cup, and I introduced a couple of new ideas or at least new terminology, the “seesaw maneuver” and the “back-against-the-wall maneuver.” I received some great comments from Todd Bryant and Yamil Duba, who mentioned the “third-rank defense” as the defender’s best try. In particular, Todd mentioned the following position, which is an especially tough nut to crack:

White to move.

FEN: 3k4/5Q2/1r6/3K4/8/8/8/8 w – – 0 1

If you haven’t seen this position before, it’s definitely worth taking an hour of your time to figure out White’s winning plan.

I was very excited to get Todd’s comment because I was curious whether the two maneuvers I discussed in my last post were sufficient to win (or at least make progress in) any position. Regretfully, I have to say that the answer is no. The “natural” move here seemed to be 1. Kc5?, but after 1. … Ra6 I could not see any way to set up either of the aforementioned maneuvers. There are many lines that almost work, but Black always seemed to have at least one resource to keep my plans from working.

I was determined, though, to find the solution without looking it up either in a tablebase or a book. And I succeeded! However, I am still struggling to frame the move in terms of a general concept. To me, at this point, it just seems like a “magic move.”

Have you found it yet? The answer is 1. Qf4!! This move is so subtle that it deserves another diagram.

Position after 1. Qf4. Black to move.

FEN: 3k4/8/1r6/3K4/5Q2/8/8/8 b – – 0 1

What is the thinking behind this move? Well, in one word, it’s zugzwang. Any Black move will make the position worse, and rather speedily.

I often tell my students that a move that does two things at once (for example, a fork or a discovered attack) is usually a great move. A move that does three things is fantastic. Well, this move is quite possibly the all-time champion, because it does eight things at once! I’ll list them in approximate order of importance.

1. It threatens check on b8 in case Black should play 1. … Ra6.
2. It threatens check on f8 in case Black should move his rook to the kingside. Also it’s important to realize that Qf8+ becomes a mate threat if Black should play 1. … Rb5+ 2. Kc6, so Black would lose his rook immediately.
3. It controls c7 and therefore prevents 1. … Kc7, which otherwise would be Black’s best move. (All things being equal, Black would like to maintain contact between his king and rook.)
4. It controls c1, a key checking square, so that 1. … Rb1 2. Kc6 would win on the spot. (This was one theme I did mention in my previous post.)
5. It threatens check on e3 in case Black should move his king to the e-file.
6. It threatens check on f6 in case Black should play 1. … Rb2.
7. It threatens check on h4 in case Black should play 1. … Rb3. (This is somewhat less important because White has an alternate way to win with 2. Kc6, but nevertheless 2. Qh4+ followed by a fork on a4 or c4 is cutest and quickest.)
8. Finally, it threatens check on a4 in case Black should play 1. … Kd7. This last line is less immediately decisive than the others, but it is clear that after 1. … Kd7 2. Qa4+ Kc7 3. Qa7+ Rb7 4. Qc5+ White has made huge progress — he has broken the “third rank defense.” Although the game is not over yet, this is enough to consider the problem theoretically solved.

There is only possibility for Black that I haven’t covered yet:

1. … Kc8 2. Kc5! (Now this move works like a charm) Ra6 (It’s easy to see that other moves do not work. For example, 2. … Kb7 3. Qe4+ breaks the third-rank defense.)

Position after 2. … Ra6. White to move.

FEN: 2k5/8/r7/2K5/5Q2/8/8/8 w – – 0 3

Now can you find White’s coup de grace?

The answer will make you smack your head, if you haven’t found it. White plays 3. Qe4!! — setting up the same position as diagram 2, only moved one file to the left! This time Black will run out of room. For example, if 3. … Kc7 4. Qe7+ K-any 5. Kb5 the rook has no safe squares on the third rank to run to; there is no square to the left of a6 (z6?). Or if 3. … Kb8 4. Kb5 there is again no z6 square.

So that’s how you win this position; now, how do you find 1. Qf4 over the board? To be honest, I don’t think that any human player could figure all of this out in a time pressure situation, with only a few seconds or even a few minutes to think. This is why you have to study the position in advance and at least roughly know the idea. I think that points 1-3 above would be especially useful to you in looking for this move. That is, it’s very helpful to have checks on both sides of the defending king (points 1-2) and also, once you realize you can’t force a win directly by a series of checks, you have to start thinking prophylactically. Therefore, preventing the move 1. … Kc7 becomes a high priority. Clearly, 1. Qf4 is the only move that accomplishes these three goals. The fact that it also leads to this wonderful variation where every piece moves one step to the left until Black runs out of room — that is just a miraculous accident.

By the way, let me say also that it’s clear that Black has really good practical chances to hold this endgame if White is not absolutely on top of his theory.  So if you ever get to a KQ versus KR endgame and you have the rook, you should not give up. Two excellent practical ideas are (1) try to set up a third-rank defense, with the rook cutting off your opponent’s king from your king; and (2) if you get to a situation where you have a choice between retreating or separating your K and R, you should choose separating over passive retreat, unless you can clearly see that your opponent has a checking sequence that leads to a fork. If you can’t see it, probably your opponent won’t either, and he will spend valuable time trying to do so. Also, (2a) if you decide you must separate king and rook, move the rook as far away as possible. I haven’t seen a single position where this isn’t good advice.