Pandolfini's Puzzler #27 - Zig Zag Zwang

Professor: Hello, class. Are you prepared to get scientific about things? That is, are you ready to talk about bishops today?

Lucian: Bishops? What bishops? Bad bishops?

Zephyr: Or good bishops?

Professor: Not quite either type. No, I’m thinking more about bishops in a particular endgame situation. The endgame setup I’m thinking of falls into the class of bishop and pawn vs. bishop, where the bishops are of the same color.

Lucian: I have a feeling there’s more to it than that, especially if we’re playing along with the fantasy and imagining we’re chess scientists.

Zephyr: I don’t know how scientific we are, but if we’re going to try to solve a problem, probably you should be more specific in setting it up, Professor.

Professor: Okay. Let’s get more specific. Let’s start by examining this position.

Professor: Obviously, if the defending bishop can sacrifice itself for the pawn, the game is drawn. To go beyond the obvious, the situation is this. It’s White to move, and there’s a forced win. Aside from that, how would you classify the position?

Lucian: Aside from that? Are you asking us to describe the position, Professor? I’d rather just search for the winning idea. Isn’t that more important?

Professor: Yes, in a way. And you’re soon going to be asked to find the winning idea. But you can learn a lot for future use and comprehension by trying to pick out the position’s key elements. By analyzing the position before proceeding, you can pretend you’re thinking like Aristotle.

Zephyr: I’ve heard that name before, a few times, but I don’t think he had anything to do with chess.

Professor: No, he was a philosopher, not a chess player. I only mention him because he was big on classification. He liked to put things in categories to help understand them better.

Lucian: I don’t know much about philosophy. But as a chess player, I’d point out that White has a bishop pawn on the 7^th rank. I’d also say that White would like to promote that pawn, and that both bishops can attack the promotion square.

Zephyr: I’m not a scientist or a philosopher either. I agree with what Lucian has said. But I’d add that we also should say something about the kings.

Professor: Fine. What do you want to say about the kings?

Zephyr: We could say the white king defends the pawn from in front of it and the black king attacks the pawn from behind it.

Lucian: One other thing. We could also say the kings stand in opposition!

Professor: All true. All interesting. Now let’s put the right angle on things and get to the initial question.

Question 1: If you had White, would you prefer it to be your move or Black’s move?

Lucian: Professor, since we already know that White wins by force, wouldn’t we want it to be White’s move?

Zephyr: I think I understand what the Professor is getting at. I think he’s possibly saying if Black goes first, he might draw.

Professor: Perhaps that’s correct. Perhaps not. But if I were you, here’s how I would proceed. First, I’d look for a winning line when Black does nothing special.

Zephyr: All right, Professor. Let’s say we do that, and we find a winning line when Black does nothing special. Then what?

Professor: Well, then I’d try to find a way for Black to get tough. That is, I’d try to determine if Black could stop White’s winning line.

Lucian: Okay, suppose we find a way for Black to stop White, what then?

Professor: At that point I’d take it a step further. I’d try to find a way to thwart Black’s attempted defense.

Zephyr: And if we find how to counter Black’s defense, what would that do for us, Professor?

Professor: I think it would enable us to answer the question in question: In the position of our first diagram, would White rather go first or second?

Lucian: Wow, there’s a lot to do before being able to get to where we’d like to be.

Professor: And when you get there, I may even give you another task. Oh heck, let’s give it to you right now. Consider this second position, which is almost like the first one.

Question 2: Can White force a win in the second position?

Zephyr: The only difference appears to be that everything has moved over toward the h-file by a single file. Now, however, it’s a c-pawn instead of a b-pawn.

Lucian: And the bishops now travel on light squares, not dark ones.

Professor: You’re both correct once again.

Lucian: Assuming we find the winning technique for the first setup, I don’t see why it wouldn’t work for the second situation. The positions seem so similar.

Zephyr: Just to make sure we haven’t missed anything, Professor, would you mind summarizing our tasks before we begin?

Professor: Not at all. I’d be happy to. Here are the tasks.

1) In diagram 1, find a winning line for White if Black just wastes a move with his bishop.

2) After finding that line, find a way for Black to try to defend.

3) If you find such a way, try to find a way for White to win anyway.

4) Answer the question, would White rather go first or second in diagram 1?

5) Determine whether or not White can force a win in the position of diagram 2 using the technique of diagram 1.

Professor: There you have it, all five tasks. See if you can put the right slant on things now. Diagonally speaking, I trust you won’t go awry or askew.

Lucian: Oh, Professor. You and your silly puns.

After everyone feigned a smile, the class took a half hour to work it all out. Taking as much time as needed, silly puns or not, can you work it all out, too?

Answer below - Try to solve ProfessorPando's Puzzle first!

ANSWER #27

For Task 1, if Black just temporizes (wastes time), White can win, for instance, in this manner: 1. Bh4 Bf4 2. Bf2 Bh2 3. Ba7 Bg3 4. Bb8 Bf2 5. Bh2 Ba7 6. Bg1. White draws off the black bishop and will soon queen.

For Task 2, if Black tries to stop White, play might go 1. Bh4 Kb6 2. Bf2+ Ka6, and White temporarily can’t follow through on the winning maneuver of Task 1.

For Task 3, with White frustrating Black’s attempt at drawing, play could go further with 1. Bh4 Kb6 2. Bf2+ Ka6 3. Bc5! Bg3 (for instance) 4. Be7 (aiming for Bd8-c7) Kb6 5. Bd8+ Kc6, and we’re practically where we started, with one small important difference: Black’s bishop is at g3 instead of h2.

That makes all the difference, and now White gains the tempo he needs to complete the winning maneuver.

Play would finish 6. Bh4!, and after Black moves the defending bishop somewhere safe along the b8-h2 diagonal, White continues 7. Bf2, and wins by the maneuver of Task 1.

As for Task 4, the answer is that it doesn’t matter whether White goes first or second. It’s still a forced win, although as you can see, it's a little easier if it's White's move.

For Task 5, let’s rely on a similar approach and see if it works. A sample line would be 1. Bh5 Bf5 2. Bf3 Bh3 3. Bb7 Bg4 4. Bc8 Bf3 5. Bh3 Bb7 6. Bg2, and Black still has a defensive square available, 6…Ba6!.

Take note

From the above examples, and their attendant reasoning, we can see an important aspect to bishop and pawn versus bishop endings. In cases where a defending bishop has two diagonals available in order to guard the promotion square (which obviously applies to all pawns other than rook-pawns), the length of the shortest defensive diagonal is critical. It must be long enough so that the defending bishop can temporize and still stay on it, so that the defender doesn’t have to relinquish control of the promotion square. 

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