2024/03/31 DPA: "Underwhelming But Overpowering"

White to move.

We obviously want to avoid stalemate:  1. d7 Be8  2. d8(=Q or R)

What about 1. Bf7 Bxf7 d7 and Black can't stop the pawn nor stalemate since the White Bishop no longer controls g8.

But Black can play 1. ... Bg4 and if 2. Be6 Bxe6  3. Kxe6, Black has the opposition and thus will draw.

So White needs to find a way to force the King to move once so White can take the opposition and win.

The problem with 1. d7 is that it's irreversible since pawns can't move backwards and the pawn is attacked [and if Black can sac his Bishop for the pawn, it's a drawn endgame].

If the Bishops are subtracted out, if White can achieve this position with Black to move, White wins because he has opposition.  For example, 1. ... Ke8  2. Ke6 Kd8  3. d7 Kc7  4. Ke7.  Or 2. ... Kf8  3. d7.

So how does White go about making this happen?  With some fancy Bishop footwork, I'm guessing.

I can't see how to do this yet so I'm going to visualize attempts, see why they fail, and then use that information to make my next attempt better.

• 1. d7 fails due to stalemate
• 1. Bf7 fails due to 1. ... Bg4
• 1. Be2, attacking the Black Bishop, fails due to 1. ... Be8  2. Bh5 Bd7
• 1. Bb5, protecting e8, fails due to 1. ... Bg4
• Moving the King allows 1. ... Be8
• 1. Be6 Be8
• 1. Ke6 Bg4+

White needs to prevent the Black King from reaching e8 because from there he can go to d8, a dark square, from which he cannot be evicted.

White also needs to prevent the Black Bishop from gaining control of d7.

Does one move do both?

Can White triangulate [taking 2 moves to get somewhere vs 1]?

1. d7 Be8  2. d8(=N) would only work if White could capture the Bishop.  Is there  a way?

Checkmating with K+B+N while the opponent Bishop is still on the board doesn't seem possible unless under highly unusual circumstances.

Save that for later.

If the Black Bishop is going to stop the pawn, it must be either on the a4-e8 or c8-h3 diagonal because that intersects the pawn's path through d7.

Is there a way White can cover every square along that diagonal such that Black's Bishop must leave the diagonal or be captured?

Ke6 immediately is a mistake because of ... Bg4+.  But what about first 1. Be2 Be8  2. Ke6, as now the check doesn't exist?  Does this accomplish anything?

2. ... Ba4  3. Bb3 Bb5.  I don't see any way to make progress.

1. Bd3 Bg4  2. Bf5 Bxf5  3. Kxf5 and Black has the opposition.

The problem appears to be that if Black can play either Ke8 or Be8 or Bd7, he draws.  And White cannot prevent all three.

This conclusion may be incorrect or it may be correct but there is another way.  For now, I'm leaning towards the latter.

The only thing saving White is that the Black Bishop is not yet on either critical diagonal.

1. Bg8 Be8

I think I have it:  1. d7 Be8  2. d8(=N) and now the idea is to plant the White Bishop on f7, immobilizing the opponent King and maneuvering the Knight to e5, where it can deliver checkmate from either d7 or g6 and Black's Bishop cannot guard.  There are all sorts of variations with Knight forks.

Hmm, there's a problem:  2. ... Ba4  3. Bf7 Bd7.  If 4. Nb7 Be8 [Black can't play 3. ... Be8 due to 4. Ne6#; but with the Knight now on b7, he can.].

But who says when you underpromote, it always has to be a Knight or Rook?

1. d7 Be8  2. d8(=B) and now Black is hosed since the King can't move:

• If the Bishop moves along the a4-e8 diagonal, 3. Bf7 and then 4. Be7#
• If the Bishop moves along the e8-h5 diagonal, 3. Be7+ Ke8  4. Bb5#

Note that White must be careful as his 3rd move is dependent on which diagonal the Black Bishop chooses.  Arrows are read in order of green, yellow, red or dark blue, purple, light blue.

The key was three-fold:  recognizing that A) there was no way to stop the Black Bishop from controlling d7; B) underpromotion was required; and C) a Bishop specifically.

I saw the possibility for underpromotion and the fact that it couldn't be a Queen or Rook due to stalemate and my mind immediately leapt to a Knight [no pun intended].  I don't think I've ever seen underpromotion to a Bishop so it didn't occur to me initially.

Instead, I spent quite a bit of time trying to work out how, after underpromoting to a Knight, White could win the Black Bishop and reach a theoretically won endgame.  But I couldn't make it work and somehow I had the inspiration of UP to a Bishop.

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Note that Black could have extended the game out with 2. ... Bf7  3. Be7+ Kg8  4. Bxf7+ but that would have led to a K+B+B v K standard checkmate.  The puzzle creator opted for the quick finish, which emphasizes the underpromotion, not the subsequent technical details.