8

Let me define the problem clearly so as to avoid confusion. I am trying to find a position where:

  • The unique best move is a promotion move.
  • Said move needs to be promotion to a bishop. Not a queen, not a knight, and not a rook.
  • Where "unique best move" means either: a move that draws while all other moves lose, or, a move that wins while all other moves draw or lose.

I have been trying to come up with such a position for more than a week now without success. The following is my thought process.

AFAIK there are two main reasons for underpromoting:

  1. Underpromote to deliver a check/attack that a queen cannot fulfill
  2. Underpromote to avoid stalemate

The first scenario should be irrelevant because a queen has all the moves of a bishop.

For the second scenario, I thought about the fundamental cause of stalemate. Promoting to queen can draw, either due to its rook-move ability, or its bishop-move ability, or both abilities simultaneously.

Reason for stalemate Rook move Bishop move Both
Example FEN 8/k1P5/2P5/K7/8/8/8/8 8/6P1/8/8/8/8/8/k1K5 8/k1P5/8/2K5/8/8/8/8
Solution Promote to Bishop/Knight Promote to Rook/Knight Promote to Rook/Bishop/Knight

As you can see, there is no scenario where you have to get a bishop. Therefore I concluded that any singular reason alone cannot produce a position where promotion to bishop is the only move. In other words, there has to be other conditions in the position that prevent the choice of another piece, in particular that of the knight.

One idea that came to my mind is that you might need a bishop-move to prevent something, but this idea got shot down pretty quickly because if you need to prevent something, that means the opponent is threatening a move, which means there's no stalemate.


Currently, the only semi-plausible idea I have left is that promotion to knight leads to insufficient material, whereas promotion to bishop doesn't. However coming up with such a position is quite difficult as you can imagine (especially given the condition that it has to be the only move), so I have yet to think of one.


I have asked this question to a few IMs and GMs on their streams to no avail (understandably so, since they still have to stream), so I am turning to StackExchange community for ideas and answers.

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  • 1
    Addendum: THX to Siegfried Hornecker, he found (back) this: Alexey Troitzky, Shakhmatny Listok, 15. Januar 1925 [[FEN F8/p3B2p/1P5P/3P4/5r2/3k4/8/6K1]], 1.b7 Rg4+ 2.Kf2 Rg8 3.d6 Kc4 4.d7 Kb5 5.d8Q Rxd8 6.Bxd8 Ka6 7.b8B. It is fun to analyze what good the second bishop is for! Feb 15, 2021 at 9:35
  • @HaukeReddmann yeah I really enjoyed this one. Black's best attempt is to run to g8, and white is unable to force the king out of the corner, which means the h6 pawn will never promote. However white can occupy both a3-f8 and a1-h8 diagonals with the bishops, and have a Zuzwang trick when black eventually runs out of moves with their a pawn. Kf7# is a pretty cool move.
    – cyqsimon
    Feb 15, 2021 at 10:09
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    Addendum: In "Let me ask you, do you know", an endgame classic by Karaklajic, there is even a study by Troitzky where not only White but also Black underpromotes to B (the latter to fight on with stalemate tricks) and now we have four blackfielders :-) (Can't find it offhand, lacks register badly. I add it later.) Aug 23, 2023 at 18:11

7 Answers 7

11

There are numerous chess problems, whether a checkmating one or an endgame study, that feature certain promotions as a necessity to win. Stalemate is the long-known reason behind doing so.

This problem is the first known one to use Bishop promotion, although it is a later correction. Even better, it comes with double the fun!

[Title "Ignazio Calvi  Le Palaméde 4/1836, White Wins (Correction)"]
[FEN "8/6PP/3Pn3/6b1/8/k3P3/p7/K2B4 w - - 0 1"]

1. g8=N! Bxe3 2. h8=B! (2. h8=Q? Nd4 3. Ne7 Nc2+ Bxc2 Bd4+ 5. Qxd4)    Nd4 3. Ne7 Bd2 4. Nd5 {And white wins!}

However, in theory, it can also be motivated by the "Dead Position" rule. Here is a flawed, hypothetical example.

Suppose White is down to seconds on the clock. They have no queens or rooks nearby-just knights. Stopping the clock to call in the arbiter might not help really. Thus, White must promote to a bishop, luckily just before the clock runs out. Now, the game is drawn and a half point is saved!

[FEN "8/3P4/8/8/8/7k/7b/7K w - - 0 1"]

1. d8=B
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    I can't believe that if you promote to a queen here that black can claim a win when white loses on time. Or at the very least you can promote to a queen and claim a draw because black has not winning potential.
    – Carlo Wood
    Apr 2, 2022 at 15:58
  • 2
    I think Carlo is right, and FIDE rule 6.9 applies: "...if a player does not complete the prescribed number of moves in the allotted time, the game is lost by the player. However, the game is drawn, if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves." I don't see a helpmate available that would make black win. Apr 2, 2022 at 16:58
  • 1
    The second problem is alas cooked. White can promote to Queen or Bishop. Queen seems better, because it has at least a chance of delivering mate
    – Laska
    Jul 24, 2023 at 12:05
  • For the second diagram: Black can not produce a series of move that leads to a win after the promotion to a Q. Therefore it's always at least a draw for white. It can lead to a Q win, but then it's a draw due to insufficient material. e.g. [FEN 8/8/8/8/3b4/8/Q7/K1k5 w - - 0 1]
    – IT M
    Jul 25, 2023 at 12:10
  • @Laska It's an otb hypothetical, not a problem. Read the text more carefully, please. Jul 27, 2023 at 0:53
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It's easy to come up with positions where promoting to knight leads to insufficient material but promoting to bishop doesn't. This one, for instance:

[FEN "N5q1/7P/8/8/8/7K/8/7k w - - 0 1"]
0
6

Various problems requiring bishop promotions. White is to play in all cases.

1) Economy record for a study (also correct as #5!)
2) Earlier really good study from 1856 for comparison
3) Economy record using 50 Move rule
4) Black in time-trouble (using special FIDE "half-dead rule", 6.9)
5) White in time-trouble (ditto)

First then, a new economy record:

[Title "1) Win - end of study by Klinkov, 1966"]
[FEN "3n3k/1P5P/7K/8/8/8/8/8 w - - 0 1"] 

1. b8=B! Nf7+! 2.Kg6! Nd6! 3. Bc7! Nf5 4.Be5+! Ng7! 5. Bxg7#!

Shifting all units one column to the left gives 2n3k1/P5P1/6K1/8/8/8/8/8: a sound study, with mate in 14, but alas no dual-free line.

By way of comparison, here is the only comparable prior art with less than 6 pieces in either of the mega-databases PDB or WinChloe. It has mate in 9, but again no dual-free line.

[Title "2) Win - Luigi Centurini, La Regence 1856"]
[FEN "2k5/8/2K1P3/b7/8/6B1/8/8 w - - 0 1"] 

1. e7! Bd8 2. e8=B! Bc7! 3. Bd7+! Kb8 4. Bxc7+ etc.

Let me show some other off-the-wall examples...

Here's one based on the 50-move rule (which must be specified in the stip, since by default it does not apply for orthodox studies).

[Title "3) Win (with 50 Move Rule) - Original, 2021"]
[FEN "7N/pP6/k7/8/K7/8/8/8 w - - 0 1"]
  1. b8=B! White mates in 35.

On the other hand:

  1. b8=N? This is a "cursed win": White could in principle mate in 104, but a draw intervenes under the 50-move rule as Black can delay the first pawn move or capture until White's 54th move.

Another example uses the FIDE “half-dead rule" Article 6.9 concerning the clock. Basically if a player times out (normally a loss) the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.

[Title "4) Best play under FIDE rules (Black in extreme time trouble) - Version 2023"]
[FEN "6rk/7P/6pK/p5Pb/6p1/p5P1/P7/8 w - - 0 1"]

Explanation

1.hxg8=Q/R+? (dp) Kxg8= 1.hxg8=N? a4 (dp) 2.Ne7,Nf6 So in all these cases no checkmate is possible, and the game immediately ends in a draw before Black has to reply.

On the other hand, after 1. hxg8=B! then game does not end immediately, because at least in principle there is the alternative lifeline 1... a4 2.Bb3 axb3 3.axb3 & e.g. a2 4.a4 a1=Q 5.a6 Qg7# and although Black wins, it takes 5 moves, there are checkmates around for either side. To seize the draw though, Black should play 1... Kxg8=, but has to execute this before the quivering flag falls.

And here's the final example, with White in time trouble:

[Title "5) Draw under FIDE rules (White in extreme time trouble) - Original, 2023"]
[FEN "7Q/4q1P1/5k1K/5r2/8/8/8/8 w - - 0 1"]

Explanation

White can win after 1.Qf8+ or 1.g8=X+, but in only one case is the checkmate certain: 1.g8=B+ Qg7+ 2.Qxg7#, so by playing this key, White locks in at least a half point if he times out before the next move.

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  • 2
    The B-promotion in "Otto Dehler, after Luigi Centurini" (a century old this year!) even shows up on occasion in analysis of Bishop endings from actual play. Feb 18, 2021 at 2:58
  • @Noam: apart from reflection, I suspect it's the only such KBPvKB position with P not yet on 7th rank. Or do you have others?
    – Laska
    Feb 18, 2021 at 5:11
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    It also works with the pawn on a few other files, and the Bishops elsewhere on the diagonal. In your diagram, bBc7 almost works, but besides 1 e7 Bd8! 2 e8B! White also wins with 1 Bg5, taking a few moves longer. Likewise it's tempting to retract 0 e5-e6+ Kb8-c8, but 0 Kd7 would also win two moves later. However, Kc5 Bh1 Pd5 / Ka8 Ba6 works: 1 Kb6 Bb7 2 d6! Kb8! 3 d7! Bc8 4 d8B! Bb7 5 Bc7+! Kc8 6 Bxb7+ and mates in 15, with each White move unique and each Black move offering the longest resistance (up to a tie with 4 . . . Ba6). Feb 19, 2021 at 0:24
2

I didn't look at existing answers yet; so maybe this was already posted. I tried and fairly quickly came up with:

[FEN "1r5K/2P5/8/k1N5/8/8/8/8 w - - 0 1"]

My line of thought was: if promoting to a bishop is better than promoting to a queen, then having more "power" must lead to stale mate. Therefore promoting to a bishop must win. Then, if you allow that promoting happens while taking a piece it is rather easy to make it the only move that wins.

I'll be interested to see if there are answers that strongly divert from this idea, especially promoting without capturing a piece. But I'll first think about that myself.

EDIT:

After just 2 minutes or so, I came up with:

[FEN "7K/P7/8/1N6/1N6/1p1P4/1k5p/8 w - - 0 1"]

Here promotion is necessary because otherwise black promotes to queen with check, and promoting to rook or knight is not going to stop black from doing that, after which you just lose your promoted piece (black promotes with fork). Promoting a queen still results in a stalemate: then black also promotes to a queen and the best thing white then has is to take it, which is stalemate.

Promoting to a bishop stops black from promoting and white will go on to win.

1
  • Nice. In the first one you can shift wKa1 & bKa3. It all still works as before but now White is not in check in the diagram
    – Laska
    Jul 25, 2023 at 7:26
2

Another addendum. Very strictly speaking, none of the positions (except the "dead" utilization by Laska) fulfil the specifications of the OP, since promotion should be the only move. But this is still easy, not even a capture involved:

[FEN "k2b4/P5P1/Kp6/1P6/8/8/8/8 w - - 0 0"]

1.g8B! and mate in the next move; 1.g8R? =, 1.g8N? Bg5! 2.Kxb6 Be3+ 3.Ka6 Bxa7 =

Addendum to the addendum. As promised above, a study where both sides underpromote. (But Black's is only a joke, the piece is captured immediately.) Not by Troitzki (I conflated that with his study where five same-field-color bishops win) but by a world champion:

V. Smyslov, Pravda 1976

[FEN "8/8/5P2/8/2k2p1p/2B1p2P/6P1/2b2K2 w - - 0 1"]

1. f7 Ba3 2. Bg7 f3 3. gxf3 Kd3 4. f8=B e2+ 5. Kf2 e1=B+ 6. Kxe1 Ke3 7. f4 Kxf4 8. Kf2 Bc1 9. Bh6+ 1-0

4. f8Q? e2+ 5. Kf2 Bc5+ 6. Qxc5 e1Q+ 7. Kxe1 = is the reason.

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    But he clarifies: "3. Where 'only move' means either, a move that draws while all other moves lose, or, a move that wins while all other moves draw or lose." Thus technically the op did ask for positions where multiple moves, besides a promotion, are legal - it just has to make at least 1/2 point difference. I agree however that point 1. then makes little sense to add and is to say the least confusing / inconsistent. Perhaps he meant in point 3 specifically the bishop promotion as 'only move', but that phrase was not used in point 2.
    – Carlo Wood
    Apr 2, 2022 at 16:04
  • Hauke puts exclamation mark after Bg5! -- meanwhile, stockfish in Troll Mode: 1. g8=N? Be7 2. Kxb6 Bh4 3. Nh6 Be1 4. Nf5 Bc3 5. Nd6 Bd4+ 6. Ka6 Bxa7 7. Nb7 Kb8 8. b6 Ka8 9. bxa7
    – Carlo Wood
    Apr 2, 2022 at 16:20
  • @CarloWood: I rather used Syzygy :-) If you use Nunn convention, so "!" means "only move", you are entirely correct - only 1...Bc7 throws the draw. "!" I rather meant as "take this, White, now the draw is obvious!" Apr 3, 2022 at 6:31
  • @HaukeReddmann it should be called the "Wunn" convention :-) (!)
    – Laska
    Jul 25, 2023 at 13:30
1

Here are two light problems involving bishop-promotion (and rook-promotion, too, to boot).

A. Kudryavtsev; Smena (Moscow), Mar 1999; PDB P1165938. #4. FEN 6B1/7P/5Pk1/8/6K1/8/8/8

[Title "A. Kudryavtsev #4"]
[fen "6B1/7P/5Pk1/8/6K1/8/8/8 w - - 0 1"]

1.h8=B! (1.h8=R Kxf6 {and White wins at move 8}; 1.h8=N+ Kxf6 {and White wins at move 31}; 1.h8=Q? =) Kh6 2.f7 Kg6 3.f8=R (3.f8=Q/f8=B? =) Kh6 4.Rf6#

Viktor Pilipenko; Sa ogneupory, 26 Mar 1987, 190; PDB P1165936. #5. FEN 6B1/7P/6k1/4P3/6K1/8/8/8

[Title "Viktor Pilipenko #5"]
[fen "6B1/7P/6k1/4P3/6K1/8/8/8 w - - 0 1"]

1.h8=B! (1. h8=R Kg7 {and White wins at move 7}; 1. h8=N+ Kg7 {and White wins at move 10}; 1. h8=Q? =) Kh6 2.e6 Kg6 3.e7 Kh6 4.e8=R (4. e8=Q/B? =) Kg6 5.Re6#
1
[fen "3n3k/1P2N3/6K1/8/8/8/8/8 w - - 0 1"]

1. b8=B Nc6 2. Nxc6 Kg8 3. Bd6 Kh8 4. Bf4 Kg8 5. Bh6 Kh8 6. Bg7+ Kg8 7. Ne7#
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    4. Bf8 also leads to 5. Bh6. Jul 23, 2023 at 23:13

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