user26603: Let me define the problem clearly so as to avoid confusion. I am trying to find a position where:

The only 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 "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.


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:

Underpromote to deliver a check/attack that a queen cannot fulfill
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.

user11144: 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 =

user20841: 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.

user8201: First I wonder what is the most economical presentation of bishop underpromotion.
[FEN "5n2/6Pk/4N3/7K/8/8/8/8 w - - 0 1"] 

White to play and win
It's mate in 6 (with a dual)

gxf8=B! Kh8 2.Kh6(Kg6) Kg8 3. g6 Kh8 4. Kf7 Kh7 5. Sg5+ Kh8 6. Bg7#

Here's the only one in PDB or WinChloe with less than 6 pieces. Are knights more economical than bishops?
[FEN "2k5/8/2K1P3/b7/5B2/8/8/8 w - - 0 1"] 

White to play and win
Otto Dehler, after Luigi Centurini, Leipziger Tageblatt 1921 (reflected)
It's mate in 9

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

Let me show some other off-the-wall examples...
Here's one based on the 50-move rule:
[FEN "7N/pP6/k7/8/K7/8/8/8 w - - 0 1"]


b8=B! White mates in 34.

On the other hand:

b8=N? This is a cursed win. Checkmate could eventually be forced, as is often the case for KNNvKP, but a draw intervenes under the 50-move rule. Black can delay the first pawn move or capture until move 54.

Another example uses the obscure Dead Position rule and the clock. It doesn't use the half-dead rule, but it isn't disturbed by that. To force the bishop, I think we need to put Black under extreme time pressure (aka "Zeitnot"). The flag is trembling... :)
[FEN "6nk/7P/6pK/p5Pb/6p1/p5P1/P7/8 w - - 0 1"]

White to play & win over the board under FIDE rules, with Black under extreme Zeitnot.
Explanation:
White can only promote. If 1.hxg8=Q/R+? then 1. ... Kxg8= stalemate. If 1. hxg8=N?, then Black might instead try 1. ... a4 with 2. Ne7,Nf6= stalemate for the other side! 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, if 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. a3,a4 etc, and there are checkmates around for either side. This is of course sub-optimal, Black should of course play 1. ... Kxg8=, but he has to execute this before his quavering flag falls.
Question is: would White bring the game into disrepute by playing like this? :)
OK here's a final one: the most economical of all, showing the half-dead position rule at work.
[FEN "2b4r/P7/8/8/8/8/8/4K3 w - - 0 1"]

White under Zeitnot to play & draw over the board under FIDE rules. No Black king!
So in the excitement of the game, bK has fallen off or been captured. By the half-dead rule, White can't win, because he can't checkmate, but he can play on for the draw. However, Black can checkmate White, so the position isn't fully dead. Checkmate does not require that the position be legal, but mere that the last move be legal. That's the FIDE Laws.
If 1.a8=Q/R/N, then a mate is possible with e.g. wKh1, wQ/R/Ng1 bBh5, bRh8 & eventually Bf3#. Even though this mate may not be forced, the possibility of this is enough to keep the game alive. However, 1. a8=B makes the position dead, as neither side can now checkmate.

user2299: 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"]


user15543: 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. Here is a small sampling.
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!
[Titler "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, it can also be motivated by the "Dead Position" rule. In the below position, suppose White is down to seconds on the clock. They have no queens or rook nearby and 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


26603: <p>Let me define the problem clearly so as to avoid confusion. I am trying to find a position where:</p>
<ul>
<li>The only move is a promotion move.</li>
<li>Said move needs to be promotion to a bishop. Not a queen, not a knight, and not a rook.</li>
<li>Where &quot;only move&quot; means either, a move that draws while all other moves lose, or, a move that wins while all other moves draw or lose.</li>
</ul>
<hr>
<p>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.</p>
<p>AFAIK there are two main reasons for underpromoting:</p>
<ol>
<li>Underpromote to deliver a check/attack that a queen cannot fulfill</li>
<li>Underpromote to avoid stalemate</li>
</ol>
<p>The first scenario should be irrelevant because a queen has all the moves of a bishop.</p>
<p>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.</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th style="text-align: center;">Reason for stalemate</th>
<th style="text-align: center;">Rook move</th>
<th style="text-align: center;">Bishop move</th>
<th style="text-align: center;">Both</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center;"><strong>Example FEN</strong></td>
<td style="text-align: center;"><code>8/k1P5/2P5/K7/8/8/8/8</code></td>
<td style="text-align: center;"><code>8/6P1/8/8/8/8/8/k1K5</code></td>
<td style="text-align: center;"><code>8/k1P5/8/2K5/8/8/8/8</code></td>
</tr>
<tr>
<td style="text-align: center;"><strong>Solution</strong></td>
<td style="text-align: center;">Promote to Bishop/Knight</td>
<td style="text-align: center;">Promote to Rook/Knight</td>
<td style="text-align: center;">Promote to Rook/Bishop/Knight</td>
</tr>
</tbody>
</table>
</div>
<p>As you can see, there is no scenario where you <em><strong>have to</strong></em> 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.</p>
<p>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.</p>
<hr>
<p>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.</p>
<hr>
<p>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.</p>
 11144: <p>Another addendum. <em>Very</em> strictly speaking, <em>none</em> of the positions (except the &quot;dead&quot; utilization by Laska) fulfil the specifications of the OP, since promotion should be the <em>only</em> move. But this is still easy, not even a capture involved:</p>
<pre><code>[FEN &quot;k2b4/P5P1/Kp6/1P6/8/8/8/8 w - - 0 0&quot;]
</code></pre>
<p><code>1.g8B!</code> and mate in the next move; <code>1.g8R? =</code>, <code>1.g8N? Bg5! 2.Kxb6 Be3+ 3.Ka6 Bxa7 =</code></p>
 20841: <p>I didn't look at existing answers yet; so maybe this was already posted.
I tried and fairly quickly came up with:</p>
<pre><code>[FEN &quot;1r5K/2P5/8/k1N5/8/8/8/8 w - - 0 1&quot;]
</code></pre>
<p>My line of thought was: if promoting to a bishop is better than promoting to a queen, then having more &quot;power&quot; 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.</p>
<p>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.</p>
<p>EDIT:</p>
<p>After just 2 minutes or so, I came up with:</p>
<pre><code>[FEN &quot;7K/P7/8/1N6/1N6/1p1P4/1k5p/8 w - - 0 1&quot;]
</code></pre>
<p>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.</p>
<p>Promoting to a bishop stops black from promoting and white will go on to win.</p>
 8201: <p>First I wonder what is the most economical presentation of bishop underpromotion.</p>
<pre><code>[FEN &quot;5n2/6Pk/4N3/7K/8/8/8/8 w - - 0 1&quot;] 
</code></pre>
<p>White to play and win</p>
<p>It's mate in 6 (with a dual)</p>
<ol>
<li>gxf8=B! Kh8 2.Kh6(Kg6) Kg8 3. g6 Kh8 4. Kf7 Kh7 5. Sg5+ Kh8 6. Bg7#</li>
</ol>
<p>Here's the only one in PDB or WinChloe with less than 6 pieces. Are knights more economical than bishops?</p>
<pre><code>[FEN &quot;2k5/8/2K1P3/b7/5B2/8/8/8 w - - 0 1&quot;] 
</code></pre>
<p>White to play and win</p>
<p>Otto Dehler, after Luigi Centurini, Leipziger Tageblatt 1921 (reflected)</p>
<p>It's mate in 9</p>
<ol>
<li>e7! Bd8 2. e8=B! Bc7! 2. Bd7+! Kb8 3. Bxc7+ etc.</li>
</ol>
<p>Let me show some other off-the-wall examples...</p>
<p>Here's one based on the 50-move rule:</p>
<pre><code>[FEN &quot;7N/pP6/k7/8/K7/8/8/8 w - - 0 1&quot;]
</code></pre>
<ol>
<li>b8=B! White mates in 34.</li>
</ol>
<p>On the other hand:</p>
<ol>
<li>b8=N? This is a cursed win. Checkmate could eventually be forced, as is often the case for KNNvKP, but a draw intervenes under the 50-move rule. Black can delay the first pawn move or capture until move 54.</li>
</ol>
<p>Another example uses the obscure Dead Position rule and the clock. It doesn't use the half-dead rule, but it isn't disturbed by that. To force the bishop, I think we need to put Black under extreme time pressure (aka &quot;Zeitnot&quot;). The flag is trembling... :)</p>
<pre><code>[FEN &quot;6nk/7P/6pK/p5Pb/6p1/p5P1/P7/8 w - - 0 1&quot;]
</code></pre>
<p>White to play &amp; win over the board under FIDE rules, with Black under <em>extreme</em> Zeitnot.</p>
<p>Explanation:
White can only promote. If 1.hxg8=Q/R+? then 1. ... Kxg8= stalemate. If 1. hxg8=N?, then Black might instead try 1. ... a4 with 2. Ne7,Nf6= stalemate for the other side! So in all these cases no checkmate is possible, and the game immediately ends in a draw before Black has to reply.</p>
<p>On the other hand, if 1. hxg8=B! then game does <em>not</em> end immediately, because at least in principle there is the alternative lifeline 1. ... a4 2. Bb3 axb3 3. a3,a4 etc, and there are checkmates around for either side. This is of course sub-optimal, Black should of course play 1. ... Kxg8=, <em>but</em> he has to execute this before his quavering flag falls.</p>
<p>Question is: would White bring the game into disrepute by playing like this? :)</p>
<p>OK here's a final one: the most economical of all, showing the half-dead position rule at work.</p>
<pre><code>[FEN &quot;2b4r/P7/8/8/8/8/8/4K3 w - - 0 1&quot;]
</code></pre>
<p>White under Zeitnot to play &amp; draw over the board under FIDE rules. No Black king!</p>
<p>So in the excitement of the game, bK has fallen off or been captured. By the half-dead rule, White can't win, because he can't checkmate, but he can play on for the draw. However, Black can checkmate White, so the position isn't fully dead. Checkmate does not require that the position be legal, but mere that the last move be legal. That's the FIDE Laws.</p>
<p>If 1.a8=Q/R/N, then a mate is possible with e.g. wKh1, wQ/R/Ng1 bBh5, bRh8 &amp; eventually Bf3#. Even though this mate may not be forced, the possibility of this is enough to keep the game alive. However, 1. a8=B makes the position dead, as neither side can now checkmate.</p>
 2299: <p>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:</p>
<pre><code>[FEN &quot;N5q1/7P/8/8/8/7K/8/7k w - - 0 1&quot;]
</code></pre>
 15543: <p>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. Here is a small sampling.</p>
<p>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!</p>
<pre><code>[Titler &quot;Ignazio Calvi  Le Palaméde 4/1836, White Wins (Correction)&quot;]
[FEN &quot;8/6PP/3Pn3/6b1/8/k3P3/p7/K2B4 w - - 0 1&quot;]

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!}
</code></pre>
<p>However, it can also be motivated by the &quot;Dead Position&quot; rule. In the below position, suppose White is down to seconds on the clock. They have no queens or rook nearby and 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!</p>
<pre><code>[FEN &quot;8/3P4/8/8/8/7k/7b/7K w - - 0 1&quot;]

1. d8=B
</code></pre>
