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Promoting to a bishop?

Actually... while the bishop and h-pawn endgame looks hard, it's probably easier than queen against rook (and pawns). After all, SF at depth 66 evaluates 2... Kxh4 as "#34" and 2... Kg6 as "#26" which is probably why it shows only 2... Kxh4 when looking at the initial position. Checking the position after 2. h4+ with multiple lines shown will show both variants.
The bishop and h-pawn endgame is a simple win for human players. 1.f7 Rxh6 2.h4+ Kg6 3.f8=B Kf5 4.Bxh6 Kg6 5.Bd2 and Black is completely helpless against invasion by the white king. The bishop is, of course, the right one for the h-pawn (a light-squared bishop would only draw!).
@mkubecek said in #10:
> If black plays 2... Kg6 instead, 3. f8Q would be a stalemate if I didn't miss anything. 3. f8B would force Kf7, Kf6 or Kf5 with 4. Bxh6. The resulting position still needs a lot of work but it should be winning for white.
>
> Edit: and Stockfish does see it that way too, you just have to leave it running at least to depth 40 or so.

Even at depth 40, Stockfish gives 2... Kxh4 as the best move (+2.4 for White as against +13.9 for 2...Kg6). Still a very interesting study in how to foil an attempted stalemate trap though!
@Wasted_Youth said in #15:
> Even at depth 40, Stockfish gives 2... Kxh4 as the best move (+2.4 for White as against +13.9 for 2...Kg6). Still a very interesting study in how to foil an attempted stalemate trap though!

Fascinating!
It's this sort of study which should make people who rely on Stockfish for the ultimate truth in a position to stop and think. It's a tool to aid analysis, and a very useful one, but it should not be relied on without critical human input too.

EDIT: Sorry, I'm being unfair here. Stockfish is right that 2...Kxh4 is the best move. The study shows why 2...Kg6 fails.
@Brian-E said in #16:

> It's this sort of study which should make people who rely on Stockfish for the ultimate truth in a position to stop and think. It's a tool to aid analysis, and a very useful one, but it should not be relied on without critical human input too.

Absolutely! It can be a drag to let it work through the variations, but the satisfaction in thoroughly understanding the solution is then so much greater.
I wonder how many more interesting examples of underpromotion could be found in the millions of openly available games in the Lichess database.

database.lichess.org/

I once played around with this in SCID. It's easy to filter for "underpromotion to bishop", but the problem is of course that 99% or so of the results are practical jokes. One would need to combine this with automated engine analysis, to filter out the very few meaningful underpromotions. So, if someone here has programming skills and is looking for a fun little project ... (;
Oh, and I now remembered this beauty from a Lichess user (a study, not from a real game):



A defensive underpromotion to Bishop is the only move to reach a stalemate.
Promoting to any other piece, or moving the king, will get you mated.
@Panagrellus said in #19:
> Oh, and I now remembered this beauty from a Lichess user (a study, not from a real game):

Very nice, though it's really just a more cluttered version of the V.Vlasenko study mentioned at the beginning of Tim Krabbé's article.

Sadly that study was flawed because this particular pawnless endgame after 1.h8=B with three minor pieces against two, assumed to be drawn at the time of the study, is now known to be a win thanks to tablebases.

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