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Once, when I felt it was time to give up, instead of resigning in some conventional way such as knocking over my king, I saw that I had a helpmate in one, so I decided to go for that. This happened when I was playing a board in a simul. When the exhibitor got to my board and I made my silly move, instead of executing the mate and shaking hands as I'd expected, he stared and stared at the board, as if wondering what the hell I was up to. Finally, embarrassed, I knocked over my king and shook hands.

Is "resigning by helpmate" totally unheard of? Is it somehow rude?

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No, it's absolutely not unheard of. It happens frequently (even at the highest levels) and can actually be seen as a sign of sporting spirit to allow the opponent to execute an excellent combination leading to a mate (instead of e.g., giving the queen instead, surviving a few more moves in an utterly lost position). This applies to the vast majority of games played on the master level that end in checkmate.

Look at Petrosian vs Minasian, 2006, for example: Instead of playing 28. ..Qb5 or 28. ..Ng5 (prolonging the game) or resigning, GM Minasian decided to allow an extremely beautiful mate in 2 with a pawn instead.

             [FEN ""]
            1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Nxe4 5. Qe2 Ng5 6. Nxg5 
            Qxg5 7. d4 Qe7 8. dxe5 Nd4 9. Qd3 Qxe5 10. Bd2 Ne6 11. Re1 Qd6 12. Qh3 Be7 13. Bd3 c6 14. Nc3 Qc7 15. f4 g6 16. g4 O-O 17. f5 Ng5 18. Qe3 Bf6 19. Rf1 d5 20. fxg6 d4 21. gxh7+ Kg7 22. Qe1 dxc3 23. Bxc3 Qb6+ 24. Kh1 Bd4 25. Qh4 Ne6 26. Qf6+ Bxf6 27. Bxf6+ Kh6 28. Rf5 Ng7 29. Rh5+ Nxh5 30. g5#

This is a case of sporting spirit. GM Minasian allowed his opponent to finish a beautiful painting for history books, something GM Petrosian will fondly remember for the rest of his life.

However, it can be weird to help mate when there is no exciting combination at hand that you want to allow your opponent to play out. Consider this position:

            [FEN "5k2/1b3ppp/8/pP6/P7/8/5PPP/3R2K1 b - - 0 1"]

In a position like this, it would be very strange to play Kg8 instead of resigning. It's just a horrific blunder, and there is no particular beauty in the move. It may even be considered rude, because it may be anti-climactic after a game where your opponent has skillfully outplayed you. You butcher their painting. An ignoble end to an otherwise charming game. It may be perceived as transmitting a message along the lines of "You didn't beat me because of your strong play, but because I didn't really make an effort and helped you", "I don't take this seriously" or "No need to be proud of yourself. Congratulations on winning against someone who would blunder mate in 1". There is just something about the deliberate carelessness/provocativeness that I do not like (as I do not see what could be nice about the move).
It reminds me of spite-check or dragging out lost positions with mediocre moves where the loser doesn't shine a good light on themselves. Taking the game and your opponents seriously and treating them with respect is a sign of good etiquette. I guess that the move you played was in the latter category (or he didn't see the fun/beauty), hence the reaction from your opponent.

I would not play Kg8 in such a position but resign with dignity.

P.S. (edit): It just appeared to me that in the framing/phrasing of your question, it already seems that you weren't taking the game very seriously, as you were looking to end the game in a funny way. This can be fun, if both players are on the same page, just as playing the Bongcloud opening can be to start a game.

This has also been done on the highest level when world champ Magnus Carlsen played it in a game against Nakamura (who laughs and accepts it) that wasn't important as both players had already qualified for the next stage of the tournament. Nothing was at stake for either player and they would have agreed on a quick draw anyway - the perfect opportunity for having some fun.

However, playing the Bongcloud can also be very malapropos. Imagine being matched in a classical tournament with a much stronger opponent. You are looking forward to a serious game and hope to use this unique opportunity to learn something from your opponent. Your opponent, however, decides that it would be more interesting or fun (at least for them) to play the Bongcloud opening. Of course, you still don't have the slightest chance, and they humiliate you in a crushing game. In this case it is one-sided fun at the expense of the other. They can then later mock how they won a classical tournament game with it.

Would you laugh, or maybe rather get angry about it. Would you feel respectfully treated? Or would your counterpart's behaviour seem arrogant to you? What would change if you played against your best friend, you didn't care about the outcome and they knew you were always up for some fun?

As long as both sides are happy with it and feel well-treated, it can be absolutely appropriate to have fun in an unconventional way ;)

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    @bof I just added a whole new section (P.S.) in my answer that I think explains the core of the issue - it's all about whether both parties think it's funny, or only one.
    – Hauptideal
    Oct 16, 2022 at 22:42
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he stared and stared at the board, as if wondering what the hell I was up to

This is probably what he was thinking.

Such an unexpected move could be either

  • a blunder¹
  • a trap

It's thus normal to look out, when the adversary does a "silly move" that it doesn't have a nasty surprise attached.

It's a bit strange however that you state it was a mate in 1, so the exam should have been pretty quick. I can only guess that it either wasn't mate in 1 or the exhibitor was studying a different variant which wold have been longer.

¹ Here you were doing it on purpose, but from a position analysis it would be equivalent to a blunder.

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