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I am looking for the shortest stalemate that has occurred in a serious chess game (there were no agreements between the players). So far, I have found only compositions, but is there a real game where stalemate has happened within the first 30 moves?

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Yes, there has been a stalemate in a serious game that is under 30 moves long. According to Tim Krabbe's "Chess Records," the fastest such game happened in 27 moves.

[Title "Sibilio-Mariotti, Ravenna, 1982"]
[fen "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1. e4 e6 2. Nf3 d5 3. e5 c5 4. b4 cxb4 5. d4 Nh6 6. a3 bxa3 7. c3 Nf5 8. Nxa3 Nc6 9. Nb5 a6 10. g4 Bd7 11. Bg5 Be7 12. gxf5 axb5 13. fxe6 fxe6 14. Rxa8 Qxa8 15. Rg1 Qa3 16. Bxb5 Bxg5 17. Rxg5 Qxc3+ 18. Kf1 O-O 19. Bxc6 Bxc6 20. Kg2 Ba4 21. Qe2 Bc2 22. Ne1 Bxe4+ 23. f3 Rxf3 24. Nxf3 Bxf3 25. Qxf3 Qd2+ 26. Kh3 Qxg5 27. Qf8+ Kxf8
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    Interesting. Black has what would appear to be a winning advantage, but the queen sac allows white to avoid a loss. Were it not for that, Black's advantages would be crushing. Black has both a mating threat via e.g. h5 Qg4++ and a queening threat on b1. If White had e.g. an extra pawn somewhere that could move but wasn't too well placed, black could win easily.
    – supercat
    Commented Aug 14, 2020 at 6:03
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    @supercat: Now I'm trying to figure out where White explicitly decided to start playing for a stalemate. I can't see any other logical purpose to 19. Bxc6.
    – Kevin
    Commented Aug 15, 2020 at 19:33
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    @Kevin According to a computer analysis from Lichess (lichess.org/rl8sul4u#45), Black had a huge advantage up to move 23, but then misplayed. Black would have kept the advantage if they played something like Bf5. White made a mistake on move 14 by not capturing the b5 pawn, and then subsequently trading pieces, which left Black with a passed pawn on the queenside.
    – Toby Mak
    Commented Aug 16, 2020 at 9:42
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    @TobyMak: Indeed, move 23 for black would look like a good move except for the possibility of stalemate, which Black probably hadn't foreseen. After that, White's best realistic outcome is a draw, and best play by both sides would lead to stalemate.
    – supercat
    Commented Aug 16, 2020 at 20:58