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Yesterday, after squandering a win, I played on until stalemate (actually, I offered a draw, but my opponent isn't a native English speaker, so I don't think she understood; in a few more plies we hit stalemate).

I realized I didn't know how to indicate this on my scoresheet and I just wrote "stalemate" in English.

Question: Is there a proper way to indicate "stalemate" on your scoresheet?

For checkmate, I believe it's usual to write #, but I'm not sure for stalemate.

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On your scoresheet you are required to record the result which 99.99% of the time will be one of 1-0, 0-1, ½-½. In the very rare cases when it is not one of those somebody will almost certainly be appealing the arbiter's / organizer's decision ;-).

You are not required to put how that result was achieved, e.g. flag dropped, resigned, defaulted, draw by 3-fold repetition, draw by 5-fold repetition, draw by 50 move rule, draw by 75 move rule (I actually got to rule that in a junior competition a few weeks ago - a real pain in the backside having to count up to 75 ;-) ), successful draw claim under appendix G in a quickplay finish that my opponent wasn't trying to win, successful draw claim under appendix G in a quickplay finish that my opponent couldn't win by normal means, checkmate, stalemate, etc. Note that I believe some national federations still allow adjudication but FIDE does not.

You get the picture! It would get a bit silly. Of course you are free to record that if you want. Just that not being a requirement there is no "approved" way for doing this.

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    It could be technically incorrect to record a draw as "0.5-0.5". The proper notation according to the glossary of the Laws (under "result", referencing 8.7) appears to be "½-½". See also "Points" (Article 10), where ½ is again used. – Post-It-Note Jun 2 '16 at 13:16
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Stalemate is so rare that it doesn't seem to have it's own notation symbol. It is not listed in the FIDE Handbook, section C.13, which is the official source on these kind of rules. Even the symbol for mate (#) is optional. I would just go for the word 'stalemate' like you did.

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2c:

Seems logical to use the symbol for zugzwang (no good move) and checkmate next to each other: ‡# (zugzwang is usually a circle with a dot at the centre.)

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