Tobacco may, but the ash doesn't. It doesn't hurt compost, but it doesn't really add anything to it.
I use a flower pot or this old ceramic bowl I threw in college as an ashtray. Works for me. Sorry. I really like the big crystal single ashtrays, though. I also remember the old-school ashtrays on stands that were in fancy hotels back in the days where you could smoke in hotel lobbies.
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