(a) fat chance = Wohl kaum, Geringe Aussichten, Daraus wird nichts, vergiss es
"All I'm saying is that there is A FAT CHANCE of you winning the competition!"
BBC
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A FAT CHANCE, of course. I should have known his psychology better.”
P. G. Wodehouse in "Laughing Gas"
a fat chance
idiomatic phrase, used ironically
- practically no chance at all
The Dictionary of Clichés
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ORIGIN
Although fat in this context suggests “good”, the term is always used ironically to mean hardly any chance.
A related expression is "a fat lot" meaning "very little or none at all" as in "a fat lot of good it will do her".
"A fat chance" dates from the early 1900s, "a fat lot" from the 1890s.
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SYNONYMS
a Chinaman’s chance, a snowball’s chance (in hell)
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Find an opportunity to SMUGGLE OWAD into a conversation:
"He has a FAT CHANCE he has of getting a promotion."
"Do think she'll lend you the money? FAT CHANCE!