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A fat chance and a slim chance are the same thing
(lemmy.world)
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
I've always loved Mace Windu telling someone "your chances come in two sizes: slim and fat" in an old Star Wars Novell called Shatterpoint.