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Improbable, or highly unlikely; about as likely as the chance that "maybe" means "yes" rather than "no."; An unbelievable eventuality.
"What, from here? On the off-chance of a maybe that you make this basket, I'll wash BOTH your cars."

Person 1:"Its today? I didn't study!"

Person 2: "Don't worry, you won't fail!"
Person 1 sarcastically: "Sure I won't! On the off-chance of a maybe Mr. Hickerman forgot to bring the exam today!"
by AllThatIsGold October 04, 2017
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