"Тройбан" is a slang word for "три" (more rude variation of 'three'). I know that also exists word "трояк", less rude and more common; affix "як" can be attached to some other numerals to make more informal, little bit ironical lexeme: e.g. "двояк", "пятак".

But affix "бан" can only be found in the word "тройбан". So, I guess, this word has a special, particular origin. I heard an interesting story: word "тройбан" is derived from "троебан", which, in it's turn, goes from word "трое ебан", i.e. "ебан тремя" (literally means 'had sexual intercourse with three persons at once'). But I haven't found any further information about this version.

So, my question is: what is true etymology of that word?

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    It's always funny how ad hoc folk etymology is completely nonchalant about creating more questions as it tries to give answers. How could something as ungrammatical as трое ебан have possibly existed? And while the double [-jı jı-] succumbing to haplology is plausible, how would it go on to lose the vowel, triggering a quantitative shift in the preceding /о/? – Nikolay Ershov Oct 9 '16 at 13:56

-бан is an argotic suffix that is used to create word that is not used in normal/official language as one of purposes of argot itself. See тройбан, щелбан, дружбан.

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    Speculatively, the ultimate source of that -бан might be German loanwords like кегельбан and автобан, where the opaque Bahn following a transparent root came to be perceived merely as a quaint noun-deriving suffix. Whether or not it's true, the augmentative suffix -ан (друган, etc.) was likely an influence. – Nikolay Ershov Oct 9 '16 at 16:18

I believe this word belongs to school slang exclusively. And concerning its roots, it's most probably derived as a pure occasionalism with a pattern similar to дерибан, щелбан etc.

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Just to prove the previous answers and to disappoint you:тройбан. belongs to school argot, "Словарь русского арго" Елистратова

ЩЕЛБАН, -а, м. Удар, щелчок. Возм. из шк.; общеупотр. «щелчок» + арготический суффикс «-бан» (ср. ДРУЖБАН, ТРОЙБАН и т. п.).

Жаргон номиналов в нумизматике

• 3 - алтын (алтынник) (с 1534 г. до начале XVIII в.) - (по Торговой книге 1670 г. 1 алтын=3 новгородки=6 денег=12 полушек), трешка, трояк, троячок, троечка, трояшка, тройбан, треха, трюльник, трюндель, , трынка, трёхкопеечник, трехрублевик, трехрублевка, трешник, трёшница; зелененькая, зеленушка (по цвету купюры 3 рубля царской и СССР)

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