Here is an explanation for “though” at the end of a sentence

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“I don’t know though”

Though is a shortened form of “even though”. A sentence ending in “though” is still an “even though sentence”.

I’ll use my first example, “I don’t know though”.

Even though I should know, I don’t know.

So, instead of saying “even though I should know”, we can shorten all of this and just say “though” at the end of the sentence.