He staggers up to the counter, and points at the guy in the middle, shouting, "Your mom's the best fuck in town!"
Everyone expects a fight, but the guy ignores him, so the drunk wanders off and bellies up to the bar at the far end. Ten minutes later, the drunk comes back, points at the same guy, and says, "I just did your mom, and it was sweeeeeeeet!"
Again, the guy refuses to take the bait, and the drunk goes back to the far end of the bar. Ten minutes later, he comes back and announces, "Your mom liked it!"
Finally, the guy interrupts. "Go home, dad, you're drunk.”
Edit: due to a series of comments in this thread I wound up creating a new subreddit: /r/drunkjokes
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