This is the variant that I've played - with the constraint that you must play at least one card, of course. We also included an endgame for the players that had managed to get rid of all their cards, though: they had to successfully guess whether the person sitting beside them was bluffing or not three times in a row in order to win, and had to pick up some cards and resume play if they didn't.

E: Since this was mentioned elsewhere in the thread, the variant I played only allows for the next player to challenge.