dweil (a floor cleaning cloth usually dirty) Branny! That's it! At least the first word. Here's what the article says, in part:
"Not Your Average Drinking Game"

The game, which some believe has been played since medieval times, calls on players to fling a beer-soaked rag from the end of a small stick toward the face of an opponent, and in the event the tosser misses the target two straight times, he must quickly down a half-pint of ale.