"Of course we do. So..a different drink for every round." He explains the game to the barkeep so that he can keep loading them up as they finish. He acknowledges it and starts them off with their first set of drinks.

"Okay so we don't move onto the next round until each of us has finished everything in the glass." And these glasses are significantly larger the the little cups they are used to. It's not going to be a quick shot and then done. But luckily the bartender does give them the ones that are about half the size of a normal drink so they at least won't pass out within the first couple rounds.

"first one that can't finish their drink within a five minute time limit..loses!" Since the barkeep is prepared, he already has a timer that he sets on the bar and agrees to reset after every drink.