Sawyer explains the rules of the game to Kate -- someone says "I never did [whatever]" and if you have actually done it, you drink -- and then the two of them get down to the rare character exposition that doesn't require flashbacks.
We soon find out that Sawyer hasn't been to college. Kate hasn't been to Disneyland; Sawyer responds, "Aww, that's just sad!" Heh. Sawyer's worn pink at some point in his life, but he defends it with "the eighties." He's never voted, something that can't be defended, period. Sawyer's never been in love, but Kate has. Shocker of all shockers, Sawyer has to admit he's had one-night stands. Then we find out Kate was married. Then she says, "I've never blamed a boar for all my problems." Sawyer rolls his eyes and drinks, but gets some of his own back with, "I never cared about getting carte blanche because I just wanted to spend some time with the only other person on this island who just don't belong." Kate drinks. And then jabs again with, "I never carried a letter around for 20 years because I couldn't get over my baggage." Sawyer gives her A Look. And instead of responding, "I never suggested that hearing your father murder your mom before killing himself is fairly insignificant," he drinks. And then he says sadly, "I never killed a man." Now it's Kate's turn to look all upset. She drinks, resentfully. So does Sawyer. He finally says, "Well, looks we got something in common after all, mood killer." More or less. Let this be a lesson to everyone on the island: if you want to play a game, don't invite Kate.