What happens to the "conversational score" when speakers in a conversation push the score for a context-sensitive term in different directions? In epistemology, contextualists are often construed as holding that both the skeptic ("You don't know!") and her opponent ("Oh, yes I do!") speak truthfully when they debate. This assumes a "multiple scoreboards" version of contextualism. But contextualists themselves typically opt for "single scoreboard" views on which such apparently competing claims really do conflict. This paper explores several single scoreboard options (...) for contextualists, opting in the end for the "gap view," on which neither of our debaters speaks truthfully. (shrink)