We have used the board game Clue as a pedagogical tool in our course on Artificial Intelligence to teach formal logic through the development of logic-based computational game-playing agents. The development of game-playing agents allows us to experimentally test many game-play strategies and we have encountered some surprising results that refine "conventional wisdom" for playing Clue. In this paper we consider the effect of the oft-used strategy wherein a player uses their own cards when making suggestions (i.e., "bluffing") early in the game to mislead other players or to focus on acquiring a particular kind of knowledge. We begin with an intuitive argument against this strategy together with a quantitative probabilistic analysis of this strategy's cost to a player that both suggest "bluffing" should be detrimental to winning the game. We then present our counter-intuitive simulation results from playing computational agents that "bluff" against those that do not that show "bluffing" to be beneficial. We conclude with a nuanced assessment of the cost and benefit of "bluffing" in Clue that shows the strategy, when used correctly, to be beneficial and, when used incorrectly, to be detrimental.