Several treatments of the Shooting Room Paradox have failed to recognize the crucial role played by its involving a number of players unbounded in expectation. We indicate Reflection violations and/or Dutch Book vulnerabilities in extant ``solutions''and show that the paradox does not arise when the expected number of participants is finite; the Shooting Room thus takes its place in the growing list of puzzles that have been shown to require infinite expectation. Recognizing this fact, we conclude that prospects for a (...) ``straight solution" are dim. (shrink)