I had originally heuristically reasoned in a similar but opposite way, to the wrong answer. To wit: 1. P_{1/6} = 1/6 [when rolling one die, you have a 1/6 chan

I had originally heuristically reasoned in a similar but opposite way, to the wrong answer. To wit: 1. P_{1/6} = 1/6 [when rolling one die, you have a 1/6 chance of getting more than 1/6 many sixes] 2. P_n -> 1/2 as n -> infinity, by the central limit theorem 3. I couldn't see any reason that P_n shouldn't be strictly monotonic. Thus I expected that P_1 < P_2 < P_3