[AaronBrown]

I think BruceZ just read your second post, which by itself gives the impression you ran the simulation first. I think he would agree that it makes sense to use the computer to check a hand calculation. The hand calculation gives a precise answer, but if you make an error you can be off by a huge amount. The computer has random noise, but usually gets pretty close (unless there's a bug in the code, but then it's unlikely to agree with your incorrect hand calculation).

I have most faith in a calculation when I do it by hand, then check it by simulation. It's easy to make a mistake by hand, and often the problem has to be simplified. But I agree with BruceZ that a simulation by itself hurts more often than it helps.