I haven't seen this problem before, but that seems extremely unlikely to work to me - I think there are 2¹⁰²⁰¹ cases (not equiprobable although you can find the

I haven't seen this problem before, but that seems extremely unlikely to work to me - I think there are 2¹⁰²⁰¹ cases (not equiprobable although you can find the weight of each somewhat "easily"), so are you really going to get a good enough sample to measure the expected value to "five decimal places" without figuring out a lot about the underlying structure?