grenv: I'm off to bed so just a quickie..

46656 / 36 = 1296 and 1296 / 36 = 36. Such a number ensures that each dice roll is represented fairly for the first three moves.

I've done rollouts to 1296 and to 12960. Similar principle; 10 goes each for each pair of opening rolls in the latter case.

The 1296s were just so many wasted CPU cycles. Even at 12960, though, the expected error value exceeded the difference between the top moves in many cases. Getting the error values small enough to reliably decide between two moves would require rollouts of 500,000 and more.

I agree with 3-1, and 6-1's up there too. Whether the results can reliably differentiate between the least popular rolls I'm not sure. I'll have a look at what I found in a few hours...