So this is based off simulation? My method led to a different conclusion but it wouldn't be the first time I made a mistake.
The numbers given were from a simulation.
I tried calculating it exactly but with average rolls exceeding 4 the numbers got too big to count.
The only surprise to me was the frequency of 6 being markedly higher than 5 or 7.
BG needed a somewhat flat distribution preceding 12, and it turned out flatter than I anticipated.
But his 6 5 4 3 2 1 argument would dominate small fluctuations.