I was wrong yesterday about the macrostate with the most microstates. I finally got round to making a chart showing the macrostates and their number of microstates. You'll see below that macrostate F has more microstates than J.
So I started the quantum shuffling with the dice from state A, the most unlikely. After 20 moves the oddity so far is state I which has been far more common than expected. It could be an artefact of starting from an unnatural point.