Czuch: Whenever someone says "it seems more often than random that ..." about a random process it seems more often than not that it's their brain seeming things and not the random process.

Without knowing how BrainKing's dice are generated I can say nothing with certainty about the rolls, however, as I see absolutely no benefit to Fencer or the players in having every dice generated according to the clock it would surprise me greatly if it were the case.

But it's moot anyway because there's no way for us to determine the timing of dice events.