No signs of anything unusual in the individual dice values from the opening rolls of my 702 games from 2008. The distribution looks normal to me.
INDIVIDUAL DICE: 1 on die = 232 occurrences 2 on die = 245 occurrences 3 on die = 234 occurrences 4 on die = 236 occurrences 5 on die = 231 occurrences 6 on die = 226 occurrences
I'm not as confident about the paired values observed in these 702 games. But I'm not alarmed by these, either.
I think most of us didn't suspect that there was anything odd about opening rolls, considered in isolation. But whether we were skeptical or not on that point...we really had no data. But now we do. Sometimes it's worthwhile to gather data that helps us eliminate areas of concern; it can help us identify exactly what is broken here.
Next on my to-do list: analysis of my next to last pairs of rolls from my games from 2009. Between the first pairs of rolls, we've already seen greatly excessive reappearance of at least 1 die from the opening rolls. What I'd like to learn: whether there is any similar excess evident between rolls that occur later in games, or whether the focus needs to be placed upon the second rolls of games--and the routines that generate them. I have no preconception here. I'm going where the data leads.
wetware: I've abandoned my efforts to gather any more data relating to 2nd roll behavior. Have submitted a Bug Tracker entry containing a summary of my 2008-2009 games, despite BK's a priori claim that problem reports involving dice are groundless.
Thanks to those of you who helped with the statistical analysis or provided other insights.