Breaking news: Dice obey laws of probability

I took a first stab at the experiment described in "My plan for a sync experiment." I rolled a pair of dice 1,000 times and entered each roll into a spreadsheet. Of the 2,000 total die rolls, this was the distribution of the different faces:

• One: 355 rolls (17.75%)
• Two: 312 rolls (15.60%)
• Three: 331 rolls (16.55%)
• Four: 324 rolls (16.20%)
• Five: 347 rolls (17.35%)
• Six: 331 rolls (16.55%)

Given those frequencies, the chance of rolling dubs (i.e. both dice showing the same face) is the sum of the squares of the above percentages, which comes to 16.70%. (I did that math instead of assuming a 1/6 probability because these are cheap dice and unlikely to be perfectly fair.) In fact, I rolled dubs 164 times. That's slightly but not significantly lower than the expected 167. So, absolutely zero evidence that I roll dubs more often than I ought to.

Which is of course not remotely surprising or interesting. But if you would have published the results of an experiment if they had been surprising, there is a moral obligation to publish anyway if they turn out not to be surprising. Hence the current post.

It's possible in principle that some very slight anomaly would become visible with a much larger number of trials, but the contingency is a remote one. I'm not inclined to spend any more time on this hypothesis.