playBunny: I think we all know the answer to that.

Just out of curiosity I looked at the 55 games in matches I have completed in 2010. There are 8 in which the first two rolls were the same (same two dice, order not considered), versus the predicted 3 and change. Both dice different, predicted 24, actual 19.

I've performed a Chi-squared test on the hypothesis that the probabilities of responder's first roll having 0, 1 and 2 dice the same as opener's roll are as they should be, that is 16/36, 18/36 and 2/36 respectively.

This is a test with 2 degrees of freedom, so the chi-squared statistic has:
 a 5% chance of exceeding 6.0 if the probabilities are correct,
 a 1% chance of exceeding 9.2
 a 0.5% chance of exceeding 10.6, and
 a 0.1% chance of exceeding 13.8

alanback's result (from 55 games) is 9.2.  A result this high or greater would happen only 1% of the time, so this is enough to cause suspicion that the dice aren't following the desired probabilities.  But it's not proof.  Also, this test is reckoned to give very accurate results only if the expected outcomes are all greater than 5.  So, with our smallest probability being 2/36, this means we need at least 90 games in our sample for me to be happy beyond reasonable doubt about the conclusion.

So, moving on to my results (100 games), I get a statistic of 102.

And lastly, wetware's results (137 games) give a statistic of 139.

Remember, if the dice rolls are working properly, there's only a 1 in a 1000 chance of this chi-squared statistic being 13.8 or higher in any individual test, so the conclusion can't really be in doubt - something is wrong somewhere.

playBunny:  Look on the bright side, pB:  we've been given a new, unannounced game/puzzle/variant!

It's quite a bit like backgammon.  It's similar enough, in fact, that those who prefer to make their moves and cube decisions just as their bots dictate (these players know who they are) can continue to do so with success.  Others can continue playing, without ever realizing that it's a subtle variant--but is not standard backgammon.  Still others eventually wake up to the fact that the normal rules no longer fully apply, and that adjustments will be necessary to maximize their equity during play.

But it's a significant challenge to determine exactly which adjustments are needed.  So it also has an added element of mystery: requiring clues, evidence, and deduction.

I rather like the social element of this new game: players working together as a team to find the solution.

And it's a whodunit.