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Some figures based upon every one of my year 2008 BrainKing backgammon games (n=702) in which at least 2 rolls are saved in the system:
Out of 702 games played, the average expectation for the number of games in which opener's and responder's rolls will be identical = 39 games. Observed number of games in which identical rolls were seen=123 games.
Roughly 3 times the expected frequency!
Out of 702 games played, the average expectation for the number of games in which responder's dice will both be different from opener's dice = 312 games. Observed number of games in which this occurred=156 games. (Somebody should double-check this. It's very close if not correct, but I'm tired.)
(hide) If you click on a person's name and then click Finished games you will have a list of games that have been completed, then click on the name of the game to get a summary of all of these games, then click on the name of the game again and you will have a game to view and analyze. (Servant) (show all tips)