Most of the histories of probability trace their facts back to Hacking and David, and I agree these two books are the best of the bunch I have read. The Hacking book itself references David. I love the Bernstein book series but I noticed his page 43-44 has some musings on why the Greeks didn't bother with working out odds behind dice games. I bet they did. Anyway, he offers an example of the so-called sloppiness of the Greek observations of dice probabilities by mentioning some facts he gleans from David - namely that when using the astragali they valued the Venus throw (1,3,4,6) higher than (6,6,6,6) or (1,1,1,1). which are, he states "... equally probable".

No, they are not. David clearly states that the probability of throwing a six as one in ten; likewise with throwing a one. And threes and fours are about four in ten events. This means that even if order is important, the Venus is indeed more likely. Second mistake, there's only one permutation of four sixes, and only one permutation of four ones. But there are many permutations of the four Venus numbers, meaning the probability of (1,3,4,6) in any permutation is even higher again than the strictly ordered (1,3,4,6).

It is this partition/permutation dilemma of probability theory, even today, which is so easy to get wrong. I just re-read some earlier postings I made on equivalence classes and their information content and key milestones in probability theory, and I still like what I wrote. Also check out a posting on combinatorics in Cardano and Lull.

It is just a throwaway comment in Bernstein's book and hardly invalidates his wonderful sweeping history of risk but is nicely illustrates the problems of thinking about event space and equivalence class.