Roger: "I made 10,000 repetitions of 226 random numbers, comparing them to Don's probabilities and counting the number of times the random number was smaller than Don's. Those counts made up a histogram and the largest number was 40 Don's 33 is 3 sigmas from center."

John: "Don's score of 33 is three sigma better than the random choice's average performance, that is, the random score only achieved a score of 33 a few dozen times out of 10,000."

So the score of 33 is being compared to the "random" median of 30. The median of 30 is defined as "the random choice's average performance". So I guess I was only way off in thinking I was way off. Pretty much I got it, sort of, maybe.

Anyway, thank God I am no longer taking sides.

"since Don probably [big assumption but Don does not reveal his method so assumptions will be made] chose his times based on when unusual levels of seismic activity were happening, it remains possible that Don's score were above average because he was essentially predicting aftershocks, as well as the more obvious possibilities that he was just lucky"

My previous shy version of this: "If so, how do you avoid the temptation to say that Don's score is only slightly higher by chance?"

I knew I would be in agreement with John Vidale eventually. I just knew it. :)