"I would have thought that the probability of getting aces six times in a row would be (12/1326)^6 ~= 1/(1.8 10^12) or about 1 in two trillion. "
Before the fact (apriori): the probability of getting wired aces : 4/52 * 3/51 = 1/221,
and
(1/221)^6 = 1 / (116,507,435,287,321) =
1/(1.16507435287321 * 10^14)