campboy, on May 25 2010, 11:49 AM, said:
As any of my first-year probability students would be able to tell you, the answer to the question "how likely is it that this board was fairly dealt given the hand I have?" depends on three things: the ab initio chance of a fair deal; the chance of this hand being dealt given a fair deal (which is, as you say, the same for every hand); and the chance of this hand being dealt given an unfair deal (which very much isn't).
Perhaps we should also consider the probability that the hand is a deliberate "joke".
I think: P(13 spades | joke) > P(random hand | joke)
I think campboy presumes: P(13 spades | dealing error) > P(random hand | dealing error)
Since there is some chance of either jokes and/or dealing error,
we must conclude: P(13 spades) > P(random hand)

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