Craig comments on Conjunction Fallacy - Less Wrong
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Maybe I am wrong but I think to get the probability of an arbitrary sequence appearing you have to construct a markov model of the sequence. And then I think it is a bunch of matirx multiplication that determines the ultimate probability. Basically you have to take a 6 by 6 matrix and take it to the 20th power. Obviously this is not required, but I think when people can't calculate the probabilities they tend to use intuition, which is not very good when it comes to probability theory.