Originally posted by DeepThought
Ok., where on that scale would you consider it proved beyond reasonable doubt that the coin is predictable? The question's assumes that either the coin is unpredictable or God exists, it strikes me that that is something of a false dichotomy - for example, has cheating been eliminated? So really the question is when is it proved that the coin is predictable (a run of 5 is already past 95% confidence) and what you've done to eliminate cheating.
I do not see where a god necessarily figures into this inquiry, though a god could be neatly tucked into the "paranormal" category. But "paranormal" phenomena are tricky things: if one such phenomenon were to be proved to be real by means of the scientific method, then by definition the phenomenon is no longer paranormal.
I'll just say that if, in the course of a single experiment done once, someone were to correctly predict X=40 coin tosses in a row, and all possible cheats were eliminated (this is again quite hypothetical), then I would be prepared to entertain explanations that might currently be considered paranormal. If pressed, I would say perhaps information is being received by the test subject by some weird quantum mechanical means that amounts to something like precognition. I don't know. It's a "what if" scenario, and again, I would say the experiment would need to be replicable, otherwise it could indeed have just been a really, really, really lucky run of guesses.
How about X=500?
EDIT: Of course, an X=10 result received four times in a row is equivalent to an X=40 result, and could be considered successful replication of an experimental result. I hear that six-sigma certainty is good enough for particle physicists to consider a new particle as being "discovered." What X value does that correspond to in the current context? My statistics books are somewhat dusty and I just can't be bothered.