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Ooooh, Nassim Taleb set up a rigged thought experiment, well that has convinced me!

Taleb couldn't convince me grass is green. I agree the rationalists are a little too credulous, but that's not so much rationalism per se as that the people espousing it round these parts tend to be very nice, well-meaning types who are somewhat idealistic and progressive and are all about the openness to experience, trust, being charitable, and giving the benefit of the doubt.

Now, as to the coin flipping: who is the guy doing the flipping? Is he trustworthy? If you want to tell me that Fat Tony is right, because Taleb is the guy doing the flipping and he's shady as fuck so this is a loaded coin, okay - but I don't think that's the conclusion you want me to draw about the trustworthiness and believability of Taleb.

You want me to trust Taleb, that he is right about Fat Tony. But if Taleb is right about Fat Tony, then Fat Tony is right that this is not a fair coin, and so Taleb is a liar, and so Taleb is untrustworthy, so why should I believe him about Fat Tony?

(1) The coin toss could be fair, and Fat Tony is wrong.

(2) The coin toss could be rigged, and Fat Tony is right.

Just from the details given, we don't know which option is correct. Now, in general and in real life, if someone is trying to get you to bet money or agree to something based on "if I flip this coin 99 times and it comes up heads 99 times, we'll bet does it come up heads the 100th time" - yeah, be suspicious.

In a thought experiment? Where the guy has the incentive to make it that Fat Tony is right, not Dr. John? Yes, that's rigged - but not about the 50/50 chance of the coin coming up heads, but about Fat Tony never, ever being wrong.

Now, as to the coin flipping: who is the guy doing the flipping? Is he trustworthy?

With 99 heads in a row it doesn't really matter. There is literally no one in the entire world that you should trust enough that you would still believe the coin is fair. 2^-99 is a ridiculously small number.