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fubarobfusco comments on Critiques of the heuristics and biases tradition - Less Wrong
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This depends on your prior for the occurrence of biased coins! If you have 10 coins of which one is two-headed and the others normal, and you draw one and start flipping, it doesn't take many flips to be pretty sure you have the two-headed coin. But if biased coins are very rare, it takes a lot more flips.
Given 2^100 odds, it's more likely the person flipping the coin is using the double-headed quarter I tossed into a wishing well in Mexico ten years previously than that the flips were entirely natural.
It works out to 6.338*10^29 against, assuming we're not favoring a series of heads over tails. At those odds, a casting mistake resulting in a chunk of ferrous material being embedded in the coin and a magnetic anomaly caused by the alignment of the microwave and the toaster and the fact that the television happens to be tuned to channel 29 with a volume setting of 9 start to become viable contenders as explanations.