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The mind-twisting part of statistics is that Fat Tony is partially right. Because although each independent throw has the probability of one half, the total resulting series is very unlikely.

So you could simultaneously be at awe of the incredible improbability of throwing another heads while proclaiming meh over the 50% chance of the last throw.

It's all a matter of perspective.

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The point is this: "Assume that a coin is fair" ... "the coin gotta be loaded"

In the example, Fat Tony is wrong because he contradicts the initial assumption. However, the example is unrealistic because, initially, you don't know if the coin is fair or loaded. You just flip it, see 99 heads and then conclude, with probability very close to 1, that the coin is loaded. (You could still be wrong, but likely aren't).

So in a realistic scenario, Fat Tony would be right, except that the scenario was intentionally set up to be unrealistic.

(edit: typo)

Tony knows the chance of head 99 times in a row is enormously smaller than the chance he's being played for a sucker.

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