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.
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)
If this was a real life situation, we would assume a reasonable prior for the probability of heads, perhaps with a spike around 0.5 and a small value everywhere else. The posterior would be centered near 1.
"Assume that a coin is fair, i.e., has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw? 2
Dr. John refers to the question as trivial and gives the mathematically correct answer of one half. Fat Tony calls Dr. John a sucker and says, “no more than 1 percent, of course … the coin gotta be loaded.”"
The point being, what are the odds of getting an artifact of statistics precisely when management is harrassing employees to get rid of them from payroll?