Just finished it, have to take a while to collect my thoughts. Powerful stuff though. Written by the creator of Dilbert of all things.
I would have answered "Probably not five hundred times."
An even split is the most likely outcome (actually, 501-499 is more likely if you don't care who wins), but it is still not very likely. Even if you only flip ten times, it's a good bet that the outcome won't be a tie. If ties were more likely, arguments in favor of voting would be a lot more convincing.
When you flip a coin a thousand times, the chance of a tie is only about 2.5%. And this is with a fair coin; voters tend to number more than 1000 and have a bit more bias.
I had to think about this. First I thought of an explanation based on weight and shape, like the narrator. Then I thought of Feynman and thought the best answer would be “That, nobody knows.” Finally I decided that the coin is part of a thought experiment in which it is defined as an object that comes up heads fifty percent of the time. It's a given.