The fallacy of the one-side bet is the presentation of something with very small odds as though it were more or less a 50/50 proposition, with evidence for and against that one would have to weigh. So suppose you thought there were only two colors, red and black, and were trying to calculate the odds of a card turning up red or black. But this deck of cards has a million colors. Once you get locked on the binary opposition, then you are tricked into a particular way of thinking, looking at lottery tickets as though they were coin tosses.
One example Andrew gives is the idea of "opportunity cost" in economics. Sure, everything has an opportunity cost, because doing something, or spending money on something, means not doing something else, or not spending the money elsewhere. But since the other things I could be doing instead of what I am doing now are infinite, how do we conceptualize what I am giving up? I'm not sure if this is what he means by the idea that opportunity cost is a fallacy, but this is what I have always thought of the concept.