Actually, before I completely throw up my hands, I should probably figure out what seems different between the one-on-one trade and the billion-to-one trade that changes my answers...

Oh, I see. It's the tiering again, after all. The infinite Fun is itself a second-tier value; whether or not it's on the same tier as a life is its own debate, but a billion things possibly-equal-to-a-life are more likely to outcompete a life than a single one.

... of course, if you replace "infinite Fun" with "3^^^^3 years of Fun," the tiering argument vanishes but the problem might not. Argh, I'm going to have to rethink this.