I am very humbled. The reason I'm wrong is that you are opposing another person's numbers - the expected dollars for a given number isn't linear. A .30 is wor

I am very humbled. The reason I'm wrong is that you are opposing another person's numbers - the expected dollars for a given number isn't linear. A .30 is worth way less than half as likely win you money than a .60 is. Because of this, the shape of your distribution matters more than its "average" value. I can't believe I forgot that AVG(F(X)) ain't necessarily F(AVG(X))