@Aether This two-envelope problem, and I'm sure a hardcore statistician would shut me down on the spot for being completely incorrect, you can think of in terms of infinite numbers. Infinity is a number SO BIG, that you can take any discrete finite number of its elements and the infinity will still not be smaller - it's a bit like with lightspeed. Then these "free" numbers that you just conjured from your infinity become the edge by which you can be better than random by using something random.