Okay, let's try and defeat Omega. The goal is to do better than Eliezer Yudkowsky, which seems to be trustworthy about doing what he publicly says all over the place. Omega will definitely predict that Eliezer will one-box, and Eliezer will get the million.

The only way to do better is to two-box while making Omega believe that we will one-box, so we can get the $1001000 with more than 99.9% certainty. And of course,

1. Omega has access to our brain schematics
2. We don't have access to Omega's schematics. (optional)
3. Omega has way more processing power than we do.

Err, short of building an AI to beat the crap out of Omega, that looks pretty impossible. $1000 is not enough to make me do the impossible.