If you allow randomization, you have an underspecified problem again. But you can fix it easily enough by saying that Omega fills the box with the same probability that you one-box.
Here's a variant that may help your intuition. Supppose that rather than let you pick directly, Omega asks you to write a computer program that implements whatever strategy you would have used, and that program chooses one or two boxes. In that case, the prediction would be trivial, and you would certainly want to provide a program that one-boxed.
Now suppose that instead of writing a computer program, you are one. Because you'e been uploaded, say. In that case, you would want to be a program that one-boxes.
The thing is, due to the physics underlying your brain, you are a computer program. A very complicated, randomized computer program which can't always be predicted by any means other than simulating it and can't necessarily be simulated without using resources that aren't available in the universe. But that's Omega's problem. Yours is just choosing a number of boxes.
The original specification of Newcomb's problem had the alien empty box B if he predicted I would use a random number generator. I'm not sure why Eliezer removed that restriction, but he did and that is a big part of what I writing about.
If you already believe that a PHYSICAL random number generator can be built based no quantum processes, and that such a generator can be interfaced with a computer and therefore called by, controlled by, with results read by a computer, then you don't need to bother with the details in the next paragraph. The purpose o...
I have not seen any place to discuss Eliezer Yudkowsky's new paper, titled Timeless Decision Theory, so I decided to create a discussion post. (Have I missed an already existing post or discussion?)