You cannot necessarily just decide to think of something random which would be required in order to be unpredictable.

Presented with this scenario, I'd come up with a scheme describing a table of as many different options as I could manage -- ideally a very large number, but the combinatorics would probably get unwieldy after a while -- and pull numbers from http://www.fourmilab.ch/hotbits/ to make a selection. I might still lose, but knowing (to some small p-value) that it's possible to predict radioactive decay would easily be worth $100.

Of course, that's the smartassed answer.