Earlier quoted context omitted.
I don't really get it either, but I think the idea is that you're supposed to somehow optimize on the assumption that your opponent is equally likely to be using any strategy. (To my mind this makes the problem very confusing because it's such an unrealistic assumption.) If you assume that the only possible strategies are "rethrow if my first throw is <= x", then you can define a function f(x,y) giving the EV where x…
And no, you don't assume that every strategy is equally likely. You assume that the opponent plays optimally with full knowledge of your own strategy, which means you're looking for a Nash equilibrium http://en.wikipedia.org/wiki/Nash_equilibrium
Makes sense. I didn't realize the problem description was for a game that would be played repeatedly with the same opponent -- i.e. one where you can gather information. If we were doing this in person instead of on a internet forum and async post/response we'd probably iron that out quickly. Thanks for elaborating.