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 in

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.