Then let's just agree to leave it there. As I said earlier, I know that the vast majority of posters here will have no use for this line of reasoning. My degree is in mathematics eduacation, but it seems that explaining this to a point of satisfaction is going to be beyond my capablities. If anyone wants to discuss this any further, and how I believe this benefits my game, feel free to pm me. For forum postings, I will continue to add trip reports and chime in from time to time on counting issues, to which I am fully committed. Regards to all, and I wish you well.