A ilttle while back on this blog I proposed that probability is fundamentally an epistemological matter. If someone had exact knowledge of the location of all of the particles in a "fair coin" as well as all of the relevant force vectors in a particular toss, then for that person the odds of heads coming up would not be 1/2 but 0 or 1. John G. in the comments section argued that while my contention is true, it is trivially so. I think not, and as a paradigmatic case of why not, I offer the Monty Hall problem . In the TV show Let's Make a Deal , a contestant would choose among three closed doors. Then, often, Monty Hall (the host) would call for one of the unchosen doors to be opened, revealing the "booby prize" of, say, a goat. Then he would present the contestant with the option of switching her pick to the other, still-closed, door. Most people's intuition is that there is no statistical advantage to either sticking or switching -- the odds the contestant ...