I am trying to settle a score on probability and odds, and I just wanted to see what everybody thought. This springs from the fact that when you watch "Deal or No Deal" and cases are removed one at a time, Howie frequently announces that there is a 15% chance that the case holds a million dollars, then later it is a 25% chance, then 35% and so on, until (if it gets there) a 50% chance. The question is, do the odds really improve? My stance is that since the there were 26 cases present when the players case was chosen, that the odds will stay frozen at 1/26 up until the point that the player gets to "reguess" (if he gets that far) so essentially if there are two cases left, his case still has a 1/26 chance of being a winner, but if he is allowed to reguess with the new information it becomes 1/2. Here is a better example. I will randomly choose a card from a regular deck and proclaim that it is the Ace of Spades without showing it. The odds of me being right are of course 1/52. As far as I can see, there are only two ways of determining if I am right: A: Flip over my card and check B: Flip over all of the other cards, and if the Ace of Spades is not there, it must be my card Do you agree so far? Would either one of these give me a better chance at getting the Ace of Spades? NO!!!!!! Now, lets take a closer look at situation B. Lets say that instead of just flipping over all of the cards, I decide to flip them over one at a time, very slowly. This is ABSOLUTELY NO DIFFERENT FROM JUST FLIPPING THEM ALL OVER! My odds do not get any better as more cards are flipped over. My chances are still 1/52. If I happen to flip over the Ace, I know that I lost, but that has nothing to do with my odds. Now, if somewhere in there you give me a chance to choose cards, then my odds become 1/however many cards remain.