I get what you are saying, but you can only pick one square to fire on next. Knowing the exact probability of every square left (differnetiating between white and almost white), does not help you if, on each move, you take the square with the next highest probability.

If you have a bag containing 85 red balls, 10 yellow balls, 3 blue, and 2 black, and had to draw one and predict its color, are you going to change your answer about red even if you are told that someone stole one of the blue balls before you picked? :)