>It calls to mind the misconception that people have that prior events affect the probability of future events. At the casino, the roulette wheel, if I have hit black 3 times in a row, the odds off hitting red on the next spin have increased. That's different than saying that if I have 4 spins, what are the odds that one of the spins will result in red.
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>Perhas, if the problem is stated in such a way that it is clear that it is a strategy that the player has adopted from the beginning, prior to opening any door, that would shed some light on the fact that we are dealing with probability over time.

Exactly, the roulette is a good example - that's what I was trying to get at, but didn't state too well before.