re: Let's Find Out How Smart You Baws Are

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Not sure about this, just seems like a reverse of the gambler's fallacy. I mean statistically speaking tails hitting 20 times in a row is almost impossible, but after 19 in row it's still 50/50 to hit tails the next time.

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The key difference is that in the gambler's fallacy scenario, there is no predicated choice; it isn't being manipulated by someone with certain knowledge of the outcome. In the shell scenario, someone is intentionally "flipping tails" each time, until the last remaining shell. The host's chance of flipping over the shell with money is 0% every time, for every shell up until the last one. Your chances of having the shell with money is still 1/N (N=number of shells). Nothing has changed that.

Basically, the more shells the host flips over, the better your chances are of winning by switching your pick to one of the remaining shells.