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[QUOTE="ckingriches, post: 2127243, member: 58784"]
You don't seem to understand how to correctly figure out the probability of a set of independent trials. Multiplying 11.76% (the probability of flopping at least a set) by 37 (the number of trials) is meaningless.
 
As hackmeplz said, you can figure out the probability of not flopping a single set in 37 trials by raising the individual probability (1 - 11.76%) to the 37th power. That gives 0.8824^37 = 0.976%. So the probability of not hitting a single set in 37 flops is just under 1%. While it isn't very likely, it's going to happen 1 out of every 100 independent set of 37 pocket pairs - there's nothing you can do about it.
 
 As for the Monte Hall problem, think of it this way. When you are given the choice of 3 doors, one of which has a car behind it, you are 33% likely to have picked the right door (assuming you can't smell the goats behind the other doors ;)). That means you are 67% likely to have picked a door with a goat behind it. Obviously whether you picked the right door or not, he has at least one door with a goat behind it that he can show you.
 
So just because he shows you a goat doesn't mean you know anything more about the door you picked, and you're still only 33% likely to have chosen the right door. So would you rather keep your 33% likely door, or would you rather switch to the door that is 67% likely to have a car behind it?
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