[Subfallen]

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I'll take a short stab. I'll assume that I'll use the first girl as a control. so p=()-1. If there are 100 girls, I'll assume that I'll need a good sample, personally I will use about 10%; thus p=()-10 (if there are 10k girls, I'll go -1,000) Assuming that this may take a while maybe a couple hours, I'll have my normal standards (I work in a health club so a 7 to me is typically a 9+ish to most guys) and I won't even consider an 8 by my standards. I would say that I'll end up with a girl in the top 3% or top 3/300, but unlikely the top girl. I'll say that I'll leave with the top girl (again, assuming that I'm the only guy doing this) about 1% of the time.
Again, this is me personally.

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Wow, kudos on missing the point with such ferocity.

The key is that when the hottest girl H comes after our control sample {1...C} at position {1...C...H}, the probability she is picked is equal to the probability that the hottest of all the girls before her (H') is in {1...C}. Like:

1...H'...C...H...N

Instead of:

1...C...H'...H...N

But ordering is independent, so this probability is C/(H-1).