Q: If I deal a gazillion hands and throw away all the ones that don't have exactly an AAA flop (keeping only those 100,000), what is the difference between doing that and dealing 100,000 flops with AAA and then distributing the rest of the hole cards?
A: Absolutely nothing! The only difference is the insane amount of time it would take to deal all those hands only to throw 99.9%+ of them away.
That logic right there alone should prove that there is absolutely no merit to your "it matters what happens first" line of thinking. If all the non-AAA (or whatever we are testing) cases are thrown away, why even bother doing them? The subset of hands we will be left with will be exactly the same as if we had put the AAA aside, dealt the hole cards, and then flopped the AAA.
And I'm still confused... did you not also say 74%? Where did that come from then?
And more importantly, how about the "real life scenario" that you have yet to address, where I say we have KK and the flop comes _ _ _ (multiple scenarios) and I want to know how likely it is that someone has a pair of Aces for each of them? Do you agree with me that the AA9 flop is safer for us than the A92 flop, for example?
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