Equity with only 3 cards to come

[kurosh]

In NL, a lot of hands won't be around to catch all 5 cards, so the flop is very important. It makes hot/cold equity kind of deceptive. AA vs some PP is usually 80% or 4:1, but if they only go to the flop, what's the equity of AA? Is there an easy way to calculate this? Or some kind of general rule that is close? You can't just do something proportions and the equity with 5 cards to come, right?

[LetYouDown]

Well, for another PP to be ahead of AA on the flop (assuming the game ends there), it would have to flop a set, without an Ace. Is that what you're referring to? I hear Olivia might know.

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In NL, a lot of hands won't be around to catch all 5 cards, so the flop is very important. It makes hot/cold equity kind of deceptive. AA vs some PP is usually 80% or 4:1, but if they only go to the flop, what's the equity of AA? Is there an easy way to calculate this? Or some kind of general rule that is close? You can't just do something proportions and the equity with 5 cards to come, right?

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Assume, for a moment, that the flop is not paired:
Then there are 47 unknown cards - so 1081 possible opponent holes, and of those, 36 beat the pocket aces.
If the board has a range of 5 cards, then there are 16 additional straights
If the board is flushed, then there are 36 flushes (1 overlaps with the straights).

Now, if the board is paired, and there are no aces. Then any hole that makes a set or quad with the pair (there are 91), and a pocket pair of the other card (6) beats the aces.

If the board is a set, then the aces are beaten by quads only (46 hands).

So, heads up, you're looking at being ahead on the flop 9 in 10 times.