[OrianasDaad]

Given the situation you describe, both players are making money in this situation.

The difference in EV you are looking for as a zero-sum situation arises earlier in the hand.

Clearly, the person on a flush draw made a mistake by even entering the pot when someone else had AA, assuming it was heads-up pre-flop. If it were a multi-way pot, the "dead money" that makes this situation +EV for both players may have come from someone who isn't contesting the pot anymore.

That's the funny thing about Holdem. Since the hand values tend to run fairly close in value EV-wise (with a few obvious exceptions), this type of situation comes up rather frequently in multi-way pots that become heads-up.

It's not an obvious answer, and one that I struggled with for quite awhile. The book you are trying to remember is "Theory of Poker. The theory you quote is "The Fundamental Theorem of Poker".

Lastly, you bet because it's got a higher EV than not betting. Plain and simple. You win a bigger pot when your opponent misses the flush.