[mikeJ]

[ QUOTE ]
Put another way, whether to threebet AQ (and any other hand that can profitably flat call, including AA) is a function of his fourbet shoving range, not his raising range, unless he is frequently going to flat call your threebets (which I doubt he will).

[/ QUOTE ]

Whether to 3-bet AQ or not depends on whether it is more profitable than flatcalling (or folding). So in determining the cEV of a 3-bet, you need to consider the raising range as well as his 4-betting range, you can't just ignore it. And when determining the cEV of a flatcall, you have to consider the tendencies of your opponent's postflop play as well as his opening range.

Consider an extreme example where your oppt is raising 100%, yet your opponent's 4-betting range was AQ+/99+, then a 3-bet would be hugely profitable (as it would w/ any 2) yet you would be correct to fold to a 4-bet if you held AQ. Obviously you would rather have a crap hand when you are bluffing, but if you happen to have a good hand that will be turned into a bluff, it doesn't mean you shouldn't bluff 3-bet, especially if your opponent has a postflop advantage (which may be positional or one of skill).