hand one kinda sucks because i don't particularly like flatting or 3betting. however i think flatting is the better option because villain's range is already so strong, and 3betting only strengthens that range, against which we have to play OOP. he probably never folds any of his opening range, so we're just bloating a pot OOP against a range which beats us and isn't folding. also flatting keeps the one hand in his range that we can expect to get more than one bet from post-flop and still have the best hand, namely AQ.

as a little detour, IF i was to 3bet AK here, i'd make it at least 4x his open. basically looking to fold hands which are technically "correct" in calling such as 77-TT or whatever.

so he gets the flop with a range that looks something like 99+,AK. we flop a strong hand in absolute terms, but when we look at his range, we don't really have much of a hand here.

99 - 6 combinations
TT - 6 combos
JJ - 6 "
QQ - 3 "
KK - 3 "
AA -1 "
AK - 6 "

you can choose to discount as much/all of KK/AA as you please. the above list is just the maximum combos he possibly can have of each hand. let's look at some calling ranges on the flop. starting from worst case scenario:

Board: Ah 5h Qs
Dead:
equity win tie pots won pots tied
Hand 0: 33.682% 05.27% 28.41% 522 2812.50 { AcKh }
Hand 1: 66.318% 37.91% 28.41% 3753 2812.50 { AA, QQ, AKs, AKo }

Hand 0: 36.852% 05.29% 31.57% 471 2812.50 { AcKh }
Hand 1: 63.148% 31.58% 31.57% 2814 2812.50 { QQ, AKs, AKo }

Hand 0: 47.832% 25.80% 22.03% 3321 2835.00 { AcKh }
Hand 1: 52.168% 30.14% 22.03% 3879 2835.00 { QQ+, AKs, AKo }

Hand 0: 51.389% 27.53% 23.86% 3270 2835.00 { AcKh }
Hand 1: 48.611% 24.75% 23.86% 2940 2835.00 { KK-QQ, AKs, AKo }

basically the only way we have >50% equity against his flop calling range is if he:
- 4bets AA 100% preflop (ie never has it in his flop range)
- 4bets KK 0% preflop AND calls a it to a flop bet with an ace on the board

so basically we're hard-pressed to get any value from his calling range. it's likely that he's either dead to two outs, or we're dead to a backdoor full-house - this is a pretty way ahead/way behind situation, so we want to take the line that keeps his range as weak as possible. i think i prefer checking the flop, and against such a nit i'm probably not calling too many streets if he decides to bet when we check to him.

now i'm gonna read everyone else's posts and realise i suck and that we should bet/fold. or something.