Originally posted by BogdanPS
KK type hands can definitely fold the turn there if you bet. I don't think they'll stick around till the river.
The question is if we can get him off weaker Ax (not AK) but that's questionable at these limits.
But let's go back to the turn range. I think this would be a good excercise for you.
List out the hands you think he gets there with and the number of combos. What's more common?
Ok, firstly, his preflop range is probably something like:
(49,02%)

Against that range, my equity on the flop is 34,48%:
Board: A♠9♥8♠
Equity Win Tie
BU 65.52% 64.08% 1.44% { 22+, A2s+, K2s+, Q2s+, J4s+, T6s+, 96s+, 85s+, 74s+, 64s+, 54s, A2o+, K7o+, Q8o+, J8o+, T8o+, 98o, 87o }
BB 34.48% 33.04% 1.44% { QhJc }
Against his cbetting range, it's probably even weaker, so despite of 28% pot odds, I don't think it's profitable to call. Furthermore, the board is drawy and floating in this situation is out of question with just a gutshot, imo.
When calling my raise on the flop, I believe his range is:
(9,99%)

So, there are 42 combos of Ax hands, 54 combos of flushdraws/straightdraws and 12 combos KK-JJ. My equity on the turn is 37,79%.
Board: A♠9♥8♠ Q♦
Equity Win Tie
BU 62.21% 60.27% 1.94% { KK-JJ, ATs+, QJs, JTs, T7s, 76s, KsQs, KsJs, KsTs, QsTs, Ks9s, Qs9s, Js9s, Ts9s, Ks8s, Qs8s, Js8s, Ts8s, Ks7s, Qs7s, Js7s, 9s7s, 8s7s, Ks6s, Qs6s, Js6s, Ts6s, 9s6s, 8s6s, Ks5s, Qs5s, Js5s, 8s5s, 7s5s, 6s5s, Ks4s, Qs4s, Js4s, 7s4s, 6s4s, 5s4s, Ks3s, Qs3s, Ks2s, Qs2s, ATo+, JTo }
BB 37.79% 35.85% 1.94% { QhJc }
Against his betting range, it's probably weaker, so I can't check/call with 29% of pot odds. If I bet, I guess he will still call the majority of his range, fold KK and JJ and raise QQ, obviously. On blank rivers, he would have 40 combos better than my QJ...

...and 51 combos that are worse than my QJ.

We are splitting if he has QsJs.
According to those assumtions, I could maybe even check/fold blank rivers because I don't expect him to bluff or value bet Ax and I will win the pot in 56% of cases. So, if we assume that he never bets the river (and that my turn bet size was the same like his was), my expected value on the river would be 3,61$. If I was him, I would fold TP to the river bet, so in that case, it would be more profitable to bet because I will win the pot every time. So, if we assume that he is folding to my river bet every time, my expected value on the river would be 6,45$ (before rake). Ofcourse, I can't assume those numbers are true with absolute certainty, but since he looks like a regular, I guess the option of betting would be much more profitable.
To, sumarize, I think betting the turn and betting blank rivers would be the best play in this hand.