Villain is a fish so I'm wondering what is the best sizing to exploit him, knowing I can safely fold to a big raise as he will probably never raise worst or turn a made hand into a bluff.

Also curious to know your thoughts on flop and turn sizing.

Stacks:
UTG (100.2BB)
CO (115.8BB)
BTN Hero (100BB)
SB (161.2BB)
BB (101.8BB) VPIP: 40, PFR: 22, 3B: 4, AF: 1,6, Hands: 83

Pre-Flop: (1.4BB, 5 players) Hero is BTN 9 A
2 folds, Hero raises to 2.4BB, 1 fold, BB calls 1.4BB

Flop: Q 5 A (5.2BB, 2 players)
BB checks, Hero bets 2.8BB, BB calls 2.8BB

Turn: 9 (10.8BB, 2)
BB checks, Hero bets 7.4BB, BB calls 7.4BB

River: 3 (25.6BB, 2)
BB checks, Hero ?

I think you should check back the flop. A9 is not a hand you can really get three streets of value with on this board, and this hand works well as a bluff catcher on later streets.

Turn I would bet a bit smaller since we want to keep V's range-wide and not bloat the pot too much with this hand on this board.

AP I probably go for a small value bet on the river against this player. Most fish would have probably raised a better hand on an earlier street, so I think your hand is best the majority of the time here.

BTN vs Blind. I'm playing similar to you here. On the river I'm probably checking. But I wouldn't be surprised if BB had a pair here.

Keeping the turn bet smaller protects us against x/r from VIL. It’d be sick if VIL raised with a hand like QJ and ran us off the best hand.

OTR go for a small value bet. People almost never slowplay the river so we’re ahead of most of VIL’s range. Plenty of aces could call us here. Checking behind leaves money on the table and is far too nitty IMO

When you go big on flop and turn you more or less need to check back the river. V still has better Ax here, we cant really get 3 streets.

We have two pair here so we beat better Ax

Ah missed that. Bet!

I think we should bet flop nearly always with this hand. If you think about ranges, villain almost never has A9 beaten and we have a ton of gutters, flush draws and other stuff that bluffs.

I think V can easily have A5s, A5o, ATo, ATs, AJo, 55 and Q5s. But that's besides the point, I agree that we usually have the best hand on this flop. The issue is that we can almost never go for three streets of value with this hand. That means we will have to check at some point, and I think the flop is a good time.

This hand doesn't really need much protection and betting won't fold out too much of Villain's equity. Also if we get check-raised on the flop we put ourselves in a really tough spot. Checking also gives Villain room to bluff, which they should do a lot on this board. We also have tons of other value on this board and considering we should have a 2:1 bluff to value ratio we should have no problem betting all our flushdraws and gutters while still being able to check these weak Ax hands. Checking this hand also helps to strengthen our checking range and makes it harder for V to barrel us off by the river.

I don't think betting is bad on this board, I just think long term checking and employing some pot control is the better strategy.

I think it's probably better to bet your entire range or close to it and force villain to defend a bunch of weak hands than to check a bunch of value hands on the flop.

If you check A9 then you can quickly end up in this trap where you're only betting like AT+ for value, and that's both really nitty for missing immediate value and also mean you're either bluffing way way too much or just giving up with a bunch of hands that would rather bet.

If we bet AT+ for value we would have 65 value combos on this board. That means we should have around 130 combos for bluffs. Assuming we check all of our Queens, fives, and underpairs then we can bet every gutshot, flush draw and backdoor flush draw and good backdoor straight draws and still have less than 130 combos of bluffs. I'm pretty sure those are all the possible bluffs we should have on this board. I think if we bet all our weak Ax on this board we'll have to bluff with a lot more weak hands that have very little equity, which means the BB can exploit us by check-raising aggresively. Our range on the BTN should be very wide so if we're betting almost all of it we're going to have a hard time playing a lot of turns and we open ourselves up to exploitation from the BB.

What's your plan if you bet and get check-raised? What's your plan if the turn comes a blank? Are you betting this hand three streets? If you aren't then I really doubt we're missing much value when we check the flop here, in fact, we'll probably gain more value by catching bluffs on the turn and river. If you are planning to bet this hand for three streets then what do you expect the BB will call you down with?

If you open a decent wide range on the button then you have an absolute ton of hands here that would like to bluff beyond the higher equity draws. All your 78o kind of hands that never win through checking and such.

Getting raised here is trivial because villain is insanely capped and we aren't. Defending is easy.

I don't know what you consider a "decent" range on the button, but I open around 35-40% and I don't raise hands like 78o because they play pretty poorly postflop and have pretty bad equity vs calling ranges. But that's a whole other topic.

Just because a hand can never win by checking doesn't mean we should bet it on the flop. As well a hand like 78o could work well as a delayed c-bet since it needs more fold equity to make it a profitable bet. Also if our hand has no equity and can improve on very few turns we should just give up even if we can't win by checking. Betting a hand like 98o here would just be bad, even if it can never win by checking.

As well just because V is capped, it doesn't mean they can't raise this board aggressively to exploit us. If we're betting almost 100% of our range we're going to have to defend vs a check-raise with a ton of weak hands or be overfolding.

If we used a smaller size on the flop, like 1/4 to 1/3 pot then betting weaker Ax and lots of other weaker hands make a lot of sense. However, since this board is relatively wet betting that small means V will get a better price on their draws which is bad. If we bet bigger we need to bet fewer hands, so betting 55% pot with our entire range doesn't really make sense.

I'm not saying betting a hand like A9 on the flop is a terrible play, I just think it puts you in a lot of awkward turn and river spots. We don't want to play a big pot with a hand like A9, since when a lot of money goes in we'll probably be behind. I just think this is the perfect spot to utilize some pot control and try to play a small pot with a marginal hand.

It really boils down to a difference in strategy. Some might want to start polarizing their range right OTF and some might bet their range and then look to separate OTT. I think either option is fine in this spot for the reasons that have been stated.

Personally, I probably check it back and look to either play bluff catcher or put in the delay OTT.

Fwiw I'm checking my lower aces there on the flop, but A9 falls somewhere in the middle. I guess vs a good reg we should bet for balance purposes and check the turn or river unimproved. But I don't think we should worry about balance with villain's profile. Here, I think checking might be best cause I'm never getting three streets of value so I might as well let his range be as wide as possible. Interesting discussion.

If you bet around 20ish bb's then nh. Don't check flop, especially vs a fish.