AQo river valuebet?

Bet is fine since you gonna be called by enough worse AX and its a negative freeroll spot. that means that you have to invest 1bb anyway by check/calling against all his busted draws he might be bluffing with but you'll lose value against Ax that he's gonna call but certainly not bet himself.

Since its a situation where both players have been in late position and have loose ranges you could be bluffing with some Kx or QJ combos that he's supposed to be inclined to call off with ax quite liberally. unless he got trips or a backdoor flush you wont be facing a raise. bet is fine and against a raise its probably a fold but not sure how bluffy he is on the river.

It is a clear check/calldown in my mind.

Exploitative reasoning: what do you do on the river if you bet the turn? Check/call vs a totally depolarised range that won't have that many bluffs? Check/fold? I think at that point it's a blockingbet type of situation, but betting the turn just to have a blockbet on a blank river seems like a silly idea to me. And yeah, Ax might call and call down here, but I hardly doubt we're ahead of his valuerange (especially if he doesn't have a raising range on the flop or has a weak raising range - as most guys do).

Balance reasoning: from my default 3betting range here (22+, A2s+, A2o+, K4s+, K8o+, Q8s+, Q9o+, J8s+, J9o+, T8s+, T9o, 97s+, 87s, 76s) you're at the 48th percentile (meaning that 48% of your range is better than AQ here), which is pretty borderline for valuebetting, it can be done, however considering your checking range, it will be really weak if AJ is the best hand you c/c with.

Now if your 3betting range is tighter (and I assume it is, since most players' are), it's gonna be even lower in your range, meaning that it becomes a definitely check/call. One of the best hands you c/c with, but still a pretty clear c/c.

Hi!

I think I preffer valuebets as played.

I would check not very much here but still... weaker Ax ...like A9- and Khigh. Out of those I would fold Kx on the river and call Ax

I would bet all bluffs which would be a lot on this board so I think we need thiner valuebets for we are getting called very lightly here imo...also I think we can provoke a bit more bluffs by betting since a lot of players assume you will c/calldown this board once u check.