Handcuffed with AKo, bluff river?

I don’t understand why you would bluff here - what better hand would fold? I guess he could fold a chop?

I think I like pre-flop and flop. I would consider folding the turn. As played, happy to check back river.

Seems like a pretty obvious check back.

Without knowing more about villain it's an obvious check back. You probably can't get better to fold and likely are facing a narrow range of worse AX that will call.
With a read that villain is very unlikely to have better when they check river a bet would make sense but you don't know that yet. There are a lot of AX and QX that are going to check/call river and you don't know what percent of villain's range you bet yet.

What are we losing to that would check the river? If villain has a Q are they really going to try and induce a bluff..

Bet 100 or so, all the weaker Aces will call and if he jams you can reassess a call based on any physical reads (but probably compelled to call based on pot odds)

Pre. sucks, I'm not sure the best move here ... vs. good players probably just shrug and go $45 but at a random 1/3 table maybe call and backraise 4bet shove is best (or fold to the 3bet, if you see monsters)?

Flop I'm not doing anything but calling.

Turn looks super strong, like AA,KK♠,QQ,AK,AQ,AT,K♠Q♠ maybe AxJ♠ ... there's some chance he's overplaying random AJ because he thinks you might just randomly be calling A7 or whatever. But people don't even tend to raise A9s pre. in this spot so... it's not good.
I probably mostly call, but I don't like it.

Just checked and we have 26% vs. that range, and that's limiting to ATs ... if you include JxJs we go up to 33%.

River is a bit weird, AT/AK/AxJ♠ make a lot of sense but then he might decide you bet A7 on river but don't call a shove.
I just check back, about the only good thing that happens is he x/f AK him x/c AJ seems v. hopium.
We have QQ/AQ/88 and maybe K♠Q♠

Turn range on river we have 46% or 56% if we include JJs.

Can't bluff the river, because can't get a better hand to fold.

Result:

It's a straightforward value bet on river for me.

This is how our live reads get in the way.

We would usually 3B pre with AKo. If we've seen V limp-call with AKo in a previous hand, and therefore we think he's only raising big PP's and AKs here, then I think I can get behind a flat call, though I'm not loving it when we're in the BB, with everyone else left to act.

Flop call with TPTK seems pretty standard, when he bets pot. But if we didn't raise with AK pre, then I'm wondering what we think we're beating here that is c-betting. Do we think he's c-betting KK on an AQ-high board? Does that align with our read?

Turn is starting to get dicey. If we flatted pre because we took AKo/AQs out of his raising range, then we're behind one combo of AA and three of QQ. I'm assuming he's not barreling turn with KK or c-betting the flop with TT. We're hoping he's got the one combo of AKcc, and we're calling to chop. But it seems to me that we're behind here 80% of the time (4 combos of AA/QQ), and chopping 20% (1 combo of AKcc).

I'm not folding, but I'm starting to wonder if we're being taken to value town by AA/QQ, or if we're chopping with AKcc, and if we might want to consider turning our hand into a bluff by raising, either here on the turn, or on the river.

River Q reduces the combos beating us to one of AA and one of QQ. If we're being logically consistent, we're hopefully chopping with AKcc, if he's only getting here with AA/QQ and AKs. So, we're checking back to chop 1/3 of the time, and losing 2/3 of the time.

If we're not 3B'ing pre, we should fold at some point post flop. If we're not folding TPTK, then we should throw the read out the window, and 3B pre, no?

If we jam river, we need V to fold around 46% of the time for our bluff to break even, which seems mathematically impossible, since he's not folding AA or QQ once he's boated up. Even if he folds AK pure, it's still not enough.

I wonder if it wouldn't be better to jam turn, when he might fold sets or AKcc, and we're more likely to have a flush than he is. We need him to fold around 60% of the time if we jam turn. If he folds AKcc pure, I think we'd need him to fold AA/QQ half the time.

If that all wounds crazy, fine. Then 3B pre. Because not 3B'ing pre, and calling the whole way hoping to chop 1/5 to 1/3 of the time is even crazier.