There’s bunch of nuts in oop range, so AA gets quite thin because of xr threat, in practice I think people will under raise, so you can get away with thiner value bets

I don't think you have to worry about XR threat in most poker games. It's mostly just GTO bots and high stakes players (good 500z regs too?) that has proper XR strategies in these spots.

I think a 33-50% sizing would get used pretty often here with AA. Target some T9s, A9s, QJs type hands. I think AA just doesn't fit into the polar sizing of 75%+ being one pair.

Thanks for the replies. I gave OOP the option to lead river for 33% and 90% in the original sim.

So if I'm understanding correctly, the idea is that OOP is supposed to lead his good but not great hands very often, and so when he checks he has give ups and check/raises, which is why we don't want to always vbet AA?

I reran the sim with a 33% river sizing, and I see that AA is pretty much always bet, and in fact the larger sizing isn't used.

What I'm not quite clear about is how 75% is a polar sizing when the turn checks through. We have an overpair in a relatively small pot vs a villain's range that contains a lot of bluffcatchers compared to nutty combos.

For example, lets imagine the runout is different, and we bet the flop and get called, and the turn is a total brick.

In this scenario, AA bets for a large sizing always.

Going back to the original hand, villain has checked twice, so surely his range should be even weaker than when we bet the turn on a brick?

In other words, I'm struggling to see exactly why AA is so much weaker on a Qs9x7x 8s 2x runout where the only bet was 1/3 pot on the flop, than on a Q97r2 turn.

I suppose its because villain is going for a check/raise a lot on the river, but I don't fully understand this either - when we check back turn we mostly have give ups and showdown value, so with his nutty hands I would expect him to lead river for a large sizing to charge our A9s/QJs type hands.

You seem to be assuming that QJ or QK will be folding a lot vs a large bet, but always calling a small one. But when he checks twice, Qx is near the top of his range, and I would expect it to call a reasonable amount vs any reasonable bet size. Sure he probably calls more often the smaller we bet, but its not like betting 3/4 means he just snap folds his bluffcatchers.

Why speculating? You got the range CO comes to the river with, right? You can see what hands Pio suggests to fold / call / raise against a 3/4 bet.

Yes you are right, here is the river calling range vs 3/4. So he's rarely folding a pair and sometimes calling AK, which means I still really want to vbet AA always!

Ran a sim myself and in my sim I get this:

We are quite capped once checking back turn so betting large gets thin when oop still have nuts in range. If you added a smaller sizing i think it gets bet alot.

Pluribus the AI bot.

six max 50/100
3 folds
btn opens $250 (2.5bb)
sb folds
Pluribus defends QsJh BB.

Flop (550) Qd-9h-7c
BB check
BTN cbet 400
BB calls.

turn ($1350) Qd-9h-7c-2s
check x2

River($1350) Qd-9h-7c-2s-3d
BB QsJh checks
Btn $675
BB check raises to $4725 a hefty 7.0 x raise.

Given pot odds $4,050 to win $6,750 which hands in your range are you supposed to call with in this spot? Also which hands actually get to this river with a bet-check-bet line?

This hand had similar board texture to your AA hand, but found the 7x river raise quite interesting with QJ here. Made me think of your AA hand. If you truely think Co 3 bet call range is capped once CO checks all 3 streets, where it goes check check on the turn and CO checks river again, I can actually see quite a few bet sizes here to target bluff catchers.

Here is the output for the river. To recap - we 3bet BTN vs CO, cbet
1/3 on flop, check back turn, and are now deciding whether or not to
bet river for 75% pot.

say btn 3 bet is 8bb, so cbet about 6bb on the flop and check back turn. River pot should be 29.5bb roughly on Q9782

Anyone want to run a sim on using over bets here? I noticed Pluribus uses a lot of huge over bet sizings as shown in the HH above. Other hands i've seen Pluribus also shove as large as 10x pot.