I'm interested in whether it's right to bluff this river, and if so at what sizing (GTO perspective, or as an Exploit vs this weak player). Feel free to comment on other decisions.

$1-$1 game. 7 handed.
Effective stacks $100
Villain is an inexperienced player (from observing his unfamiliarity with procedures/etiquette). Not a fool but certainly not a good player. He's been raising to $4 with quite high frequency, regardless of the number of people who've already limped in. I haven't observed anything about his stickiness versus potential bluffs. We've been playing a couple hours, assume he sees me as an average experienced player.

OTTH

Two limpers, Hero limps with 2s2c in CO.
Villain raises to $4 from the SB, BB calls, Hero calls.

Flop ($13 before rake, 3 ways) Ah4c3h
Villain leads for $5, BB folds, Hero calls.

Turn ($23) 4h
Villain checks, Hero bets $12, Villain calls.

River ($47) Th
Villain checks, Hero bets $16.

Thoughts, especially on the bluff sizing?

I would not bet the turn. I don't expect a LLSNL villain to ever fold Ax on the turn, and definitely not versus that sizing.

Your river bluff is probably profitable, I think it works the needed 25%.

I have no idea about the GTO of this hand though... Solvers don't do multiway pots and the pre action is so far out of the GTO world that I'm not even gonna try and make a guess.

I don't think this is a good situation for a bluff. This sort of inexperienced player will often have an AX in this situation. Something they don't feel confident betting after the board pairs and a flush comes in but which they won't give up often enough. This is a good situation to have actual value because you can get way too much money from inexperienced villains but it's bad for bluffing for the same reason.

If you do want to bluff river then something bigger is the way to go. $25/$30 is much more likely to get a fold. But really river bluff after the 4th heart hits is immensely villain dependent. Depending on my live read I might always give up turn/river (and that is the most likely course of action) or bet smaller.

Villain's that inexperienced usually don't really have any view of you at all. They usually have trouble keeping track board and their own hand and stack. What other people are doing is too much information for them to track yet.

I have no idea what GTO is on the river but I expect it's a relatively small percent of bluffs. It's so easy for either player to have randomly backed into a flush that there needs to be some bluffs but not many because you will be bluffing into a good flush some of the time.

I've only recently started properly understanding GTO, with the precise formula of GTO bluff-to-value ratio of s/(1+s). I've looked at the toy game (the AKQ game). I think this principle can be applied to this river situation (at least versus a good player who will fold properly based on a read of my range) even though the action up to this point is far from GTO, and the 3rd player saw the flop.

What is the correct use of GTO versus a weak player? Is it necessary to just disregard it completely? Or maybe use it as a starting point and adjust from there (size up in this spot)? Or factor in some chance even a weak villain can be scared of a single heart in such a simple spot as this river? I think this Villain wasn't so bad as to be completely ignoring an opponent's possible hand here.

I bet small mainly to fold out a weak player's hands like JJ-KK no heart though to be fair he has a lot more AX than KK-JJ no heart. This guy had been doing weird things, as mentioned, and I find weak players in these games can be c-betting too often and they can also get to the river with some random stuff.

I agree weak players do call the river way too wide with AX no heart. It might be best to size up to $25-30 to make weak players fold that, but it's risky as they might call even $25-30 with AX no heart.

With the Ah on board, there's only a 20% chance he has a heart when he has AX. It might be profitable to bet big, even full PSB – then surely even a weak player will fold out AX no heart. Also a weak player would bet a decent heart almost 100% of the time here (they've usually arrived at river with AX broadways or maybe sometimes KK-JJ, so it's a high heart when it is a heart). So it's probably way less than 20% chance that they have a heart now.

Versus a good player, and using GTO, I think the one third sizing is actually pretty ok, though maybe sizing up a touch is just good in reality. I think I just have very very few bluffs here, but a ton of value hands.

GTO is a starting point. No one plays perfect GTO poker. You should deviate from GTO by finding the mistakes the players at your table are making and exploiting those mistakes. For most of the population that plays similar to the player you described, it is ambitious to get them to fold an Ace here. Its ambitious to get them to fold JJ-KK as well.

You exploit these players 2 ways.

1) Seldom - likely never - bluff. Their mistake is that they call too much. If you bluff, they will call you too much.

2) Value bet them heavily. With a TPGK hand or better, keep betting till they raise. They call too much. If you value bet, they will call you too much.

For a lot of the population, sizing up won't matter. If they wanna call, they're gonna call. The flip side of this is you can often size up your value bets and get paid. No need to get fancy.

Playing GTO at these stakes leaves a lot of money on the table. You'd need GTO for good players, but really, you should be staying out of the good players way. There is easier money to be had from the bad players. Start noting mistakes. Examples - 3bets too wide; calls preflop, folds often to Cbet; calls flop, folds often on turn; raises OOP with weak top pairs; calls down too lightly; bets big with bluffs, small with good hands; bets big with good hands, small with bluffs.

People rarely call without a heart here, wtf. River is a mandatory bluff in practice and in theory it depends on how your river range but 22 no heart should probably be in the bluffing range since it's a 0 EV checkback, and you have very few of those.

Both player's ranges have a lot of hearts after a turn bet and call, so a smaller sizing is probably good with high non nut hearts. You can go larger with boats and maybe Kh, and obviously "GTO" would be to balance each sizing, but I think a smaller bet is likely a little higher EV as a bluff.

Result: He thought for 8-10 seconds, then shrug-called with AQ no heart

Never heard the adage – don't bluff rec/weak players?

They don't know enough to fold. They are playing their hand value and barely paying attention to the board/bets. GTO play would be to almost never bluff (they don't fold) but value bet to death when you beat one pair.

Should fold the flop on this hand. Inexperienced players are pretty face up. When he bets he has a pair. Your hand won't improve so you should let it go.

Turn should be a check-back with hope of getting a free showdown. If he has a 4 he now has trips, even less likely to fold his hand.

River is spew. V don't have anything worst to call.

BTW river bluffing frequency is a advanced concept for higher stakes games. Don't bother with that at low stakes.

Not a good board/runout to bluff.

GTO is a defense, please don't use it at 1/1.

Grunch: I’d value bet a mid heart at $16-20 on the river. If I were bluffing an inexperienced player off an apparent A here I’d go more like $35 ish.

Seriously. Don't bluff at low stakes, ESPECIALLY against recs or mediocre players. The biggest weakness most low stakes players have is they call too much.

Don't overgeneralize. Plenty of people have fold buttons and even the population overfolds plenty of spots. If you don't bluff you're leaving money on the table, and very easy to play against for the occasional player with half a clue.

grunch

River seems fine after you bet turn, but why are you betting turn?

Agree that ‘bluffing’ and ‘taking orphaned pots’ are quite a bit different. Lots of money to be made stealing. Harder to make money trying to get a less good player to fold a paired Ace.