Minatorr I think there are two things you might not be appreciating in this hand history:

1. the shorty fish is shoving for only $70 as the 3b and live players can have a lot of really stupid hands in this spot. So a person in SB with AQ+, JJ+ is likely to feel ahead of both our UTG raise range and this shorty shove.
2. in the mind of an average SB, a large 4b will be KK+, so to credibly represent weaker hands like AK, TT, etc trying to iso the fish we might be inclined to make it small with the weaker part of our range. GTO is probably to make it bigger to make him fold out JJ when we have AK, TT type stuff that's ahead of shorty but flipping or behind SB, but as an exploit in a 1/3 game when we have AA we want to keep his entire range in the pot. Blowing him off QQ-TT, AK is a big loss for us.

Personally I don't think it's a horrible size, since almost any size is going to be +EV thanks to fish shorty's large 3b. But I would have gone to like $200 and strung along SB's obvious QQ-TT, AK.

Also I think we are extremely screwed on this flop unfortunately.

I think some definitely do fold JJ/QQ here and there's really a lot of guesswork going on wrt what size they'll call and what they'll fold. Also another thing is most live 1/2 players won't think you're 4betting AK here nearly as often as you're 4betting KK/AA. Smart players know we can have AK in this spot but 4bets are so sacrosanct that they'll fall back on their hundreds of hours of live play and remember it's always KK/AA. The only way we can get them to commit more money is if we make it a painful size for their obvious TT-QQ, AK and peel the flop because of the price.

I don't think any "theory" is going to tell us to 4bet to $220 with a $570 stack. I'd be interested to see someone run this through Pio or Snowie though.

The reason I brought up tournaments is to prove the point that all preflop raises should be either jams or non-committing amounts. This applies to both cash games and tournaments. You don't raise to $35 pre in a 5/10 cash game when you're sitting on an $80 stack. Similarly, if you're $50k deep in a 2/5 cash game, and the UTG player decides to make a ridiculous open raise sizing of $5k, you're not going to now 3bet to $20k from the SB; you'll either 3bet to $15k or you'll 3bet jam $50k. In both cases, you either jam the entire stack in, or you pick a non-committing size.

See how I just gave you an analogy where you're 10,000bbs deep in a 2/5 cash game, yet you actually want to size down, rather than size up?

And as for ranges: I think there's a >30% chance that villain folds TT/JJ/QQ/AK/AQ if we make it $230 pre on a 1/2 cash game, whereas I think that there's a <20% chance he folds if we make it $165 pre. Of course, this is all guess work, so I can't lay out the maths specifically, but I'd wager that the EV of a small 4bet here outweighs the EV of a larger 4bet, given that hands like AK are almost drawing dead against our hand (except on silly runouts like this rare one).

I was just saying as a general rule in standard spots where we dont have absurd circumstances. I could find a counterexample to your statement with made up and extreme circumstances that would never happen in real life, that all 3-bet sizings should be either jams or non-committing amounts, but it’s
not useful in the grand scheme of things. So i dont think your analogy is very useful IMO.

Let’s say you’re 50k deep in 2/5 and the guy opens to 5k, and we have AA and we know if we 3b to 35k there’s a 83% probability he folds and if we 3b jam he folds off 97% of the time. Obviously we are choosing the 35k one, which is a committing raise sizing and is over 2/3 our stacks.

I just gave you a counterexample/analogy to your statement. Is it useful or practical, or even realistic? No. Neither is yours.

Also if someone opens to 5k and you 3b to 15k you should already be committed. I don’t know what you’re 3betting with but I’m only doing so w/ AA.

If someone opens to 5k and you have 50k in a 10000bb deep game you’re in a way effectively 10bb deep so it does make sense to 3b small or just jam it in. The $5000 raise is so high compared to the BB that the $5 BB becomes negligible and in a sense the $5000 raise becomes the BB. So in a way it still proves my point that the shallower you get you’d 3b smaller or jam, and deeper you’re basically 99.9999% sizing up your 3bs and 4bs

Didnt you buy pio?

Also 6b, didnt you level yourself recently into stacking off vs KK that 4b you with a marginal hand because you thought he’d have made it bigger if he actually had AA and thus trashier hands bc he made it so big? I could pull it up but im not at home atm

I mean I don’t know for sure that whether $210-$235 is the most +EV, it’s somewhere between $165-$245 but I think it’s more like the highest yielding EV sizing is between $190-$235. I’d personally choose $210. I mean, you chose $200 and they’re pretty close right? Haha

Yeah I think it's based on feel and how much you think you can get away with and keep in the entire range. $165 definitely accomplishes this and doesn't give odds to set mine so it isn't a horrible size imo. I think horrible would be a really large size to let a fish get away with a big pair correctly.