SPR of 2; pretty easy to GII, against flopped straight you GII anyways, maybe the turn some random 2 pair, pick up a weak fd, etc. So yeah, you might get a bit more value, altough shoving is really high EV. Both options are high in EV, simply through handstrenght.
I also think that then essence of referred video was more about bad judgement about a "wanting to bet" approach in very thin spots in which we know that no matter what we do, we wont win much money.

You have a good hand and there's a lot of money in the middle, no need to get fancy, just stick it in. I'm getting that someone has a straight about 56%, although I'd guess it's a little less likely when they check to us, and in any case our equity against a straight is fine. Betting the flop is clearly very +EV, so let's think about why checking might be better:
-Induce a bluff - seems very unlikely
-Let someone catch up to a second best hand - not too likely either
-Let us get away from our hand when we're beat - I don't think that's what we're trying to do here

I actually think we're a bit more likely to get action from second best hands by betting right away. We do benefit some from protection as well, since any Qx hand that doesn't have a straight already is fairly likely to have an open-ender.

So I like betting the flop. You could consider betting less than pot to encourage action from hands we beat, but it's probably unlikely to make a difference.

Why is it better to check against a straight? Are you planning to fold to a pot-sized bet on a blank turn? If you're not folding regardless, you don't save yourself money by checking - the money goes in anyway. Meanwhile, there's a chance someone correctly folds a straight with 0% equity on a board-pairing turn.

In the hand i checked back and the utg player who is very passive, potted into 3 people on a blank no fd 2 and i folded. It s just never a bluff from this type of guy. And actually i was planning to fold to such action and bet turn if checked to, call if i get the odds. If you are 100% sure you dont get bluffed out and no worse hand pots and also few hands to protect against. But im gonna buy PJ again and do a cal coz im really interested. Ongame it seemed a no brainer shove to me as well but then i started thinking why DO i bet? For value ? For protection?

If I had to boil down the reason for betting into one phrase, it's "win the pot," which is incredibly valuable with this much in the middle.

A, Q, 9 kill your action from lower sets and give a lot of hands that didn't flop a straight a straight. That's more than a quarter of the deck.

too much said here already, dont need to repeat after them, just want to add to your question why do you bet, whether for value or protection or what. this kind of thinking doesnt fit into this situation at all. i would say more adequate question is whether bet or check has higher EV and why, then you will come to the answers that were given here. also you have around 38% eq. against a straight if they dont hold your outs, double bdfd adds some % on top. if your opponents collectively hold a straight 56% of the time, then SPR of 2 becomes a huge caption of the pot for you, since you get to fold them out 44% of the time. if they call you more hands, that means higher EV for you since u will be favorite. never check back on this flop.

This is a concept I watched in Phil's Death of EV Unexpected value video back then, and it just came to my mind- I think its quite relevant.

I found the title of that video unfortunate, and maybe in this thread we see why. It's not about death of EV at all, he actually makes the exact opposite point; to consider the EV of all options and pick the highest. He talks about it as pot share, but technically it's the same thing. I'm sure the intent was that it's more intuitive to some people to think about it that way. It's just the title that is misleading imo, and maybe that's what's confusing you here?

Fwiw, I do agree that checking is an undervalued option in many situations. This is just not one of them. You've flopped a monster and the chips should go in. There's no way checking can be higher EV in this case.

However, it might be a good exercise for you to come up with some situations where checking would actually be better, but where players often bet. This thread would actually be a good place to share some such situations, if you want some feedback on them.

Yeah. Perhaps it should have been something more like:

The death of the "Is this a +EV play?" and the birth of "Is this the highest EV play?"

As often times players were just asking "is this a +EV jam?" or "is this a +EV bet?" while just looking at their equity or fold equity or combination there of instead of considering that they need to compare that to the EV of all the alternatives.

Then the potshare concept is useful in comparing the EV of a shove or a bet to what your actual share of the pot should be. That is to know if something is likely the highest EV play by comparing it to your potshare.

Troubling b/c my intuition fell on the side on Ephedrine's check

Seems like there are quite a few variables here. So I will try to fix a few and see if maybe some math can 'prove' my intuition superior!!!

Assumptions:
i- 3 players ranges = 50%!AA
ii- Still have AQxx in ranges after checking
iii- Know that a bet on the turn is from AQ and will make the proper decision
iv- Q9 folds to shove w/o 2p+ to go with
v- TT+ w a Q will also call
vi- Pot = 1; stacks = 2
vii- All bets are committing shoves

EV of a shove:
i) how often you get folds
- Opponent 1 has it 16.5
- When he dont, Opponent 2 has it 17.5
- When both dont, Opponent 3 has it 18
-> we get...... 100 - (16.5 + 17.5 + 18) = 48% folds

ii) equity when we do get it in
- vs one oppenent we have 43
- vs two opponents we have 40
- vs all three opponents we have 38.5

Dont feel like figuring out the proper math, but I think this is close
- up against one .83 * .83 * .17 + .83 * .17 * .83 + .17 * .83 * .83 = 35
- up against two about 1/4 as ofter = 9
- up against all three about 2
-> that equals 46 so we need to add 6 percent to get us to the 52 percent of the time we get it in. Let's add 3, 2, and 1 respectively. So we are getting it in vs one, two, and three with 38, 11, and 3 opponents respectively.

EV of a Shove:
(folds) + (one) + (two) + (all three opponents) - (cost) = EV
(1 * .48) + ((5 * .43 * .38) + (7 * .40 * .11) + (9 * .385 * .03) - 2(.52)) = .67 psb
or you can write it like:

Checking back:
i) what can happen (outcomes)(probability)
a- board pairs (we win entire pot)(7/45)
b- blank FD card(we check back or we call with 39% equity vs AQ)(18/45)
c- blank off-suit card(we check back or we fold with 23% equity vs AQ)(20/45)

Assumptions:
i- no more action on board pair
ii- realize exactly our equity when calling or checking back turn
iii- only up against one player on the turn if we face bet
iv- we check back again facing no turn bet
v- we face turn bet 1/2 of the time
vi- AQ is still in their ranges after checking twice (we have around 38% on random turns that don't pair the board or give us a FD)

ii) EV of checking back:
-> (board pairs) + (call on FD and win) - (call on FD and lose) + (fold on brick) + (win when checking back on brick)
-> (7/45)(1) + (18/45)(2)(.39) - (18/45)(-1)(.61) + (20/45)(.5)(0) + (20/45)(.5)(1)(.38) = .80

I believe that my math is correct (if not please let me know).
If so and you still think that shoving is the play. Where are my assumptions out of line.

Thanks

Goal: I am going try to set in stone a few variables to see if checking back or betting would be better under those conditions. While trying to make it simple enough that it does not take me all day.
First let me make some assumptions. While they may be highly questionable, but we can debate and change adjust them later.

i- all three opponents have ranges of: 50%!AA
ii- all three opponents still have 100% of their AQxx hands after checking
iii- if we face a turn bet: we know that it is from AQ and we will act appropriately
iv- a flop bet will get Q9 to fold if it doesn't have 2p+ to go with it
v- a flop bet will get action from the following worse hands: TT+:Q
vi- Pot = 1; stacks = 2
vii- All bets are committing shoves

.............................................................................................

EV of a shove = (fold %)(pot) + (equity when called)(pot size)(1-fold %) - (cost of the bet)(1-fold %)

Fold % translates to "how often nobody has AQ, Q9:(KK,JJ,TT,KJ,KT,JT), (KK,JJ,TT):Q
Fold % = 56.5%[1]

Equity when called for all three cases of how we can get it in on the flop:
- vs one opponent we have 39% and it occurs at 37.3% frequency [2][3]
- vs two opponents we have 38% and it occurs at 6%
- vs all three opponents we have 37% and it occurs at 0.2%
STORY CHECKS OUT as 37.3 + 6 + 0.2 + 56.5 = 100

EV of a Shove = (.565)(1) + (.39 * 5 * .373) + (.38 * 7 * .06) + (.37 * 9 * .002) - (1-.565)(2) => .59 of the pot
or you can write it like this:
EV of a Shove = (.565)(1) + (.39 * 3 * .373) - (.61 * 2 * .373) + (.38 * 5 * .06) - (.62 * 2 * .06) + (.37 * 7 * .002) - (.63 * 2 * .002)=> .59 of the pot

...............................................................................................

Checking back:
- before estimating the EV of checking back, lets divide the turn cards into three groups (and then assume how each group will play out)(and at what frequency):
i- board pairs (we win entire pot)(7/45)
ii- turn we turn a FD to go with our set (we check back if checked to or we call with 39% equity vs AQ)(18/45)
iii- blank (we check back or we fold facing a bet with only 23% equity vs AQ)(20/45)

More Assumptions:
i- no more action on board pair
ii- realize exactly our equity when calling or checking back turn
iii- only up against one player on the turn if we face bet (doing this for simplicity)
iv- we face turn bet 1/2 of the time (this is about how often AQ shows up in someones hand, so it seems reasonable)
vi- AQ is still in their ranges after checking twice (we have around 38% on random turns that don't pair the board or give us a FD, and 50% with a FD)

EV of checking back:
-> (board pairs) + (call on FD and win) - (call on FD and lose) + (win on FD after checking back) + (fold on brick) + (win when checking back on brick)
-> (7/45)(1) + (18/45)(.5)(.39)(2) - (18/45)(.5)(.61)(1) + (18/45)(.5)(.50)(1) + (20/45)(.5)(0) + (20/45)(.5)(.38)(1) => .37 of the pot [4]

................................................................................

Given these assumptions and the (hopefully correct) math it looks like betting outperforms checking.

...............................................................................

Thanks for pointing out my sloppy work and thinking. Please let me know if you see anything else.

Work Cited
[1] https://gyazo.com/e5c92e79c406a44e0c23dbcd95cc0c11
[2] https://gyazo.com/124a951b05de84daebab4f9ba0a03576
[3] https://gyazo.com/aa9ca5413eb07e071643929e580ec70e
[4] https://gyazo.com/fa168d7cd6b619123984c9f5544e5fa2