Thanks for the kind words.

3betting vs cold calling: While you could run solves to calculate this it will get somewhat complex because of 4betting, 5bet jamming, folding range etc... .
What happens when you end up in a 3bet pot? You reduce the SPR so you will see similar results in equity realization as you saw in this SRP.
You can get 4bet. This is fine for our hands that continue, mainly reducing SPR again and making that effect larger. For our hands that fold we would reduce our equity realization by the frequency at which we get 4bet.

If you get 4bet 10% off the time and you 3bet fold A5s. Then your A5s equity realization can be reduced by 10% because you have to fold all your equity 10% off the time. To then see if a 3bet or cold call would be better you would want to see if the effect of the reduced SPR overtakes the % that you get 3bet.
That's pure about equity realization though. The equity itself will also differ as your opponents range becomes smaller when you 3bet (he will fold hands). And no longer lineair (he will 4bet top end of his range).

3betting vs cold calling: While you could run solves to calculate this it will get somewhat complex because of 4betting, 5bet jamming, folding range etc... .

It's wild how lost you can get in this. I spent two hours trying to simplify a dumb question about this and the answer was still very unsatisfactory.

Turn barreling and river barreling are interesting indeed. Would need to think about some general ideas that we can apply. My current way of creating videos is with a decent amount of empirical data. For turn and river spots that seems harder to do. I'll see what I can think off. Feel free to suggest specifics.

Shaun Pauwels I feel like the river is a bit easier than the turn given we are v betting or bluffing and we derive bluff hands based on blockers and our freq derives from the number of value hands. I feel the turn is more nuanced and incorporates semi bluffs and bets for equity denial. I suppose we should narrow our focus to the turn.

I think oop turn barreling is more difficult than ip, but I feel huge mistakes are made with both. We can narrow our focus to ep vs btn cold calling or bb 3bet vs btn call for oop turn barreling and mp vs bb for ip barreling.

I suppose I am unsure what I would be looking for specifically. Perhaps general patterns in what happens on a dry, wet, or bway turn? Bet sizings used for each?

Sometimes I feel I just wing it on turns or get by with a basic thought process of "that card looks good for me so fire away with 66% or overbet".

A whole of rambling there. Don't know if that helped. Thats why I still suck at poker ;)

Realization is just how many streets you see. so if you see the flop you’ve seen three of the five cards, if you check back the flop you’re seeing a fourth card if it should go check check again you see a fifth card, so by that definition it means the IP player can realize their equity more easily than the OOP player because they have a decision to end the street by checking back, the OOP player doesn’t get that positional advantage

If this would be the case then we would not have a single hand below 60% equity realization as all off them have seen a flop. Yet we see some below 60%.
The passive guy where we always see a turn would be 80%, yet there are still below 60%. And passive turn where we always see a river would be 100%. Most are above 90% yet not all are 100%.

It is true that the IP player gets to realize equity more easily because of the check and see a new card/showdown option.

I think the Equity Realization "as calculated" or EQR is just a way of saying that some hands have more or less EV than their raw equity may imply.

That's what it is yes. The raw equity against the actual result or EV.

Imo the reason some hands have a higher pot share than their raw equity implies is due to these hands having the ability to continue betting and raising on future streets increasing the size of the pot therefore increasing the EV.

It mainly has to do with being able to continue when they do connect initially.
In Matthew Janda's book "Applications of NLH" he mentions that a hand that either hits 100% equity on flop 1/3rd off the time or 0% equity 2/3rd of the time vs a hand that always hits 33% equity will be easier to play. And therefor realize it's equity more.
The ability to get to showdown is what's important, not the ability to see the river.

we could say that the ability of a hand to continue betting or raising future streets over all possible runouts says a lot more about its ability to capture EV than its pot share relative to its raw equity

Sure. Being able to put more money in the pot (and winning) will increase your EV, and therefor your equity realization as well. You can only do this over a large sample (163 flops) if the hand either has lots of raw equity (such as AA) or either hits big or goes home (100/0 vs 33). The second reason is why suited hands outperform their offsuit counterparts so heavily.

so i end up back at EQR "as calculated" is just a way of saying that some hands have more or less EV than their raw equity may imply.

Yes.

If there was never any betting and we got to showdown then EV = equitypot.
What betting does is make it so that EV <> equitypot. You want to make your opponents EV < equitypot.
It doesn't really matter how you call it, I called it Equity Realization because I assume it's how everyone would call it. This entire study shows to which extend specific hands EV is reduced compared to equitypot. As in, how well can our opponent make our EV < equity*pot.

when we see the flop we realize 60% of our possible full equity (x%) if we get to see the turn we realize 80% of our possible full equity (x%) and when we see the river we have realized 100% of our possible equity (x%) in order to realize our full equity we must be able to get to the river and see SD.

We can't have realized all our equity when we see a river only. You yourself state that we need "to get to the river and see SD". The showdown part is the relevant. You only realize your equity if you get to showdown or your opponent folds.
If you have a hand that has 10% equity and you always get to the river you'll have 10% equity on the river. If you always check your opponent can check or bet. If he checks you realize your 10%. If he bets you likely have to fold, not realizing that equity.
Therefor EV < equity*pot.
If this was not the case then there is no incentive to bet. Ever.

I look forward to every video you release.

Thanks, this means a lot. Shows my effort is worth it.

My 6th video will be a bit less theory oriented, yet you'll find a lot of interesting things in it. My 7th is a lot of math and theory though!
I plan on sticking to theoretical videos. I like them myself.

(1) (a simple one) When equity is displayed in a solver is it realizable equity or raw equity? I've never thought about this before. And of course we can easily calculate realizable equity from EV. never mind, @Mudkip answered, it's raw equity

Couldn't Mudkip just answer all the questions? How lazy is he! :D

(2) (a more complex one). When thinking about opening raise sizes, is the raise size alone decreasing equity realization or is it the change in appropriate range with raise size? Do you think they are independent

I isolated all factors on their own. If someones range stays the same yet they open bigger the result will be that the SPR is smaller. Which causes a lower equity realization for most hands. It's small in single raised pots though.
Generally when people open bigger (or in theory) they should open a tighter range. If you take the change from UTG range to CO range you notice Equity Realization increases. When someone opens tighter it will be the other way, Equity Realization will decrease.
When you see a larger open size the equity realization will drop for most hands, top hands will increase slightly.

Third - a bit of feedback. I find your summary slides very important to understanding the concepts you talk about. It might be helpful to preface the findings with the summary slide, and then include a second summary slide where you remphasize the findings and include a brief explanation of how and why.

Interesting point. "What am I going to say, say it, say what I just said". That idea yeah?

Fourth - what drove you start thinking about solvers in such a fundamental, theorhetical way?

I find it important to understand why something is happening. Even things people take for granted or overlook. Everyone seems to have preflop ranges they use, blindly accepting them without looking into the why. I even had a discussion with a coach once that I considered better than me about RFI ranges. The solved ranges opened a hand UTG for a certain frequency yet it was according to the solve at -0.2EV. He blindly accepted he should open that hand for that frequency. I said it was a flaw in the solve and we should never open it.
I found that a lack of understanding the basics, in this case "always take the highest EV line" combined with "solves aren't solved to 100%".

I also consider it an asset to be different from the rest when trying to become the best. A lot of people seem to focus on other things, more detail oriented. Often looking at a hand they played, solving that and trying to find lessons out of that. I tried a way I considered good for my overall understanding, aggregated reports. Given that I like math it was a good fit.

For this specific topic: I wondered why BB defends the way it does. Why is gto deviating from pure stuff like pot odds, MDF, ... . Equity does not translate perfect to results (EV). There has to be reasons. So I went digging for reasons.
In the end, these reasons and their changes in equity realization make it all applicable in game. You can be like that one coach and study preflop ranges where you set everything at 100BB's and 2.5BB open, 7.5BB 3bet etc. Someone opens 3BB or 2BB and they'll be guessing on how to adjust.

Interesting point. "What am I going to say, say it, say what I just said". That idea yeah?

Yes exactly.

How often hand will be nuts by the river. This is reason why AA-KK have high EQR, or for postflop strong draw almost always have EQR>100%. Nut hands have high EQR because they can value bet, so they win much more then pot.

I doubt AA and KK are often nuts by river in single raised pots. Still, them making sets is a decent part of it yeah. We see the same with all pockets because of this.

SPR-The closer to zero SPR the close to 100% EQR is for all hands

At 0 SPR everyone is all in and then there is 100% EqR. Yet this isn't true for 1SPR on the flop. We only see 3 cards and the urgency to have a hand right now is there. EqR decreases as SPR decreases and then shoots up at 0 SPR. Unless you have found different things than I.

Who has initiative/range advantage. Stogner range will do most of the betting and won't face that much pressure, so it's easier to get to SD with weak hand and you are forcing your opponent to fold out lot of equity otf/ott. I think BB on average has EQR of 80% in srp, but in SBvBB SRP SB will have close to 100%, maybe 95%.

This seems more of a solve setu thing. I didn't include the option to lead for BB in my solves. Initiative is not a thing we should think about these days. Range advantage is true.

I would guess that the real of a hand is when we both players are playing GTO on all streets given the preflop ranges.

Expected value is the number that GTO+ gives me for the hand. The amount of money that hands gets when it plays out. That is the real value we expect to get.

If we instead just look at the raw equity we would do potsize multiplied by equity.

These two numbers are not the same. Comparing these two gets me the Equity Realization %.

Glad you liked it!