1.) If villain realises more equity, then we also do too, as the free card can help us both. Perhaps we have a backdoor flush draw that turns into a flush draw when the flop checks through and now we have a profitable check/call on the turn. So this works both ways.

2.) If villain folds all his bluffcatchers, then by definition we make no money from our AA, KK, AK and QQ on a K,7,2 board, so we just lose a tonne of value with that part of the range. He only calls with the hands that we are giving value to, which is bad for us. Unless you are advocating that we check all our value on boards that are good for us and bet all our air?

It seems like you are saying that our opponent will not likely make many calling mistakes on a board that is good for us. I agree with this part, and so therefore we should check a lot of our range and see if our opponent will make betting mistakes instead. We would need to include some check/folds as part of this range so that our opponent does see that he gets to win the pot sometimes with his bluffs when we check from OOP on a board that is perceived to be good for us, therefore we include A5s with no flush draw as a hand we are happy to check and fold to a bet.

Do you mean you agree and that pure bluffs (bluffs without much or any equity on the flop/turn) are generally considered -EV?
Or do you mean the opposite and you disagree, so you're saying pure bluffs can be +EV?

1. If villain realises more equity, then we realise less, because poker is a zero sum game.

2. Ordinarily, villain folding all his bluffcatchers would not be a bad thing, because our bluffs gain whatever ev that our value hands lose. It only starts to become a problem when you are not bluffing enough/only betting hands with equity/checking A5 on K72.

1.) What is 'realising equity'? It is seeing more cards. Those extra cards can help either player. Perhaps we check A5s and hit an Ace on the turn and move ahead of villain's TT-88. Is the villain 'realising equity' there or are we?

2.) If our opponent has an easy time of playing his range well and taking all of his 'folding = 0EV' spots and being correct for doing so, this is bad for us. We want our opponent to be making mistakes and handing us additional EV, perhaps by him taking 'betting = -EV' lines. I agree that us range-betting that kind of board is +EV for us, but it might not be max +EV, and instead some lazy ass minimal +EV. That is not necessarily good exploitative theory, even if it might be good GTO theory.

You win bro, flatting a 4b with AA is fancy play syndrome and bad. Also bluffing without equity is bad. Don't do any of those things, preferably against me.

You are being rude and disrespectful which is a shame.

Also, I am waiting for keuwai's response on this and you should perhaps reply to Yeodan who is asking for your thoughts on 'pure' bluffing.

They're generally neutral or +EV IP. Usually -EV OOP.

I like the question. I don't like your answer to it.

Realizing equity isn't just seeing more cards. Some hands have high equity realization (ER?), while others have much lower ER especially OOP.
AA for example over-realizes it's equity, because the hand is fairly easy to play most of the time.

Hands like 86o OOP would have low equity realization, meaning you would win with them less than their equity.
For example on the flop we have 40% chance to win, but we only win 30% of the time, because villain can pressure us to fold our weak holdings like TP or 2nd pair easily.

If we have a 40% chance to win a hand at any point, from that point forward we should win 40% of the time, that's equity realization.
But because of position and pressure, especially with weak holdings, we often have to fold out a portion of our equity, making us under-realize it.

Another factor in low equity realization hands is that they're too weak to play aggressively a lot of the time.
86o OOP for example, we wouldn't be able to bet on most flops, which makes our ER drop a lot.

It really doesn't matter what the next cards are or who they help.
It does in a single hand, in the long term and from a theory perspective it shouldn't.

I do wonder if we can have lower ER than we should when we're IP?

This is related to position though, not so much 'how well a hand realises it's equity'.

For example, 3betting an off-suit hand like AQo IP, often means that it wins much more often than it should and that it's pure equity dictates, even though it is an offsuit hand. The same hand OOP when opened and someone in position flat calls you, means those same cards win a lot less than they should.

If you can remove position from your argument, it would make it stronger that the actual hole cards effect this. However 86o plays just fine flatting in the BB vs an SB steal at a 6-max or 9-max table for example, and wins more often than it should. The same with A6o. However both 86o and A6o play awfully OOP. Obviously if either hand are suited then this increases the number of boards that 'fit' the hand, so you can continue more often.

So essentially when people talk about 'realising equity' and relate it to our opponent gaining free cards after we've checked, well we gain those free cards also, hence the 'free card' perspective on realising equity can benefit either player.

1. Let’s say you have A5 and villain has 88. Hitting an ace on the turn is part of your 12% equity share. Most of the time the turn will not be an ace, which is why 88 has 88% equity against your hand. If both players check it down, you win 12% of the pot on average, meaning you realise exactly your equity.

Now say you decide to bet the flop instead, and 88 folds. You have just won 100% of the pot, with a hand that only has 12% equity. You’ve realised more than 8x your equity, a significant improvement compared to checking.

2. Going along with the same example, yes our opponent has correctly folded 88, but why would that be bad for us? Hypothetically, if villain’s range comprised solely of bluffcatchers and he was folding all of them, we would win 100% of the pot 100% of the time. This is literally the best case scenario, because if we were to win more than 100% of the pot, villain’s potshare would have to be negative. At that point even open mucking his entire range would be an improvement, since that would increase his potshare to 0.

1.) If we have AKo then we have 91.2% equity so betting here is perhaps bad as we only increase our actual equity by 8.8% to 100%? I am not sure that I can be on board with looking at it this way. What if we were to try and check it down and then put a small bet out on the river to make it look like we are trying to buy the pot, and he bluffcatches incorrectly and we win some extra money?

2.) Ditto with this one, it seems to be about pot share and trying to win the maximum amount of pots that we can win, rather than perhaps winning slightly less pots but a bigger average pot size, (that requires our opponent to invest further money incorrectly on average), so that overall we win more money per hand than if we just attempted to win as many pots as we can by being super aggressive.

In essence, just because we believe that we have the best hand, and that our opponent will believe that we have the best hand, I don't think it means that we should always bet to collect the pot, I believe that more nuance is needed.

keuwai clearly knows what he's talking about so instead of talking back at him with random bs every time he makes a point, just try to understand what he is saying that you clearly ignore

Stop being mean please, I expect more of you!

He probably is, he's giving out tons of great advice freely in this forum, I've learned a lot from him, you can too.
Not sure why he's angry at you, but you should probably stop disrespecting him.

If our opponent believes we have the best hand, we should 100% be betting to collect the pot, because checking would just be giving him a freeroll.

He can just check fold the turn if he doesn’t improve, and the only time he puts any money into the pot is if he sucks out on you.

I guess your point is that he might bluff occasionally when you check, but if villain is playing like you (only bluffing hands with equity) then the hands he will bluff with are hands that would have called a flop bet anyway. So whatever bluffs you induce, you make the same amount of money by betting, with the crucial difference that you fold out some hands that would have sucked out on you.

+1

So because 'initiative' isn't really a thing, if we limped in the CO with a wide range, the BTN 2bets us, we 3bet with some part of our range, the BTN 4bets us with the range AA, TT-88, KTs+ and we call the 4bet OOP with JJ+,AK, AQo, AQs etc. and the flop then comes K,7,2; would you then advocate donking with our entire range here because the board is better for us?

Correct

You show concern for hands that could suck out on you, but you advocate flatting Aces to a 4bet and allowing their range to see three extra cards?

It seems a bit contradictory, but then I guess that is poker for you. Never do everything 100% of the time.

Context matters, folding out air is important when the board is good for us, because air will not bluff much in this situation when checked to anyway.

When we flat the 4bet however, we are doing so with a relatively weak and wide range (compared to the 4bettor). This means that we can expect him to cbet a lot, since most flops are going to be good for him. This makes it more attractive for us to slowplay AA.