sup guys,

new to theory so sorry for the noobish question

I basically just want to know how we are supposed to play/judge what we should call otr (how many combos, what %)

also if anyone does have an answer, is this the same for earlier streets.

any help would be great

Range the villain obv but sizing is key. For example, if villain bets full pot and you fold more than 50% of the time, villain wins with any two cards. River stats take a while to be reliable so make sure to take notes on who bets rivers with what, who bluffs, their sizing, who realizes SD value, etc. Some villains will auto pot a lot of rivers if you check back the turn. Some bet half pot. Others don't bet at all. Are you asking from a GTO perspective or an exploitative/villain-dependent perspective?

im asking from a theory perspective, I can make the exploitative adjustments but I feel im still majorly overfolding. just not sure how much we should defend vs bet sizing basically

When out of position with a weak range vs a strong range heads up on the river, you must allow your opponent to profit with the bottom of his range by folding slightly more than minimum defense frequency would suggest, or else your opponent could exploit your high calling frequency by checking back the bottom of his range on the river and value betting thinner.

When out of position with a strong range vs a weak range, I'm not so sure.

When in position with a weak range vs a strong range, still not sure.

When in position with a strong range vs a weak range, I think we should call a bet slightly more than minimum defense frequency would suggest.

If you're playing in the micros, your opponents are probably overly value-heavy (i.e. not balanced at all) on the river, so I wouldn't worry too much about being exploited. You can generally give micro villains a lot more credit when they bet the river than if you were playing against a high stakes crusher (against whom you need to defend at much higher frequencies).
Just look at the river call efficiency stat in your tracker. If your number is particularly high (e.g. over 1.6) you could call more often, because you've probably been folding the best hand too often.

I think we should allow a slight profit for the in position player's bluffs that makes him indifferent to bluffing or checking the river with his junk hands. Sometimes his junk hands will have zero average showdown value and thus they will be indifferent when ev bet = 0. However, I think most of the time, particularly when preflop ranges are correctly constructed, that every hand will have a shred of showdown value because of the way the ranges interact.

I think we should forget our junk hands and consider our bluffcatchers and slowplays as our whole range. A slight profit may be allowed for the out of position player's bluffs because of the strength of his range in addition to the profit (pot*junk combos)/total combos = X where X is the fraction of the pot that the out of position player earns in the long run vs our junk hands.

What if otr one player has 1 PSB stack 2 value combo and one junk hand that win 1/10 SD when he checks.What is his strategy?If he dose not bet junk then we fold 100 % so he should bet his junk,but if he dose bet his junk then we start calling and then EV of betting junk is 0 so its better that he checks it.
I guess solution is some kind of mix strategy, but Im not sure.

Assuming the value hands never lose, jam 100% of combos. You will capture 100% of the pot with your range which is the highest possible for a strategy in Nash equilibrium.

Even if your "junk" hands won 90% of the time on showdown, you should still jam every hand. If you checked all of the junk in position and jammed all the value, you'd win 2.9pot over 3 combos because your value hands' EV only exceeds their equity when you bluff at least 1/3 of the time. If you started betting just some of the junk, you'd win more than 2.9pot but less than 3pot over 3 combos. And if you don't bet the value you of course can't bet the junk.

It can be correct to lower the EV of a combo in a range when it raises the total EV of your range by at least that much, so the EV of your junk going from .1 to 0 in your example is not a problem. It is only a mistake when the EV of any combo goes negative.

When you're out of position, I'm not sure that your junk hands necessarily have any realizable showdown equity because the in position player should bluff all worse hands.

So if the ev of checking your junk hands out of position is 0ev, then it's easy to construct the indifference equations for betting and checking a junk hand.

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I have a loose theory that when checked to in position, all hands have an ev >0. I've checked back and won with as little as seven high; that's ev that cannot be denied as part of my winrate. In this era of poker, which imo is the post minimum defense frequency era, I think you should be very sure that you have the bottom of your range before you bluff the river heads up in position. This is particularly true vs players that don't bluff enough.

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more specifically:

I agree at a glance.

A hand's candidacy for bluffing is of course based on both how little showdown value it has and its removal effect. On drier boards the former is more important than the latter, and on more coordinated boards, the opposite. But I think even on the driest of boards the former is never nonexistent, although often difficult for humans to consider. This should mean that even junk hands win >0% of the pot out of position as an optimal strategy shouldn't purely be about counting the amount of combos to bluff and starting from the least SDV and going up.

I think you can have your cake and eat it too in position on the river. You can bluff with the bottom of your range and you can bluff hands with good blockers. It doesn't have to be one or the other. So there is no contradiction in bluffing from the bottom of your range and with blockers.

Jand said all the time every hand must take highest ev.I think you are right about betting every hand but calling range should call less then MDF because if he calls just MDF we should just jam value hand and check beck the junk.He should call just enough to make our junk indifferent between betting and checking beck.