In NLHE, can it ever actually be correct to make a river bet that can't get worse to call or better to fold? (Which only gets worse to fold and better to call).

I remember I recently played and found myself making a small bet, OOP on the river with a hand like A4 on something like an 246ssT3 runout. That actually doesn't look very correct to me, but the point was (1) I didn't feel like I could check/call because villain would have too much value in his range, (2) I felt like villain would feel compelled to bet the river if he missed his draws
(like 78 and flush draws). So basically I felt like I'm going to lose close to 100% of the time if I check, unless I x/r bluffed, which felt too risky -- so instead I bet small knowing that I'm still going to be bluffed occasionally with a raise, and most better hands would call me - my bet mostly only got worse hands to fold. But nonetheless it felt better to me to bet to fold out villain's air, rather than try to bluff-catch for a bad price.

Can that be correct? Is it ever theoretically correct to bet on the river just to get worse hands to fold?

(Again, that runout above isn't actually correct, just close-ish)

There is a bet size that gets better to fold, and worse to sometimes bluff-catch. You may not always have enough chips left in your stack to place such a bet.

No. You may think you've spotted such a situation, but there will be better options than betting in those cases. For instance your A4 hand...if you expect villain to bluff when you x then x. That's not really a reason to bet.

Suppose that my range is mostly polarized between overpairs and ace high hands (I forget exactly how this played out, but I think I had 3bet pre, and villain defended with what I think is a fairly wide range to defend against a 3bet). My range, essentially looks capped to overpairs - even though I may have made the straight one-liner with a few very rare hands. The problem, then, is that villain might start "bluffing" with the best hand.

And anyway, the point of betting would be to set a lower price for the times we lose. If betting size were fixed, then it's obvious that check/call would always dominate bet in a situation like this.

Redo the post, with a good example of a hand, and add the bet sizing. At this point, all we can agree on is that small bets get called or raised more often than larger bets.

But villain can still raise you and most of the times you're called you are beat. So you only set the price in the situations his hand is just strong enough to call.

Why do we expect villain to bet more than we would? On average won't he bet about the same? Although I've found people typically bet less than I do both as value bets and bluffs.

If villain can bluff with the best hand then we are outside the parameters of your hypothetical question. If he has the best hand but considers it a bluffing hand, then clearly our bet CAN get him to fold a superior hand.

If it never gets called by worse, and never folds out better, then I can't see how betting makes any sense.
But I think there are spots where some hands that aren't technically "value-bets" (i.e. that win >50% of when called) will do better by betting than check-calling. GTO play sometimes features small "blocking bets" OOP that apparently prevent villain making a larger bet that you can't call. In effect, you can try to set the price of seeing a showdown, and you'll have a higher EV with a bet (that rarely gets called by worse) than with a check that induces a larger bet you can't call. Something like that, anyway. Sklansky wrote about it, and it's been discussed in this forum as well.

There are also some/many spots where you have a weak hand OOP that will do OK if the river checks through (as you'll sometimes win at showdown), but if villain bets, you have to turn it into a bluff and check-raise it, if calling is not going to be profitable.

There's the classic example where villains range is 2:1 value to bluff, villain bets pot and you bluff catch 100% with ev=0 (or fold 100% with ev=0).

Now if you think you can exploit villain by instead leading, say, 1/3 pot on some rivers where they raise half of their value (you fold and lose) and call half their value (you lose) but fold their bluffs then you win (-1/3-1/3+pot)=1/3pot.

In fact as long as you bet less than 1/2 pot you make a profit if they are exploitable in this way.

I would think there are many situations where this is true in a practical sense.

I don't know what this bet would be called because it's not a bluff or a value bet. It's like an ev-maximizing bet.

But you have villain calling only half his value hands so with the other half we are getting a better hand to fold. So this example is outside the scope of the proposed question.

The hypothesis was as to whether it's ever correct to bet a hand that can't get called by worse hands or fold out better.

I don't see how. If better hands don't fold, then they either call or raise and we lose our bet. If worse hands don't call they either fold or raise. When they fold we win no additional money but do get the pot. When they raise we lose the pot and our bet assuming we fold.

Blocking bets are partial value bets. With a blocking bet we are sometimes called by worse hands. So I don't think they make an exception.

The related question of whether we need worse hands to call 50% may not be true always but is also not the question posed by OP.

Reread my post. I said we lose our 1/3pot bet every time vs a value hand but we win against their bluffs. If we check however, we either lose to their bluffs by folding 100% or lose more to their value hands by calling 100%.

If we blocker bet 1/3pot and they play an exploitable strat of folding all bluffs and calling/raising all value we win 1/3 of the pot. In other words, we win against the 1/3 of their range that is a bluff.

We are making a worse hand fold, but it is +ev for us to do this which answers the OP. I'm unsure if this concept would apply in a GTO situation though. Villain should balance the value raises with the bluffs and we should include some strong hands in our 1/3 blocker bet. But this is not what we are trying to solve is it? We are simply trying to find an example where leading to make a worse hand fold is +ev.

M Very interesting. Before really thinking about this, I had always considered it as obvious that if a bet, when called, does not result in a win over 50% of the time, then it’s a bad bet. And I’ve been slightly tilted at times when villains have made bets like this - where I felt handcuffed from raising to the size I wanted, but nonetheless felt it was a stupid bet because it was mostly getting better to call, and worse to fold (but maybe it was best for them if they were going to bluffcatch anyway).

I am pretty sure I read it correctly but I'll read it again. Yeah, I still think you have not given an example satisfying OP's criteria.

We are looking for an example where

A) Betting can get no worse hand to call
B) Betting can get no better hand to fold
C) Betting is still optimal

Equivalently,

A) The only hands that fold to a bet are worse hands.
B) The only hands that call a bet are better hands.
C) Betting is still optimal

Note I mean optimal as in maximally +EV not GTO.

OP didn't ask if it can be profitable to bet getting worse hands to fold. I followed your example and it looks logical. But you're assuming villain folds his value hands half the time. If he folds his value hands half the time, then our hand CAN get better hands to fold and criterion A fails. Recall OP's question was specifically

"In NLHE, can it ever actually be correct to make a river bet that can't get worse to call or better to fold? (Which only gets worse to fold and better to call)."

The "only" in the parenthetical part is critical. If our bet gets any better hands to fold as in your example then it is outside the scope of the question.

Perhaps I have misunderstood your example. If so, please elaborate as to where I am missing something.

"But you're assuming villain folds his value hands half the time."

Ummmm no, I'm not assuming villain folds his value hands at all. Read it one more time.

Lets simplify by having villain CALL 100% of value hands.

We bet 1/3 pot into villain. Villain calls 100% of value hands and folds 100% of bluffs. We win 1/3 of the pot if villains range is 2:1 (value to bluff). However, if we check, villain bets full pot 100% of the time and we break even no matter what strategy we employ. Therefore by forcing villain to fold worse hands we are increasing our EV.

(Note also that if villain folds bluffs to all bet sizings the best blocker bet is a min bet. In practise this could be true nearing the end of a tournament where stacks are small.)

I think what I was looking for was more like what ArtyMcFly said... Basically, if there’s a spot where it would be absolutely horrible to bet if the opponent had to check back when you don’t bet, is it still sometimes good to bet in those spots because the opponent is allowed to bet, and specifically because the opponent is allowed to make bigger bets.

This is essentially the blocker bet concept, but my I had always assumed that even blocker bets, when called, should win more than 50% of the time (assuming we’re talking about value-blocker bets, which will always be called by a better hand).

And yes, as sort of a secondary curiosity, I’m also wondering how close to 0% that number can become in a GTO setting.... It would be quite rare to find that exact hand and betsize where *everything* better calls (or raises) and *everything* worse folds (or raises), but maybe even there at that exact cutoff on specific board runouts it could make sense to bet?

"Now if you think you can exploit villain by instead leading, say, 1/3 pot on some rivers where they raise half of their value (you fold and lose) and call half their value (you lose) but fold their bluffs then you win (-1/3-1/3+pot)=1/3pot."

Okay I can see I misread this. You're saying villain either raises or calls with value hands. I saw "call half their value" and somehow missed the raising frequency leading me to assume villain is folding half his value hands. My bad.

I'll look at the example again. It makes no difference to us whether villain calls or raises so combining those frequencies,

Our EV would be

P(fold)*pot - (1 - P(fold))*betsize

1/3p - 2/3(1/3p) = p/9

Or 1/9 psb profit. How do we get 1/3 psb profit?

We are assuming he has exactly 2 to 1 bluffs to value hands for this to work.

So this is a weird scenario but seems to make sense. I can't at the moment find fault with it. However it only shows there are cases where betting is +EV.

But...how do we show betting is maximally +EV?

And I'm not following the example you give where we x and villain always bets pot.

In the case we check and villain bets 100% we lose if we always fold, but he has 2 to 1 bluffs to value so if we always call our EV is

2/3(p+p) - 1/3p = p

So we profit 1 psb always calling pot sized bets assuming we can beat his bluffs. Since they're bluffs I'm assuming we can since bluff means inferior hand typically.

Looks like I messed up quite a bit, first mixing up some posts by youareawesome and pocketzeroes, second by writing the example was 2 to 1 bluff not 2 to 1 value. With 2 to 1 value the EV of betting is

1/3p - 2/3(1/3p) = 1/9p.

I still get the same answer.

When we check and villain bets 100% a PSB then our EV always calling is

1/3(p+p) - 2/3p = 0

As predicted.

OP, sorry if my confusion has made you more confused. I am also learning and very capable of mistakes reviewing and doing math on a phone.

Also, as per your last post, note WHEN CALLED is a different scenario than the examples presented.

Although it isn't hard to find cases where we don't need 50% worse hands calling. Imagine we bet 1% psb and villain has called. Clearly this is profitable even if we only win vs 5%. But we need to beat SOME hands. If we beat literally zero hands when called, then when called we lose money.

I'm trying to show how theoretically there may be some spots where villain has 2:1 value/bluffs in his range on the river and will bet his entire range for a pot size bet. In this scenario if we have a bluff catcher that beats the bluffs and loses to the value hands it doesn't matter what we do after checking, our ev is 0. However, if we lead for 1/3pot and villain folds all their bluffs then we win >0 (it doesn't really matter whether it's 1/3p or 1/9p, just as long as it's greater than 0). We increase our ev by making worse hands fold. That's the strange bit...

Spoiler alert: Having a river oop betting range is +EV.

This happens because villain isn't bluff-raising our very small bet, but is bluffing when we bet 0 (check). I don't think the scenario OP posed can happen at equilibrium, but it clearly can in practice.

What if firing on the river, or just firing in general causes opponents at the table to be more cautious with us? Elton Tsang immediately comes to mind.

Right, I finally got it in my last post

Though I still get that our EV is 1/9 pot not 1/3 pot...

This can work as an exploit, but if you're up against a good opponent, I think it will be a huge blunder. The better play will be to check/fold.

In YouAreAwesome's example, villain can chose to fold slightly but still bet the pot anyway. Now we just gave away free money.

After betting 1/3 pot, if villain bets the pot, we will be getting 2/9 on a call. This means Villain needs (7/9) / (2/9) = 3.5 times more value hands then bluffs. 3.5 / 2 = 1.75 and (1.75 - 1) / 1.75 = 3/7.

So if villain folds 3/7 of his bluffs, but still continues with 4/7 of them he'll be making even more profit while still keeping us indifferent.

Rough calculation below:
EV = .85 * -(1/3) + .15 * 1 = -.13333333


Okay, there are situations where it could make sense to bet a hand that could be +EV as a bluff catcher if you have value hands in your range, but don't have any bluffing hands. Since you don't have any bluffing hands you have to take from your bluff catchers.