That's like an axiom in Stud Hi: If you call 5th you're calling 6th. If that helps in this discussion.

Sure, though it would be strange to be complaining about a stud axiom and give a hold'em example.

There are still bad situations on 6th that will make you fold. For example, if your opponent pairs his door card and you brick.

I think the reason that axiom exists is structural to stud. You have three streets of big bets, and that middle street is simply not as volatile.

One of the big reasons for folding on the turn is because the price you have to pay is much steeper. If you take that away, I think there would be significantly less folding on the turn, and a parallel "axiom" may apply.

In fact it's the reason why in stud (or high-only stud, at least) the fifth-street decision is crucial.

But in hold'em discussions I have heard a lot of "why am I going to call this flop if I am going to fold most turns?" and no small amount of "I'm bluff-catching on the turn with my weak value hand, why am I folding to another bet on the river?" There's a lot of that in NLHE strat discussions.

I think the answer to those questions is this:

Because the ev comes when future streets check through.

It's also true of Stud/8.

Okay. This context doesn't seem too surprising.

I think it’s entirely possible that a +ev call on the flop or turn can lead to check folding 100% on the next street. The reason this is possible is because of the free showdowns. For example vs someone that gives up on the river too much, I expand my turn bluffcatching range on the turn. Vs someone that always barrels the river with bluffs, this range of river check folds should be eliminated. This latter case would be the example where we don’t have those free showdowns.

While I suppose it's theoretically possible under some extreme circumstances, I'm fairly doubtful that this is true. I can't imagine a single realistic scenario in which you could make a +EV call on the turn and have absolutely zero cards that could nudge your hand up to a call on the river.

I'm also not sure how well this ties back to your original question or the point you're trying to make.

This was your original question.

Obviously not. Take the classic "ace on the river" scenario in which the worst possible card falls and now whatever medium pair you had is behind virtually everything your opponent had, except for maybe some unpaired broadway combos. Now you're behind so much of his range that even if he bets 100% of his unpaired hands, there are just too many value bets in there for this to be a call.

Basically opponent has to bluff with worse hands greater than 1/P frequency on the turn but less than 1/(P+2) frequency on the river.

I think that's a pretty realistic - albeit uncommon - scenario. It shows up when you have a nitty image and they bluff the turn but when you call they're like oh he's got something; or when they're bluffing with a strong hand and decide they'd like a free showdown too.

You don't think that the dynamic of your hand possibly getting stronger changes this? Any time I imagine the worst hand I'm calling with on the turn, I can always imagine a river card that significantly changes the strength of my hand relative to the rest of my range. I'm always able to imagine pulling ahead of something else. So after the river card, my range has been reshuffled a bit, and things don't match up the way they did before. The various categories of hands get rearranged, and that changes everything.

The claim is obviously true if your opponent *only* bets the nuts on the river. So I know it's possible. But that's seems fairly unrealistic. What you describe definitely seems odd, but I guess it could be possible.

But under normal-ish conditions (defined by "the big blind is a strong limit holdem player"), I just don't see this happening. It seems to me that you and your opponent would both have to have quite polarized ranges (so that your hand improving cannot cause it to shift that much higher in the ranking) and that your opponent must be checking behind with an abnormally high frequency.

I'll be explicit here. Let's say that I'm bluff-catching with K-high and a K falls on the river. I cannot come up with any reasonable ranges for which:

1) Calling with K-high on the turn is +EV
2) Calling with a pair of kings on the river is -EV

You can change K-high to virtually any hand that could be classified as a bluff-catcher. It seems there's always something that improves your hand quite significantly.

I agree. The statement I made at the end of the op was false.

I think the point you're trying to come to terms with is that your calldown odds on the turn are worse than the immediate turn odds, and your true call downs odds include calling a bet on the river, so your effective odds from the turn on are worse.

In the Seattle region it's not even uncommon. I'd say go crazy semibluffing the turn then check/fold misses on the river is standard for maybe 40-60% of the LHE player base. Just anecdotally, it seems to be common for Asian, and more specifically Vietnamese, players.

I try to empathize with opponents to understand how they think, but this tendency is hard for me to get a handle on. I think it has to do with the perception of two different kinds of uncertainty--uncertainty caused by human agency is categorically different than if it's caused by shuffled playing cards. Jamming your gutshots on the turn is fun because the cards might still win for you. Bluffing on the river is different because the only thing that can win for you is another person's decision; your cards are either certain winners or certain losers.

Obviously the counterstrategy (call turn light / fold marginal hands on river) is pretty profitable.

What if the turn puts 4 to a flush on the board?

Then you didn't draw your best king. Remember that the claim is that you're calling the turn but check folding every single river.

"I'm calling this turn because I think I'm getting the right price. The absolute best card in the deck hit. Crap. I fold." I just don't think it actually happens in real life.

Edit: Sorry, I misread that as "what if the river puts 4 to a flush on the board." You're talking about calling with K-high with a 4-flush on the turn, and then pairing your king on the river and not being sure if you would call a bet? One could reasonably doubt the quality of the turn call in that spot. I'm doubtful that K-high is an actual bluff-catcher. You would have to show me some details for me to believe it.

You're probably correct here. With the A7o hand from the original post we can hit a pair on the river.

So I misspoke here:

Should have said that it's entirely possible that a +ev call on the flop or turn can lead to check folding the next street unless our hand improves.

Okay. But unless I'm missing something, this now seems rather trivial. The statement above is clearly true of drawing hands. You can be +EV to chase a draw, and just fold when it doesn't come in. (I know that's not what you're talking about, but the language is open to that reading of it.)

Even at a heuristic level, it would seem very surprising if this statement were false. If you just imagine a static two-street [0,1] game with folding, it would be odd if calling a bet on first street meant you were committed to calling a bet on the second street. The betting player gains information from the call, and probably reduces their betting range on the next street, which would lead the caller to fold some hands. (Maybe this calculation has been done somewhere. I don't know.)

You're welcome at my table any time.

Is it true that 5th street is a very important decision point for razz? Yes.

You have to get to fifth street for it to be important.

Coincidentally, the (0,1) game Aaron described there would be hands that called the turn to check fold the river 100%.

Calling 5th and having to fold 6th happens regularly in Stud8. I love the game but that part is the most aggravating thing in all of poker to me.

You're not wrong, but the point is really strange in the context of responding to "the fifth-street decision is crucial."

I'm a little confused by what the coincidence is, but yes, that's exactly what I said. I was saying that I would find such a conclusion unsurprising (though I don't know if it's been calculated explicitly).

The thing that *would* be surprising is if check-folding the river 100% of the time, even if you improved, were something that happened in reality.

What about in no limit games facing overbets?