Assume your opponent is playing GTO. When he bets he has enough bluffs and value bets.

Is it still possible that you can check overfold correctly at any point in the game?

When does this occur?

I believe it's certainly possible because of the probabilistic nature of poker (i.e. events can happen randomly we can't fully account for in our play alone).

I would assume that it's somewhat rare as most equilibrium strategies try to prevent being taken advantage of in such a manner.

Also I wanted to clarify a lot of people assume minimum defense applies to one's entire range and not just the range of hands that have the equity to call given the pot odds you are offered.

So it may be that your opponent bets pot and you are supposed to defend 50% bit that's only with the hands that have at least 1/3 equity vs that betting range, so it might be overall one is folding more than 50% of their entire range.

Thank you.

I didn't understand the last point. Why should mdf be applied to only hands with sufficient equity? One should get punished for having too many weak hands facing a bet, intuitively.

Is it because the ev of hands that don't have equity is negative and therefore they are better off folding than calling even if it means villain gets to auto profit? because if these hands called, villain would profit even more ?

I played around a bit in pio and found some spots where pio check over folds.

1. If it is mainly betting, when it checks it check over folds. ( for the limited sample of boards I verified this on)

2. If it bet really big on an earlier street, when it does check the next street, it check over folds.

Because if you can't beat villain's bluffs then your bluff catchers don't "make back" the money they pay to villain's value range and you lose more money than if you had folded.

Correct. You have to be able to win the pot vs villain's bluffs. If you cannot then you are better off folding.

I should note I'm not necessarily talking about drawing equity here. Say it's on the flop and you have a 25% chance of drawing to the nuts on the next card and villain bets pot. It's very likely that even though you aren't getting the immediate odds for drawing, you will make more money with future rounds of betting.

Mdf seems to work best on the river were equities are fully known (i.e. draws aren't going to come in).

Working with Mdf before the river is a bit trickier because draws can actually gain more EV than their equity share of the current pot.

Looking at defending before the river has more to do with the current and potential future distribution of high equity hands in each player's range.



Correct. Essentially villain gets his equity share of the pot plus the equity share the bet I am putting in and I don't get compensated enough by my equity share or future betting (if we're talking specifically about bluff catchers only).

Yes, makes sense now.

So if btn opened and we called in bb and the flop is QJTr. .we check bb and btn bets 2x pot...it would be correct to fold more than 2/3rd of our hands that called the bb.

https://forumserver.twoplustwo.com/1...22/?highlight=

Correct. Not only do you have a low concentration of current nut hands but also nuts on future streets (i.e. you have no full house draws or many straight draws or backdoor flush draws that can continue).

BB check/folds at a frequency slightly greater than 1-a in most spots.

Confirmed.
If we're defining "overfolding" as folding more than MDF calculations suggest, then over-folding occurs when one player has a significant range/nut/equity advantage and the other doesn't have enough hands that can profitably continue. It frequently occurs in the BB vs the PFR's c-bet, as Brokenstars mentioned, and the BB's range disadvantage often arises because he had better pot odds pre-flop, so he calls with a weak range and is therefore "expected" to lose the pot more than half the time.
It's fine to check-fold a lot if continuing at the MD frequency would mean you lose money. To put it another way, the player in position with the range advantage is expected to win the pot more than his equity share, and there's not a lot the other player can do about it. (You literally can't stop the button auto-profiting with his bluffs if his range is much stronger than yours).

Other fairly common spots (on the river in particular) are those where there are 4 cards to a flush or straight (or both, on the super-connected runouts). It's really hard to defend at high frequencies when the bettor has a higher proportion of nutted hands than the potential caller.

I agree with Arty tough one reason players often have a range advantage on a monotone board is because they just bluff their draws and nothing else so they happen to be unbalanced.

But sometimes also a players may naturally have an Ax advantage so nut advantage on the 4 flush.

Thanks for the responses all.

BB call pre defend post flop spot seems to be the most common situation for over folding on flop.

4 to a straight or flush seems like the clear spot to check over fold on river.

What about over folding on turns?

I used the standard the CO open Button flat range in Pio and gave CO 2 different cbet sizes. Few different types of flops.

When it bets the bigger size on flop, it check over folds somewhat often on turns.

When it bets the smaller size, it does not check over fold too much on turns.

I will post details later when I have access to Pio.

Also when Pio responds with a check raise and check call, it check folds more often than if it only responded with check calls.

A lot of the check over fold spots involve aggressive check raising from Pio.

I think this often occurs as a consequence of check-calling the flop and arriving on the turn with a somewhat capped range (especially if the turn is a complete blank - or a great card for the PFR's range - that encourages the c-bettor to overbet).
Many of the hands that check-call (rather than check-raise) on the flop are "bluffcatchers" with showdown value. They are not the sort of hands you happily call down with on all three streets, especially if villain is bombing it. You want to play small pots with them, and not get taken to valuetown. After all, if you check-call on the flop with something like second pair, you tend to sigh if villain blasts away on a blank turn, and you're kind of "drawing to a check" with top pair and are praying villain doesn't bomb the river. Since you already know you won't be able to call another big bet on the river with much of your range, you'll often cut your losses by folding your weak made hands on the turn.

A couple of visual examples from Snowie.

1. A blank turn that doesn't help BB's range very often (only A6 and T6s improve), and the draws aren't getting the right price to continue. This causes the BB to check-fold about 65% of the time to the PSB.



2. A turn card that enables the BTN to overbet with a polarised range that gets max value with monsters (sets, straights, two pairs), and max fold equity with air/draws, causing BB to sigh-fold SDV hands as strong as A9, since they could be drawing dead and would hate to face a river bomb. (BB's folding freq is over 70%).

I used to think that all of these statements were true:

https://forumserver.twoplustwo.com/1...10/?highlight=

Now this is how I look at it:

my position and the preflop action dictate proper postflop play. If I think my opponent is playing a good starting range, then I assume they're decent postflop until proven otherwise. If I think my opponent makes preflop errors, then I'm thinking about how to best exploit that tendency. Let's focus on the former situation.

For example, I raise 3x in the cutoff vs JustGrindin, ArtyMcFly, and Brokenstars. Two folds, Brokenstars calls.

flop a) AAJr

flop b) 443r

flop c) JT6r

flop d) 678r

I think the big blind should put in more and more action as you go down the list.

I think the median hand of the list is JT6, and other similar boards like 984r, and QT6r, these boards are the marginal boards where there's a gray area of exploitive profitability vs most players; I think on these boards, we may bet a large size with a very polarized range, or we may also bet a small size with a less polarized range. The closer we are to the margin, the more we are at liberty to exploit.

To add:

the reason that I believe JT6r and similar boards are the median is because I'm not sure if very low equity bluffs would be profitable at high frequencies.

I think that on flops (a) and (b) there is enough bluff value to be had to make very low equity bluffs profitable, or as profitable as checking, while on flop (d) I believe that there isn't enough bluff value to be had to make low equity bluffs as profitable as checking. If low equity bluffs are not as profitable as checking, then I think it would follow that the big blind isn't folding close to the minimum defense frequency.

I don't have the time or inclination to study those flop situations in depth right now, but a quick look at Snowie's suggestions - if I force the CO to c-bet half pot (it actually prefers a smaller size on AAJ and a larger size on JT6) - reveals the lowest folding frequency (by far) is on 443. It also continues more on JT6 than 876. Naturally the c-betting frequency is different on each board, and the strength of the c-betting range would therefore vary, thus creating various counter-strategies, but it's kind of interesting that BB rarely folds on 443r, a board where neither player connects strongly.

Are you seeing Snowie prefer smaller sizings on the flop on boards where a lot of hands in each player's range have equities that run close together?

Then conversely are you seeing larger sizings where on player has a significant amount of hands with very high equity?

This is only a portion of the story.

It can be possible equities run together with one range containing greater overall % of "nut hands" and this along with being ip/oop can change the equation drastically.

Although potentially more subtle (honestly hard to say) the SPR plays a big factor too.

It's really really difficult to be able to come with general statements unless the constraints going into the situation are readily defined (this includes spr/ip/oop/and overall ranges).

I agree it is an over generalization I just seem to remember Arty mentioning small bet sizes in Sims in scenarios that fit the ones I described.

Thanks for your input as always.

Sometimes it really pays off to be wrong. Thanks for the gold guys.

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I'm curious to know how often the big blind donk bets those flops, but if you don't have the time then no pressure intended.

I bring it up because I'd expect the flop donk betting frequency to go up as we go down the list:

AJJr

443r

JT6r

678r

In answer to JG's question about Snowie's sizings, I'll just reiterate Broken's comment:
I need to do more study, because (as I said in Broken's PGC thread), it's actually quite hard to spot trends/patterns. That said, from the numbers I've got in my spreadsheets for Snowie's "single-size for entire range" strategy, there does NOT seem to be a correlation between bet-size and overall equity. It's very hard to learn Snowie's sizes and frequencies, because Snowie will choose different bet-sizes on flops that look - to a stupid human like me - roughly the same. e.g. For the BTN v BB, Snowie might choose different sizes on AT4tt and A84tt.
One thing I was very surprised about when I first studied using Snowie was that it more commonly bets BIG on "dry" boards. e.g. On flops like K83r or Q72r, where we all know that "You only need to bet small to make villain fold, because he can't have a draw", Snowie usually uses a large size.

I'm not sure if this is useful in any way, but based on CO opening 3x (using a 100NL 6-max simulation) here are Snowie's donking frequencies for the BB on those boards:

AJJr - 0.84% (1/4 pot)
443r - 33.70% (1/2 pot)
JT6r - 3.4% (1/2p)
678r - 29.36% (1/2p)

I kind of see the 443r board as one where you can get into "leveling wars". Since no one ever has anything, there's scope for all kinds of weird aggression and floating. e.g. BB donks 34%, CO minraises 9% (and only folds 27%), BB 3-bets 1.4%, CO calls (only folds 1.6% of his flop-raising range), there's 39bb in the middle and it's still possible for both players to have 7-high.

EDIT: Sometimes CO 4-bets with 76s/65s, sometimes it flats. When it 4-bets, BB will often 5-bet 76s/65s, to balance quads and 33.

These actions only happen at low frequency, but here's a visualization of how Snowie could play this spot:

88bb in the middle and 7-high is the best hand.

Let's talk about how the cbet range in position is affected by the donking range for the big blind on the example flops:

443r: lots of donking, which weakens the big blinds checking range to the effect that the in position player can value bet thinner and bluff more as a result.

678r: lots of donking, but more risk for the in position player, which should bring down cbet frequency in position.

JT6r: negligible donking, lots of protection value for top pairs, which should bring up the sizing and frequency of the flop bets.

AAJ: little protection value for strong hands, which brings down the sizing a bit.

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I think.....ha.

When you raise and get an IP caller, you bet flop, bet turn and the river is a card that completes most draws. You check. At this point IP's range has almost no pure air so when he bets you fold most of your range. It might seem like you're being "exploited", but you're not, because villain had to pay the flop and turn bets to have a chance at getting his good river.

In fact the entire concept of overfolding doesn't really exist in optimal play. It's just that there are some situations where it seems like you're being exploited and you're folding too much, but that's just an illusion created by looking at the game in a vacuum on a single street.

I think there's some truth to that, but unfortunately, it's not quite that simple. Although the BB might be donking often, there's a lot of mixing happening, and many of the hands that lead out also work well as check-raises or check-calls.
e.g. On 443r, the BB could donkbet quads or 33 at some frequency, and balance with some draws, some overpairs, random overs+BDFDs like Q8s or JTs, but BB could also check with all those hands, along with A4s, K4s, 54s and various wheel draws and pocket pairs. So it's not as if CO can say "Oh, he didn't donkbet, he must be weak, I can c-bet at a high frequency", because the BB can still check-raise trips, pairs, A2s, A5s, 65s/76s and the combos of 44/33 that it didn't donk with. Although neither player has a ton of nutted combos, this is a pretty good flop situation for BB because it's very hard for CO to have trips or better. (According to Snowie, 44/33 and 54s are not in CO's range if he opened for 3x). Since BB has more combos containing fours, he can be a bit more creative/aggressive with his range, whether he starts with a donkbet or tries for the check-raise.

In summary, we could say "BB could donkbet this board pretty often, but he can also check-raise it a lot". (The same is true on 876r. The BB check-raises that even more often than 443r, so CO should check back pretty often). In short, checking on boards where high frequency donking occurs doesn't necessarily imply a high c-bet frequency is used when the OOP player checks.