Question about Equity and using it to call on the flop

I've watched videos about Equity Final-calls and am confused on if we can use the Required Equity formula for the flop?

Hero holds Ad,Kc

Villain has stats 43/28/12 , Hero raises $.0.06 pre-flop from UTG and Villain calls on BU ( this is just an example).

Flop comes : 5s,3d,3h (pot: $0.15)

We input villains range into the Flopzilla and we are ahead of his range 77% of the time.
Our hand equity is 63.8% compared to his ranges Equity of 36.1%

I don't want to C-bet because we have nothing to bet for value and villain most likely isn't folding on the flop, but do we check call because we are ahead most of the time, can we use the equity calculation for final calls on the flop or does it not work that way that's where I'm confused.

we check and Villain bets $0.10
$0.25:$0.10= 2:1 pot odds

$0.10/ ($0.25+$0.10)
$0.10/$0.35= 29% Required Equity and we have 77% Equity so we can call and see a turn to evaluate the next street?

( Edit* I forgot to discount some pocket pairs from his 3-betting range so our equity would be in the 60s but the question still stands )

If by "Required Equity Formula" you're talking about the equation we've used to evaluate calling all-in, then yes and no.

That equation is so simple because once someone is all-in, there can be no more betting. Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate. We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either.

The next equation you'd want to look at is the equity of an all-in shove. This is more complicated because Villain has 2 choices, each of which represents a non-0 equity to our EV. If villain folds, we win the dead money in the pot right now. If villain calls, we win our equity in the pot (on average, over many "equal" events).

The total EV of the combination of every bet and it's probability of happening times it's equity is the "true" way to know the EV of your betting line.

In practice, that's just too much to wrap your head or math around. What is true and that we can hold on to is that if EVERY one of our bets is +EV, then our line is +EV. What we won't know is whether or not that line represents the max +EV line, though.


43/28/12
What are those stats? We can probably assume the first is VPIP, but that's a guess and the other stats are a crap shoot to guess at. Please always explain what the stats are when you post them. Just their names is probably enough. I don't need you to write out "Voluntarily Paid Into the Pot"

Assuming the first is VPIP.
Is that VPIP from the Villain's current position, or an average of their VPIP from all positions?
If the former (it probably is), then is Villain positionally aware? Do they play the same 43% from UTG as the BTN?

Understanding what a stat is actually telling you is the number 1 thing to know before you use a stat to motivate a decision.

What was the pre-flop action? Were you the aggressor? If so, and it's a heads up pot, fire a C-bet. If not, x/c.
I'm not folding AK OTF to one bet without a strong read or if it's a ridiculous overbet.


Villain's range before they bet OTF is almost certainly not identical to their range after they bet OTF. Unless they C-bet 100% of the time in this spot.
That decision splits their range into 2 parts. You don't care about the part that they would have checked behind, so much. You care about the part they bet with. (Though knowing whether this split is balanced can help you make some very easy decisions against a specific villain)

Every decision made means fewer hands in the range than before the decision. Every decision splits a range. (Except in the cases where you will do something 100% of the time, no matter what, which could well be the case in certain spots against certain villains).

43- VPIP
28 -PFR
12- 3 betting %

I will keep that in mind to bring stats in with names in the future sorry about that,
the stats were just a basic example on a video I was watching , the player didn't have a named position at the table but just a villain LAG in position who calls our utg bet.

I am having a hard time understanding the beginning of your answer

"That equation is so simple because once someone is all-in, there can be no more betting. Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate. We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either."

I understand that its easier on the river because there will be no more betting rounds, so you do the calculation to see the equity you need to call and decide from there. When we are on the flop what math dictates our decision to call after checking without a made hand?In the example we are way ahead even without a pair and if villain bets us his bluffing range is huge, but do we need to do equity calculations on the flop like this or not so much more or less on the river?

As for naming the stats, don't sweat it.
Just study exactly what each stat is telling you before using it to motivate a decision.

This player's VPIP is 43%. That's OK for when it's folded (or limped) to you on the BTN, and assuming this stat is an average over all positions, we can conclude that this player's pre-flop hand selection is stupidly wide, and that he's relying on his Villains to fold a lot to his aggressive bets post-flop in order to recoup his terrible pre-flop losses. It's about impossible for this player to be positionally aware with a VPIP that high.
No other position plays even 1/2 as wide as the button. If button is opening ~40% of hands when limped or folded to them, CO can raise a bit over ~20% of hands and HJ is down to less than 15%. Those are the positions you play the most hands from and just averaging over those hands is way less than 40%.

Their PFR is a healthy fraction of their VPIP, which probably means they're not limping in too often pre. It's a little bit low, but that probably can be attributed to calling raises in late position, as this Villain doesn't likely fold many suited cards or any Ax PRE.

Oh god damn it. I've been assuming that all the hands that were used to accumulate those stats were played 9-handed, and you haven't even told me how many players were in this hand when the cards were dealt.
These stats are about useless without knowing that much. We at least need to know that the stats were collected from similar hands to this one, or we can't extrapolate.
43% VPIP is abysmal for 9-handed, but only pretty bad for 6-handed.


This is what I mean by saying we need to know exactly what each stat is telling us before we can use the stat constructively.

Quote:

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I am having a hard time understanding the beginning of your answer

"That equation is so simple because once someone is all-in, there can be no more betting. Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate. We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either."

I understand that its easier on the river because there will be no more betting rounds, so you do the calculation to see the equity you need to call and decide from there. When we are on the flop what math dictates our decision to call after checking without a made hand?In the example we are way ahead even without a pair and if villain bets us his bluffing range is huge, but do we need to do equity calculations on the flop like this or not so much more or less on the river?

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Sorry about that. Let's break it up.

"That equation is so simple because once someone is all-in, there can be no more betting."
The equation for calling an all in is simplified because there are no later bets. Once someone is all-in, there cannot be any other bets in the pot. That means the success of this bet is not contingent on any future events other than the dealing of the cards, which was predetermined before the hand started.
This simplifies things.

"Furthermore, the value of Hero folding is exactly 0, so plays no role in the final equity we calculate."
When we calculate the equity of a decision, we have to calculate the value of all possible outcomes of that decision. Then we sum the value of each outcome by the frequency of that outcome occurring. The total EV of a decision is
{probability of outcome A}*{value of outcome A} + {probability of outcome B}*{value of outcome B} + ...
With the constraint that all the probabilities alone would sum to 100%, meaning we've accounted for every possible outcome.

We take the sum of terms, each of which is a product. If any part of the product is 0, then the product is 0, and we don't have to account for it in our sum. (accepting that the total probability of all events will still sum to 100% if we double check that)

"We completely ignore the term, as it cannot contribute to your winnings if you fold, but it doesn't cost you anything to fold, either."
Since the cost of a fold is 0, and the reward for a fold is 0 (you do not win the pot 100% of the time when you fold), the value of a fold is 0. So no matter the probability of folding, a fold contributes 0 EV to the total.

Let's say you shove on me and I will fold 25% of the time and call 75% of the time. When I call, I have 40% equity against you.

The value of your all-in shove is
25% * (current value of the pot) + 75% * [ 60% * (value of pot after all the chips are in) ]

EDIT: Oops.

Let's say you shove on me and I will fold 25% of the time and call 75% of the time. When I call, I have 40% equity against you.

The value of your all-in shove is
25% * (current value of the pot) + 75% * [ 60% * (value of pot after all the chips are in) - 40% * (the value of your all-in shove) ]

Notice that the total probability of my responses to your shove is 25% + 75% = 100%

Also notice that the total probability of what happens when I call your shove is 60% + 40% = 100%

The "nesting" of conditional probabilities (I mean the 60/40 is "inside" the 75% part) should never break this fundamental constraint.