Hi guys i have a question that i can't resolve.
Can you help me?

Let's make an example

John_VH925 (UTG+1): $500 Blinds 20/40 + 10
Hero (MP1): $500

Pre Flop: ($140) Hero is MP1 with A♥ T♥
1 fold, John_VH925 raises to $120, Hero calls $120, 5
folds
Flop: ($380) 8♥ 3♥ K♣ (2 players)
John_VH925 bets $370 all in, Hero…
Should the hero call?


What is the maximum bet the hero should call?


• In general, decision rules will be made based on Expected Value

• In Scenario A,
– our Hero is facing a bet into a pot of $380
– EV = W% * (380 + x) - L% * x
– La soglia di chiamata è a EV = 0


• Pot Odds are the relationship of the call amount to the size of the pot
• In general, a call will be +EV if Win% > CallAmt/(PotAfterCall)
• For example in our scenario,
– If the bet were $100 into pot of $380
– Pot Odds would be $100/$580, where $580 = (Pot + Bet + Call)
– Hero’s call contributes ~17% of the pot
– He can profitably call if Win% > 17% of the time
• Win% is based on “Outs” (cards that result in a win)
• Outs are 9 hearts to hit flush

FIRST QUESTION

Considering 3 cards on the board and 2 hole cards that we know ( our cards)
We know that 52-5= 47 cards remain in the deck
So to calculate our odds will be

1-(38/47)*(37/46) =
1- (0,80851)*(0,80434) = 1- 0,6503 = 35%

I'm wrong? I know that the percutual changes little, but is this correct? In the calculation our two cards must also be excluded

• Win% = 1 – (40/49 * 39/48) ≈ 34%. This gives us the odds to call
• EV = 34% * $480 - $100 * 66% = $97.2

Now the example will continue and I have not changed the calculations


Concept – Pot Odds
• Breakeven is when EV = 0
• Bet is x into a pot of $380
• Chance of hitting flush is 9 Outs * 4% (since we get both cards)
• Win% ≈ 36%
• Exact Win% = 1 – (40/49 * 39/48) ≈ 34%.

Here is the second question!
What did the 404 calculation come from? I can't understand, can someone show me all the steps?

• EV = 34% * ($380+x) - 66% * x = 0 at x = $404
• So the maximum bet we should call is $404
• Check with 404 / (404*2 + 380) ≈ 0.34

Thanks

You have a relatively simple EV analysis situation. The pot is 380 and villain makes an all-in bet of 370 which you must either call or fold.

EVcall = Pr(win)*(Pot + Bet) – Pr(lose)*Call

Pr(Win) is gotten by assuming if you hit the nut flush it wins. You showed the correct formula giving a result = 35%. There are 47 unknown cards and 9 give a win.

Thus, EVcall = 0.35 * (380 + 370) – 0.65*(370) = 22

Since EVfold = 0, you should call.

By making Bet a variable and setting EVcall to 0, the maximum bet to call can be shown to equal (35/30)*380 = 443.33

Your calculation at the end is the right method but the wrong equity is used. Instead of 370, set the Bet to equal X as you showed, set the result to 0 and then solve for X. You get what I wrote in the previous paragraph.

What is "percutual"??

Villain is shoving less than pot, so you need less than 33.3% equity to break even. Even the naked flush draw has over 25% equity vs the nuts (top set). Vs top pair hands like KQs, AThh will have about 43% equity, making it a snap call.

It's impossible to calculate the largest bet size you can call (and at least break even) unless you provide villain's exact range.

The pot odds mean you require 370/(380+370+370) = 33% equity.

You've got about 35% chance of making a flush, but against some hands you have much more equity than 35% (your ace might be an out, or you could already be ahead of a weaker flush draw) and against others (sets, 2pairs) you have less.

As Arty has pointed out, you need ranges assigned to be able to completely solve the position. Also, the answer will be more interesting if the stacks are not so shallow. Then you can learn what combos in range you can call with and how much of a bet each combo can call.

As is, all you learned is not to fold the nut flush draw for a single pot sized flop bet.

Thanks for the reply =)

But where does 30 come from?

If your nitty opponent only jams a set then you have to fold. So, now what?

:meh:

From operating on the EV equation set to 0 to solve for X. => 65-35 =30


While I understand the thinking, I don’t agree with the “impossible” conclusion

First of all, you never or at least rarely know villain’s exact range. OP assumed that if the nut flush draw hits, it’s a win. That implicitly defines opponent’s range.

The best villain can have is KK, 88 or 33 each of which has 7 outs for a full house or quads, thus beating a flush. But the chance for those villain hands is only 3 * 3/C(47,2) = 0.0083. And, as noted by Arty, hero could win without the flush with his AT, so the win/lose effects might cancel out.

There are other possible situations such as hero hitting a straight or villain having two pair. Again, it is not unreasonable to assume a balancing out if there is no obvious advantage to one side.

Certainly, doing an analysis based on ranges is preferable but I do not think that not having a range estimate makes an EV-related estimate impossible if factors not explicitly considered are accounted for by reasonable assumptions such as very small occurrence probabilities or a balancing of plus and minus factors.

Sorry but I still do not understand the calculations you did.

Is correct?

x = max bet

0.35 * (380 + x) – 0.65*(x) = 0

133 + 0.35x - 0.65x = 0

133 = -0.35x + 0.65x

133 = 0.3x

x = 133/0.3 = 443,33


what is the second calculation?

Correct.

The second calculation was in response to Arty's comment of needing an exact estimate of villain's range to do an EV analysis. I showed that for your example, the chance of villain having very threatening hands, i.e., KK, 88, 33 is very low, therefore the assumption that you will win if you hit the nut flush draw was reasonable.

The chance you have KK, say, given the flop is equal to 3/C(47,2). The 3 is the number of combos for KK given 3 remaining kings. The denominator is the number of combos you can be dealt from the 47 unknown cards. The 3 multiplier accounts for the other 2 possible sets you can have.

With a fairly typical 18% opening range for MP [55+,A2s+,K8s+,Q9s+,J9s+,T9s,98s,ATo+,KJo+,QJo] villain wouldn't ever have bottom set, but 8/215 combos of that range on this flop made top two or top or middle set. That's 3.72% of MP's range.

When hero's cards are factored in, the card removal effects mean that a typical MP villain has KK, 88 or K8s 4.42% of the time.
Although this is a small number, monster hands are a significant part of his range, and they are even more significant once he shoves the flop. He's not jamming air like JTss, unless he hates money.

In real life I think villain is mostly jamming top pair or better and any flush draw. Against that range AThh has almost 42% equity, so it's an easy call.

Board: 83K
*******Equity*****Win*****Tie
Vill****58.29%**58.29%***0.00%*{ AdAs, AdAc, AsAc, KdKh, KdKs, KhKs, 8d8s, 8d8c, 8s8c, AdKd, AsKs, KdQd, KhQh, KsQs, KdJd, KhJh, KsJs, QhJh, KdTd, KsTs, Kd9d, Kh9h, Ks9s, Qh9h, Jh9h, Kd8d, Ks8s, AdKh, AdKs, AsKd, AsKh, AcKd, AcKh, AcKs, KdQh, KdQs, KdQc, KhQd, KhQs, KhQc, KsQd, KsQh, KsQc, KdJh, KdJs, KdJc, KhJd, KhJs, KhJc, KsJd, KsJh, KsJc }
Hero**41.71%**41.71%***0.00%*{ AhTh }

However, I think that the example is strange because here villain has only 12.5bb and opens what in reality you never see but do more openjam or fold scenarios

So making a precise estimate of the range of oppo I think it's really difficult

Villains then is from UTG + 1 arty, not from MP that is instead hero to be in that situation

I think his range UTG+1 is very close 10% about
although it is difficult to make an estimate because I think openjam a lot of hands

But let's try to continue with this surreal example thinking that it is a fish to play in this way

128 combos check to its range and so I assign two only possible combinations of sets and none of double pair KK and 88.

The best villain can have is KK, 88 or 33 each of which has 7 outs for a full house or quads, thus beating a flush. But the chance for those villain hands is only 3 * 3/C(47,2) = 0.0083.

can you explain this calculation to me? what chance would it be? to have set on the flop?

How do I calculate the probability that he close full to the river or quads?

I could calculate the ev of all possible single events to make a total ev if I knew the% of times that closes a better point

Anything?

If you list out villain's range, I can put it into Equilab and tell you what proportion of it made a set.
If the 10% range was [77+, ATs+, KTs+, QJs, JTs, AJo+, KQo] (9.95%) then he has no two pairs on K83, and just has 3 combos of KK and 3 of 88.
That 10% range is 132 combos pre-flop, but your AThh reduces the number, as does the flop itself. In fact, villain is left with just 96 combos on the flop.
6/96 is 6.3%. That's how often he has a set in this spot.

I think Statmanhal's calculation was based on villain having any two cards. Sets would obviously make up a tiny part of his range if he was playing ATC (because he'd have hands like 32o and 95o which obviously can't make a set), but if a large chunk of his opening range is pocket pairs (AA-66), then more of that range will flop a set. (Just generally speaking, any typically playable range tends to flop a set about 7% of the time).

Here's a image from Equilab showing which combos in the 10% range I used have top pair or better, or a flush draw on that flop:



In case it's not clear, he has 6 combos of sets, 3 overpairs, 26 top pairs and 3 flush draw combos. If he jammed all those, he'd be jamming 37.5% of his range.

Against that range, your AThh has 39.3% equity.
If he just jammed 100% of his range then you have 47.91%.

I gave vilain that kind of range even though it is an absurd hand in itself probably playable only against a fish or a lot of face up against other players who want to trap with AA and KK I believe

That said, I think the call is the right choice, thinking that it's right for him to get 37.5% of his range

What do you say?

Yes, it's basically a snap-call. He bet less than pot and you have way more than 33% equity vs a reasonable shoving range.