AK 3bet pot IP

Fold with less than top 2P here.

I don’t think he would play this line with a flush draw or weaker ace or you have crazy reads on him. That’s why this is for me a clear fold.

Cheers,
SDK1987

Agree, he can have 2p, sets. TPTK is not enough to go along with. Fold and move on.

He has nothing but AA or overplayed premium hands (QQ KK)

I wouldn't 3bet AKo MPvsUTG.
OTT it is close and probably folding is better. I don't see him shoving with weaker hands.

Utg is a bit loose so we can 3b this hand.

Originally posted by nitrol
Utg is a bit loose so we can 3b this hand.

I'm a fish myself but my two cents here:
I'd 3bet pre all day long AK against a loose player UTG from MP to isolate against him, his range is too wide and we will going to be ahead and IP most of the time. If we cold call we'd have a multiway for sure with CO and BTN jumping in and we'll be in a sandwich OOP or we'll face a squeeze from the CO, BTN, etc ... From what I know from NL2 I've seen villains stack off with AT+, QQ+, in that flop, depends on how crazy is the villain.
I like OP's information on villains aggressiveness.

Optimistic scenario:

Board: 4♥A♠7♣
       Equity   Win  Tie
MP2     9.86%   9.71%   0.14% { TT-66, AQs-A5s, K9s+, Q9s+, JTs, AQo-ATo, KTo+, QTo+ }
MP3    90.14%  90.00%   0.14% { AdKs }

So we'd have to invest 59 BB to a pot of 142,5 BB with rake of 3%
EV=142.5·0.90·0.97-59·0.0971=+118.67

Pesimistic scenario:

Board: 4♥A♠7♣
       Equity Win  Tie
MP3    75.78%  70.93%   4.84% { AdKs }
CO     24.22%  19.38%   4.84% { 99+, 77, 44, ATs+, ATo+ }

So we'd have to invest 59 BB to a pot of 142,5 BB with rake of 3%
EV=142,5·0.7093·0.97-59·0.1938=+86.60

I ask for the others repliers to correct me constructively if im wrong!
EDIT: corrected EV equations.

If I'm not badly mistaken, when you calculate this you include only the current pot + villains bet in your winnings. You don't win your own call. So you risk 59 to win 142, not 201.5

Originally posted by la55i
If I'm not badly mistaken, when you calculate this you include only the current pot + villains bet in your winnings. You don't win your own call. So you risk 59 to win 142, not 201.5

I had a misconception and I associated the Pot in ev to pot odds , calculated as (pot+bet)/bet. Further reading brought you can't win your own call. So I'd like if you don't mind to clarify the thing.

EDIT: For future readers the correct way to calculate pot odds is: (pot size)/(amount to call), i.e. villain bets 50$ in a pot of 200$ then you have to call 50$ into a pot of 200+50=250$ giving you 250:50=5:1 pot odds.

The needed equity you calculate with bet/(pot+bet) tells how much of the pot "belongs" to you. So we can figure out how often you have to win to break even.
EV is a monetary value that tells you how much you will win on the long run: (win$*win%) - (lose$*lose%).

I'm not completely sure why do we calculate our own call when calculating the pot odds. I'm not very good at math. But the formula is different. In EV calculations you don't win your own call.

Originally posted by la55i
The needed equity you calculate with bet/(pot+bet) tells how much of the pot "belongs" to you. So we can figure out how often you have to win to break even.
EV is a monetary value that tells you how much you will win on the long run: (win$*win%) - (lose$*lose%).

I'm not completely sure why do we calculate our own call when calculating the pot odds. I'm not very good at math. But the formula is different. In EV calculations you don't win your own call.

You can't win your own money; heads or tails (coin can't land on its edge) I pay 2:1 your bets and you bet 1$:
EV=1$*0,5-1$*0,5=0 as expected because "Pot odds"="odds".
Then, we want to demonstrate "1/equity=odds" , i.e. 33% equity 3:1 we'll hit.
Pot is what is already in the pot (at before's example it would be 0$ in the pot).
So EV=(Pot)*Equity-bet*(1-equity) ;
So, reagrupating EV=Equity*(Pot+bet)-bet=Equity*(Pot+bet)-bet, for EV=0
(Pot odds)=odds :
Equity*(Pot+bet)-bet=0 ; So Equity=bet/(Pot+bet) and odds are 1/equity therefore Odds=(Pot odds)=(Pot+bet)/bet.

What really happens is that "pot/bet"<"(pot+bet)/bet" so the equity we think we need will be higher therefore it's a more conservative approach on the safe side or the EV+ side. Let me demonstrate:
50$ in a 250$ will be EV=0 if pot odds are 6:1=(250+50)/50 so we'd need 16,67% equity to break even.
But if we just do 250/50=5:1, we are calculating on the safe side as 5:1 is 20% equity we think we'd need and with that equity we will have EV+.

As a rule of thumb if the bet is half the pot or more we can't use the simplified formula because it is too conservative. If the bet is 0,4 the pot or less we can use it:
40 in 100:
40/140=28% ; 40/100=40%. So the absolute difference is 10%. This difference will give us an EV=100·0.4-40·.6=16 BB

So I see that "pot odds"=pot/bet it is a EV+ way to calculate pot odds

you can call me crazy if you want, lol.

PS. BUT VERY IMPORTANT:
THE POT IS WHAT IS ALREADY IN THE POT AND DOES NOT INCLUDE YOUR CALLING; includes dead money which are blinds, and bets that were raised.

Example:

blinds 1.5, hero raises 3BB, BTN raises all-in to 100BB
Dead money: 1.5+3+100 (already in the pot).
Hero's pot odds would be then (pot+bet)/bet == (104.5+97)/97=2.07:1 or an equity of at least 48% to break even. Let's check it:
EV=48.13%·104.5-51.87%·97=0. so that's it!

If we do pot/bet calculation we'll get 104.5/97=1.07:1 92% equity (what is almost calling the all-in with the absolute nuts) as the bet clearly exceeds half the pot is not wise to simplify to pot odds=(pot/bet)

Sorry if it is not clear, i don't explain myself very well with numbers.

That was not very clear indeed
But one thing that I am sure of is that pot odds and expected value are two different things and pot odds is NOT a more conservative way of calculating it.

If pot is 100 and villain bets 50. We need 50/(100+50+50)= 25% equity to break even. That is bet/(pot+bet), the pot includes villains bet.

That means we have to call 50 to win the initial pot+villains bet, not our own call. So we risk 50 to win 150. If we win this with 25% probability, we should have EV=0.

(Win$*win%) - (lose$*lose%) --> (150*0,25) - (50*0,75) --> 37,5 - 37,5 = 0

I hope you see now that these are 2 different formulas that calculate 2 different things.

To your example:

Let me demonstrate:
50$ in a 250$ will be EV=0 if pot odds are......

Is this hero betting or hero calling? There is a difference. If we use the bet/(pot+bet) formula --> 50/(250+50) would be required fold equity when villain is betting and 50/(300+50) would be required equity when hero is calling. The other one is not "more conservative". It is a totally different calculation.

Originally posted by la55i
is easy to prove as bet/(pot+bet) < bet/pot
therefore calculating pot odds as pot/bet is EV+ forcefully as EV(bet/pot) > EV( bet/(bet+pot)) >0

Villains bets 30$ in a 100$ pot hero calls?
you calculate pot odds as equity to make your ev=0 which is the definition because you are wanting odds bigger than that so you make money when you hit: Your pot odds are (130+30)/30= 5.333:1 your equity 0.1875 and it is the inverse of that pot odds and gives you ev exactly zero.

Snap calculate 130/30=4.333:1 and your equity by this method is 0.2307

EV(0.2307)> EV(0.1875) =0 Therefore it is a ev+ move to call if our hand has 0.2307 equity while it is a break even movement (rake not considered) to call if our hand has 0.1875 and it is more difficult to calculate both equity and pot odds by adding a number to a second number and dividing.

So calculating pot odds as pot/bet (pot including villain bet) we make 3 things good if the bet is not higher than half a pot.
1) We calculate faster and more accurately
2) We demand ourselves calling with draws with equity slightly higher than we need to break even
3) we land on a safe zone of EV+

In fact:
lets do things properly. when is too much error?
After preflop action we have a pot which value doesn't really matters if it's "small enough as we want"
Given villains bet in a pot with bet=k·pot with 0<=k=<1
then our legitimate EV=pot(1+k)·X-k·pot(1-X), we want, at least to break even right?

EV=0; X=k·pot/pot(1+2k)=k/(1+2k) being our pot odds the inverse of equity so "pot odds"=(1+2k)/k

"Easy pot odds" will be (pot+bet)/bet=pot(1+k)/k·pot=(1+k)/k ; being the inverse of our easy odds "Easy equity"=k/(1+k)

Well it is easy to check that "easy equity"=k/(1+k)>=k/(1+2k)="equity" for any k in 0 to 1 so we are getting EV+ calling hands that match our odds calculated "by the easy method".

Lets see how much differ those calculations, will be a curve, but we can get the extreme values for k=0 and k=1
for k=0 we have a difference of equity of 0 and our EV will be 0 "checking as we have nothing to call"
For k=1 the difference is 1/2-1/3=1/6=0.16 which is big. but what about a half a pot bet or less? (the error decreases as k is closer to zero) in this case k=0.5:
.5/(1+0.5)-0.5/(1+2·0.5)=1/3-1/4=0.0833
8%!! and what would it be our EV?
EV=pot(1+k)·X - k·pot(1-X) ; X=k/(1+k) then
EV=pot(1+2k)·X - k·pot=pot(1+2k)·k/(1+k) - k·pot=pot·k^2/(k+1)
EV=pot·k^2/(k+1)
For k=0.5 EV=1/6·pot=0.1667·pot=(16% of the pot) if we call with a hand with odds are better than those calculated with our easy method.

For k=0.5 we are calling with hands which would have 33% equity but require 25% to break even converting it into a EV+ move.

So: Without even thinking of implied odds, calculating our pot odds (and therefore calling with hands for value that satisfy that odds) as (pot+bet)/bet; being the pot the existing pot and the bet the one villain do is an EV+ movement, is easier and is safer for our money. the negative part is if the bet is too high we can overfold certain draws or a good point is not to make marginal calls.

I'm not super good at math but I have taken the "long" math course in out high school some years back and I have been calculating required equity, required fold equity and EV calculations for some years now. And I have never heard of that. And I don't understand your formulas.

Just to make sure we are on the same page. We are talking about two different ways of calculating this.
1) villains bet/(initial pot + villains bet + our call) --> shorter bet/(pot/bet)
2) villains bet/(initial pot + villains bet)

First one would give you that 18% and the second one 23%. With the 30 into 100 example.

The second one is not more conservative, it is not more accurate.
The first one is used to calculate your required equity to make a break even call. The second one is used to calculate required fold equity to make a break even bet.
So you are calculating 2 different things. And of course the second formula will make sure you have +EV move since it always returns higher number. If the first formula tells us we need 18% of course we are making profit if we think we need 23% instead.

To me your calculations and reasoning look like this:
Matt wants to eat 1 orange and 1 apple, how many fruits Matt needs?
Your answer:
Well, we could calculate it 1+1 but better way to calculate this would be 2+2 because it is more accurate because Matt really is more hungry.

Originally posted by la55i
I'm not super good at math but I have taken the "long" math course in out high school some years back and I have been calculating required equity, required fold equity and EV calculations for some years now. And I have never heard of that. And I don't understand your formulas.

Just to make sure we are on the same page. We are talking about two different ways of calculating this.
1) villains bet/(initial pot + villains bet + our call) --> shorter bet/(pot/bet)
2) villains bet/(initial pot + villains bet)

First one would give you that 18% and the second one 23%. With the 30 into 100 example.

The second one is not more conservative, it is not more accurate.
The first one is used to calculate your required equity to make a break even call. The second one is used to calculate required fold equity to make a break even bet.
So you are calculating 2 different things. And of course the second formula will make sure you have +EV move since it always returns higher number. If the first formula tells us we need 18% of course we are making profit if we think we need 23% instead.

To me your calculations and reasoning look like this:
Matt wants to eat 1 orange and 1 apple, how many fruits Matt needs?
Your answer:
Well, we could calculate it 1+1 but better way to calculate this would be 2+2 because it is more accurate because Matt really is more hungry.

Yes you are right and I am too, it is an approximation what I said. Undoubtedly as EV is the summatory of all the outcomes and the probability that individually have to happen. What it happened initially and what was giving me a hard time is instead of extracting the formula myself (Which i usually go just fine, civil engineering master degree here not a genius though but I really dealt with some shady math that would make many lose their mind) I wrote it down from some shady place googled.

The math in my previous reply is just the math proof of what I'm saying is not only true but as accurate as you want being an aproximation given that in your screen you are given the pot including villains bet and the amount you have to put in to call. Then I realized it is easier and EV+ to just divide those number more-or-less quickly quickly instead of adding/dividing and still land into a EV+ comfort zone if we call (still to be considered the implied odds)
So to clarify I'm a big fish but my math (when i don't rush) is correct and I appreciate to be pointed out if I'm wrong (very frequently) and of course still a big fish in the poker world wanting to absorb solid knwoledge as fast as I can.

The accurate way to calculate pot odds is without any doubt:
The pot as including previous dead money and the villain call.
Then pot odds, which has to be the inverse of the equity which makes EV=0 it's just the times you have to hit your draw to break even. You want to have better (lesser) drawing odds than pot odds.
Mininum equity required is an easy calculation. We use the EV(X)=pot·X - call(1-X)=0
Therefore X=call/(pot+call), note that is the inverse as the pot odds.

But an approximation can be made and that was the point of all these shenanigans and bamboozles. If you just divide the pot info that poker stars gives you which is the pot used above you divide by your call and you get pot odds that if are superior or close to your drawing odds you can call, as proven getting up to 16% of the pot every time if the bet is up to half the pot indecently of the size of the pot landing always into a EV+ zone.

Sorry for the misunderstanding, currently i write this while on a bus trip!

Okay so maybe your math was just a bit too complex for me
I'm used to using the simple formulas.

Originally posted by la55i
Okay so maybe your math was just a bit too complex for me
I'm used to using the simple formulas.

Your good solid math and you extensive of poker game knowledge is a spot where i find motivation and relief for a lot of doubts and for sure I'm more than glad and grateful to you guys that deal with fishes donking the forum day by day!
And of course is not that advanced math. With math we get comfy about it and lose tempo but you just have to get to the dark side and begin to play with variables and be cautious every step when you operate, it's tedious but rewarding (sometimes).
We are not going to reinvent the wheel but trying to reach somewhere by your own thinking/process is a way to learn to learn!