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Old 01-24-2009, 01:55 PM   #1
Quasar30
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Calling a 4-bet PF in PLO

Scenario:
The game is Pot limit omaha. CO raise pot.
You hold 9864ds on the BTN and 3-bet. CO 4-bets.
  • Let's say we have 100BBs.
    It is 25.5BBs to call the 4-bet and villain has 37.5% of his stack in the pot.
  • We are almost certain villain got AA** which means we are not likely to be dominated by a better rundown

If we call another 25.5BBs PF with an equity disadvantage of

Hand Pot equity
AA ** 56.35%
9c8s6c4s 43.65%


56.3 to 43.6, how often do we need to hit the flop good enough for this to be EV + and do we hit the flop this often?

(37.5 * 2) * 0.4365 [Preflop] + (62.5 * 2) * X * Y [Post Flop] > = (100-12) [already invested 12]

Where X is the equity post flop and Y is how often we are able to continue.
This can not be calculated without some sort of integral calculus, but we can make a rough estimate.



Let's say we continue on all flops where we have odds to call his pot-sized shove on the flop.
We need around 30% equity cause the shove is a little less than pot.



Therefore we call on 68% of the flops. Now we calculate the average equity on these flops.

68%*30%+54%*10%+40%*10%+27%*10%
+16%*10%+8%*10%+4%*10% =

0.204+0.054+0.040+0.027+0.016+0.008+0.004 = 35.3%

And the triangle-shaped pieces

[(68%-54%)*10%+
(54%-40%)*10%+
(40%-27%)*10%+
(27%-16%)*10%+
(16%-8%)*10%+
(8%-4%)*10%+
4%*10%] /2

= [1.4% + 1.4% + 1.3% + 1.1% + 0.8% + 0.4%*2] / 2

= 3.4%

So overall, we have

35.3 +3.4 = 38.7% equity on average.

__________________________________________

Finally X = 38.7% and Y = 68%. The formual gives

(37.5 * 2) * 0.4365 [Preflop] + (62.5 * 2) * 0.387 * 0.68 [Post Flop]> =? (100-12) [already invested 12]

32.74 + 32.90 = 65.6 which is a lot less than the 88 we need

Conclusion: It is massively EV- to call the PF 4-bet

___________________________________________

Where are the misstakes?

Last edited by Quasar30; 01-24-2009 at 02:06 PM.
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Old 01-24-2009, 02:11 PM   #2
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by Quasar30 View Post
Where are the misstakes?
er, uhhhhh...
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Old 01-24-2009, 02:19 PM   #3
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Re: Calling a 4-bet PF in PLO

This post does not belong in SMP (Science, Math, Philosophy) so I moved it here for mauling, castigation or ultimate destruction/deletion. Anyway, it certainly has more of a chance for useful answers involving poker/omaha here than in SMP.

-Zeno

Last edited by Zeno; 01-24-2009 at 02:31 PM.
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Old 01-24-2009, 04:23 PM   #4
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Re: Calling a 4-bet PF in PLO

you are just an idiot guy
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Old 01-24-2009, 05:23 PM   #5
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Re: Calling a 4-bet PF in PLO

Interesting - I've been calling here always, but mostly cause that's what DJ Sensei and RBK were doing in their vids
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Old 01-24-2009, 06:06 PM   #6
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Re: Calling a 4-bet PF in PLO

nice post,
dunno if it's relevant but
one point may be that there are some flops we easy can give up and so we save ~half of our stack.
also there are flops AA** is playing c/f
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Old 01-24-2009, 06:48 PM   #7
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by Quasar30 View Post
Scenario:
The game is Pot limit omaha. CO raise pot.
You hold 9864ds on the BTN and 3-bet. CO 4-bets.
  • Let's say we have 100BBs.
    It is 25.5BBs to call the 4-bet and villain has 37.5% of his stack in the pot.
  • We are almost certain villain got AA** which means we are not likely to be dominated by a better rundown

If we call another 25.5BBs PF with an equity disadvantage of

Hand Pot equity
AA ** 56.35%
9c8s6c4s 43.65%


56.3 to 43.6, how often do we need to hit the flop good enough for this to be EV + and do we hit the flop this often?

(37.5 * 2) * 0.4365 [Preflop] + (62.5 * 2) * X * Y [Post Flop] > = (100-12) [already invested 12]

Where X is the equity post flop and Y is how often we are able to continue.
This can not be calculated without some sort of integral calculus, but we can make a rough estimate.



Let's say we continue on all flops where we have odds to call his pot-sized shove on the flop.
We need around 30% equity cause the shove is a little less than pot.



Therefore we call on 68% of the flops. Now we calculate the average equity on these flops.

68%*30%+54%*10%+40%*10%+27%*10%
+16%*10%+8%*10%+4%*10% =

0.204+0.054+0.040+0.027+0.016+0.008+0.004 = 35.3%

And the triangle-shaped pieces

[(68%-54%)*10%+
(54%-40%)*10%+
(40%-27%)*10%+
(27%-16%)*10%+
(16%-8%)*10%+
(8%-4%)*10%+
4%*10%] /2

= [1.4% + 1.4% + 1.3% + 1.1% + 0.8% + 0.4%*2] / 2

= 3.4%

So overall, we have

35.3 +3.4 = 38.7% equity on average.

__________________________________________

Finally X = 38.7% and Y = 68%. The formual gives

(37.5 * 2) * 0.4365 [Preflop] + (62.5 * 2) * 0.387 * 0.68 [Post Flop]> =? (100-12) [already invested 12]

32.74 + 32.90 = 65.6 which is a lot less than the 88 we need

Conclusion: It is massively EV- to call the PF 4-bet

___________________________________________

Where are the misstakes?
In your post flop equity calc of .387, you've calculated the average equity of the times you have the right pot odds to call, so by multiplying .68 aren't you effectively double-counting the percent of the flops you can continue? since you're average equity calculation was weighted by the percent flop, i think the 0.387 is a 'true' equity calculation assuming that 68% of the flops will give you the right odds.

also, why didn't you put in MMMM instead of 9864 since any middle rundowns are effectively the same.
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Old 01-24-2009, 07:09 PM   #8
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Re: Calling a 4-bet PF in PLO

I find it hard to respond to long posts. So I'll simply post this before I forget it.

You equate the (summation of Xi * Yi) to (N * Xavg * Y avg), which might not be true for the distribution of X and Y, especially at the edges.

Is there a way to get scientific notation to display properly on this site?

Also assuming that the 3-bet is inherently break-even, we have an equity overlay preflop as well which you fail to include in this computation. Or you could even argue that the 3-bet is inherently a -Ev proposition, ad you need to make up equity postflop.

You have not discussed your assumptions which seems that the flop is always a shove by the opponent, which is not always true, as there is an equity overlay because of bluffing/semi-bluffing involved.

ps: This is just from a quick read since you havent given many cliffs notes for your calcs.

______________
1) 88$ to win $200 @43.65% gives you a loss of 0.70$ as it seems. So are you askig if its better to shove or flat?

2) Why do you think that the area under the graph represents our average equity?
(more edits coming)

Last edited by uphigh_downlow; 01-24-2009 at 07:34 PM.
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Old 01-24-2009, 07:21 PM   #9
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Re: Calling a 4-bet PF in PLO

I don't have time to break this down in-depth right now, but I'm really suspicious of your little squares and triangles counting method that gives you 38% equity on average when you can correctly call a flop shove. In fact, I'm 100% sure that it's wrong. There's no way that your average equity on good flops can be lower than your preflop equity. I think you may actually need to divide that by .68 to get your average flop equity as GoChoo suggested.
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Old 01-24-2009, 07:47 PM   #10
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by uphigh_downlow View Post
I find it hard to respond to long posts. So I'll simply post this before I forget it.

You equate the (summation of Xi * Yi) to (N * Xavg * Y avg), which might not be true for the distribution of X and Y, especially at the edges.

Is there a way to get scientific notation to display properly on this site?

Also assuming that the 3-bet is inherently break-even, we have an equity overlay preflop as well which you fail to include in this computation. Or you could even argue that the 3-bet is inherently a -Ev proposition, ad you need to make up equity postflop.

You have not discussed your assumptions which seems that the flop is always a shove by the opponent, which is not always true, as there is an equity overlay because of bluffing/semi-bluffing involved.
I tried to make it as simple as possible.
This is hard enough for someone who hasnt read a single poker book

Something is wrong in the calcs for sure...was wondering what that might be and if its possible to fix it or maybe even the method is wrong?

Quote:
Originally Posted by uphigh_downlow View Post
1) 88$ to win $200 @43.65% gives you a loss of 0.70$ as it seems. So are you askig if its better to shove or flat?

2) Why do you think that the area under the graph represents our average equity?
(more edits coming)
Im asking about flatting his 4bet.

I assumed that the area represented the average equity but maybe it is wrong also.

Last edited by Quasar30; 01-24-2009 at 08:07 PM.
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Old 01-24-2009, 07:49 PM   #11
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Re: Calling a 4-bet PF in PLO

The answer is to raise less when you 3-bet. Seriously.
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Old 01-24-2009, 07:57 PM   #12
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by GoChoo View Post
In your post flop equity calc of .387, you've calculated the average equity of the times you have the right pot odds to call, so by multiplying .68 aren't you effectively double-counting the percent of the flops you can continue? since you're average equity calculation was weighted by the percent flop, i think the 0.387 is a 'true' equity calculation assuming that 68% of the flops will give you the right odds.
But removing 68% seems wrong also...i think...

You got 38.7%(if my calcs are correct, which they probably arent...) on the flops you dont fold and if you dont include 68% its like you call on every flop with on average 38.7%, right?
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Old 01-24-2009, 08:06 PM   #13
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Re: Calling a 4-bet PF in PLO

scrap my last post.

Your presentation is spot on.

allow me this

Quote:
(37.5 * 2) * 0.4365 [Preflop] + (62.5 * 2) * X * Y [Post Flop] > = (100-12) [already invested 12]
The LHS of your equation is sklansky dollars of the call

The RHS is what you have left.

I dont see how you can equate the two.

you can compare the s$ of the call with the s$ of the fold( which I believe to be -24)

Allow me this:

You finish the hand Y times and win X *200
You do not finish the hand 1-Y times and lose 37.5

This has to be better than -12*2

X * Y * 200 - {(1-Y) *37.5 } >= --24

0.12 > -24

profit. Whats wrong ?

Now back to checking out the graph, although the area seems the right equity to be concerned about.

Last edited by uphigh_downlow; 01-24-2009 at 08:35 PM.
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Old 01-24-2009, 08:09 PM   #14
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Quote:
Originally Posted by Quasar30 View Post
I tried to make it as simple as possible.
This is hard enough for someone who hasnt read a single poker book

Something is wrong in the calcs for sure...was wondering what that is and if its possible to fix it or maybe even the method is wrong?



Im asking about flatting his 4bet.

I assumed that the area represented the average equity but maybe it is wrong also.
My guess is that you have to come up with a probability distribution function to accurately calculate the true equity, which is not a trivial task. Considering this problem appears to be non-linear...

Using your method, my interpretation is that you said that 68% of the time you have a 30% equity plus 54% of the time you gain 10% equity. If you're going to use that approximation, I think you also need to subtract the equity that is past 30% for the sake of consistency (undecided how precise it is yet).

I haven't excercise my math skills beyond excel for 10 yrs so I dunno how much more useful I can be in this discussion. Its a good start and I'm also interested in the results along with other situations.
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Old 01-24-2009, 08:10 PM   #15
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Re: Calling a 4-bet PF in PLO

I find it much easier to use to following formula:

EV(Post Flop) = CALL% [$Flop Pot Size * AvEq - $Amount to call on Flop]

CALL% = % we can call (around 30% as u stated in your example)
AvEq = Average all-in flop equity when calling

I cannot take credit for the structure of this formula as i read it somewhere else, the one i previously used was a little longer and similar to yours. however i cannot remember who/where it was posted (not on 2+2 i am sure), so apologies to the original source.

Ill make a very hastily and rough attempt at solving this. ill use an example of a .5/1 game so 1bb = $1 (and exactly 100bb stacks). after the initial 3-bet its $25.5 more to you ie; post flop EV must be >$25.50. thus on the flop you are calling $62.50 to win $137.50 = 2.2:1 = ~31% ev required (will use ur graph)

Im not posting my calcs as i simple cbf, but:

EV postflop = .68 * ($137.50 * .558 - $62.50)
=$9.60


which would imply that calling is indeed -EV
I used Quasars numbers for the most part, and also did this exceptionally fast, and therefore could be even more incorrect than the original
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Old 01-24-2009, 08:14 PM   #16
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by Quasar30 View Post
But removing 68% seems wrong also...i think...

You got 38.7%(if my calcs are correct, which they probably arent...) on the flops you dont fold and if you dont include 68% its like you call on every flop with on average 38.7%, right?
Think the .68 is OK, I did a similar calc in a post that a bit simpler not too long ago. The 38.7 is definately wrong though. Don't need advanced calculus, adding up area under curve by hand is correct, but you added wrong.

Looks like you're trying to do a Riemann sum (fancy term for adding up squares and triangles) but theres some weird 68% * 30% thing at front. Why are we adding in the equity for the times we fold? We're not calling 100% postflop.
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Old 01-24-2009, 08:20 PM   #17
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Quote:
Originally Posted by Scar18 View Post
I find it much easier to use to following formula:

EV(Post Flop) = CALL% [$Flop Pot Size * AvEq - $Amount to call on Flop]

CALL% = % we can call (around 30% as u stated in your example)
AvEq = Average all-in flop equity when calling

I cannot take credit for the structure of this formula as i read it somewhere else, the one i previously used was a little longer and similar to yours. however i cannot remember who/where it was posted (not on 2+2 i am sure), so apologies to the original source.

Ill make a very hastily and rough attempt at solving this. ill use an example of a .5/1 game so 1bb = $1 (and exactly 100bb stacks). after the initial 3-bet its $25.5 more to you ie; post flop EV must be >$25.50. thus on the flop you are calling $62.50 to win $137.50 = 2.2:1 = ~31% ev required (will use ur graph)

Im not posting my calcs as i simple cbf, but:

EV postflop = .68 * ($137.50 * .558 - $62.50)
=$9.60


which would imply that calling is indeed -EV
I used Quasars numbers for the most part, and also did this exceptionally fast, and therefore could be even more incorrect than the original
The mean equity is different from the median equity. So .558 is not likely to be correct.

Also if the EV is $9.60 then isn't it +EV to call?
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Old 01-24-2009, 08:24 PM   #18
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Re: Calling a 4-bet PF in PLO

Alright just eyeballed it. Just eyballing it, looks like the graph can be broken up "approximately" into two fairly straightish segments, the 0 - 8% of flops with between 80 and 100% equity (lets say ~90 on average) and the 8 - 68% of flop with 30ish to high 70sish (looking at the midpoint as38 on the X axis, looks like 52% or 53% equity is the midpoint).

so 8/68 * 90% + 60/68 * 53% gives .575 as our average postflop equity when we call. Not exact but I'm lazy and don't want to add like 10 segments up.
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Old 01-24-2009, 08:28 PM   #19
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by Peeda View Post
Think the .68 is OK, I did a similar calc in a post that a bit simpler not too long ago. The 38.7 is definately wrong though. Don't need advanced calculus, adding up area under curve by hand is correct, but you added wrong.

Looks like you're trying to do a Riemann sum (fancy term for adding up squares and triangles) but theres some weird 68% * 30% thing at front. Why are we adding in the equity for the times we fold? We're not calling 100% postflop.
Yepp, a Riemann sum.
68%*30% is the largest rectangle below the graph.

We are not folding these times. 68% is all the flops we call and we got 30% equity at least on these flops. Then i add Z*10%, each smaller rectangle below the graph, to get the correct sum.
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Old 01-24-2009, 08:28 PM   #20
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Re: Calling a 4-bet PF in PLO

This is a really interesting topic I've been wondering alot about but don't know how to do the math of it... looking forward to more replys
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Old 01-24-2009, 08:30 PM   #21
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Re: Calling a 4-bet PF in PLO

Seems reasonable since we only care about the average equity when we have a favorable board texture which I presumed to be much higher than 38%.
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Old 01-24-2009, 08:34 PM   #22
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by GoChoo View Post
The mean equity is different from the median equity. So .558 is not likely to be correct.

Also if the EV is $9.60 then isn't it +EV to call?
You are correct, and i have completely forgotten how to do this, so i am as intrigued by this thread as anyone.

however, EV (post flop) must be greater than the preflop call in order for the call to be +EV, ie; in my incorrect calculations you would be calling $25.50 to return $9.60 for a loss of $15.90 on the call.
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Old 01-24-2009, 08:37 PM   #23
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Re: Calling a 4-bet PF in PLO

alright you added up the areas horizontally, which can't be right. you have to add up the areas in vertical strips since we're trying to average the value on the vertical axis. You took an average of the value on the horizontal axis, which is not what want
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Old 01-24-2009, 08:40 PM   #24
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Re: Calling a 4-bet PF in PLO

I think you have the wrong area. You should be looking at the >30% equity area and not <68% flops

The are has to obtained 'vertically', because we are interested in the average of equity * %flops for the average equity.

And in addition the sklansky dollar equation needs to be modified.

Assuming 12$ ante

You finish the hand Y times and win X *200
You do not finish the hand 1-Y times and lose 25.5

This has to be better than -12*2

X * Y * 200 - {(1-Y) *25.5 } >= --24

Would you be kind enough to do the sum

Last edited by uphigh_downlow; 01-24-2009 at 08:48 PM.
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Old 01-24-2009, 08:41 PM   #25
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Re: Calling a 4-bet PF in PLO

Quote:
Originally Posted by Peeda View Post
Alright just eyeballed it. Just eyballing it, looks like the graph can be broken up "approximately" into two fairly straightish segments, the 0 - 8% of flops with between 80 and 100% equity (lets say ~90 on average) and the 8 - 68% of flop with 30ish to high 70sish (looking at the midpoint as38 on the X axis, looks like 52% or 53% equity is the midpoint).

so 8/68 * 90% + 60/68 * 53% gives .575 as our average postflop equity when we call. Not exact but I'm lazy and don't want to add like 10 segments up.
Im not good enough on these things to understand your calculation.
But if i try the same i get

8%*80%+8%*20%/2+60%*30%+60%*50%/2

= 0.064 + 0.008 + 0.18 + 0.15 = 0.4

which is almost the same i got in the orginal calculation.
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