Two Plus Two Publishing LLC
Two Plus Two Publishing LLC
 

Go Back   Two Plus Two Poker Forums > >

Notices

Beginners Questions Poker beginner? Ask your (possibly) naive question here and our community will attempt to help you.

Reply
 
Thread Tools Display Modes
Old 11-27-2017, 05:14 PM   #1
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Club Postflop probabilities

Does it makes sense to say that in HU if hero holds Q,Q then there's a 4.24% chance villain is ahead after a J,7,2 flop excluding draws?

Villain pockets that put him ahead:
JJ, 77, 22, J7, J2, 72, AA, KK

Probs using a 47-card (post-flop) universe are:
JJ, 77, 22 each are .002775
J7, J2, 72 each are .008326
AA, KK each are .004525

Sum = .042352 or 4.24%
Sandman is offline   Reply With Quote
Old 11-27-2017, 05:40 PM   #2
madlex
Custom User Title
 
Join Date: Jan 2009
Posts: 9,031
Re: Postflop probabilities

The short answer is "no, it doesn't make sense".

The thing you should think about is what equity your hand (or your range) has against his range.
madlex is offline   Reply With Quote
Old 11-27-2017, 08:37 PM   #3
Bob148
Carpal \'Tunnel
 
Bob148's Avatar
 
Join Date: May 2012
Location: takin it to the streets
Posts: 9,876
Re: Postflop probabilities

Quote:
The thing you should think about is what equity your hand (or your range) has against his range.
I agree.

First figure out which hands "should" be in your range depending on the individual equities. Then figure out how you should play your range depending on the range vs range equities.
Bob148 is offline   Reply With Quote
Old 11-28-2017, 07:25 AM   #4
ArtyMcFly
Carpal \'Tunnel
 
ArtyMcFly's Avatar
 
Join Date: Dec 2014
Location: Enchantment Under the Sea
Posts: 9,597
Re: Postflop probabilities

The 4.24% number (assuming you've done the maths correctly) would only make sense if villain sees the flop with 100% of hands. In the real world (especially in a multiplayer game, not HU) villain is unlikely to be seeing the flop with 72 or J2 or even J7.
Build a real range for villain and then use Flopzilla or Equilab or Combonator to find out how often he can beat top pair on J72r. It's not very often, especially if his pre-flop action was "call" (meaning he can't have QQ+, unless he's a passive whale).

EDIT: As a quick example, if you opened QQ UTG and villain was in the BB and called pre with a nitty range like JJ-22, AQs-A2s, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, 65s, AQo-ATo, KJo+, QJo (he 3-bets QQ+/AK), then on J72r, he has 9 combos of sets representing 5.3% of his range. He never has two pairs or an overpair, so you'd be ahead about 95% of the time.

Last edited by ArtyMcFly; 11-28-2017 at 07:30 AM.
ArtyMcFly is offline   Reply With Quote
Old 11-28-2017, 09:16 AM   #5
SpewingIsMyMove
veteran
 
SpewingIsMyMove's Avatar
 
Join Date: Jun 2015
Posts: 2,285
Re: Postflop probabilities

You are answering the wrong question. the question you are answering is:

"What is the likelihood that I am ahead if I hold XX, Villain is playing any two cards preflop, and action stops on the flop?"

Your math is correct in analyzing this question, but this question is completely meaningless from a poker standpoint.

I guess we need to back up a abit and ask, what problem or situation are you trying to analyze?
SpewingIsMyMove is offline   Reply With Quote
Old 11-28-2017, 10:08 AM   #6
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Club Re: Postflop probabilities

Is the next step when calculating equity to determine probability of winning? I.e. if villain is ahead calculate probability hero hits his outs, or if hero is ahead calculate 1 minus probability villain hits his outs?

For simplicity let's put villain on a specific hand: 55

Therefore villain has 2 outs: fives

To determine prob hero wins, would we calculate total probability of following scenarios then subtract from 1?
1. Turn is a 5, river no help to hero
2. Turn is a 5, river is a 5
3. Turn is no help to hero, river is a five
Sandman is offline   Reply With Quote
Old 11-28-2017, 10:26 AM   #7
SpewingIsMyMove
veteran
 
SpewingIsMyMove's Avatar
 
Join Date: Jun 2015
Posts: 2,285
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
Is the next step when calculating equity to determine probability of winning? I.e. if villain is ahead calculate probability hero hits his outs, or if hero is ahead calculate 1 minus probability villain hits his outs?

For simplicity let's put villain on a specific hand: 55

Therefore villain has 2 outs: fives

To determine prob hero wins, would we calculate total probability of following scenarios then subtract from 1?
1. Turn is a 5, river no help to hero
2. Turn is a 5, river is a 5
3. Turn is no help to hero, river is a five
On the turn, there are 43 out of 45 cards that do not help villain. On the River, there are 42 cards out of 44 cards that do not help villain.

Likelihood turn does not help villain, 43/45. If turn does not help villain, likelihood that river does not help villain is 43/44. To figure your total likelihood of winning, multiply the probability of both of those events together.
SpewingIsMyMove is offline   Reply With Quote
Old 11-28-2017, 11:38 AM   #8
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Re: Postflop probabilities

Continuing with a simplistic example, let's put villain on following range: 66,55,44.

Is prob hero wins (39/45) x (39/44) = .768 ?

If so, what about the fact it's really only 2 outs that are applicable to each hand in the range. Villain has either 66 OR 55 OR 44. So not ALL six outs will actually help. Do we apply any discounting or adjustments to calculation to account for this?
Sandman is offline   Reply With Quote
Old 11-28-2017, 11:46 AM   #9
madlex
Custom User Title
 
Join Date: Jan 2009
Posts: 9,031
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
Continuing with a simplistic example, let's put villain on following range: 66,55,44.

Is prob hero wins (39/45) x (39/44) = .768 ?

If so, what about the fact it's really only 2 outs that are applicable to each hand in the range. Villain has either 66 OR 55 OR 44. So not ALL six outs will actually help. Do we apply any discounting or adjustments to calculation to account for this?
No matter which of the possible hands he has, he has only two outs to win. There's no difference between him having back 4s or red 6s.

So you calculate his probability to hit his outs on the flop or/and on the river.
madlex is offline   Reply With Quote
Old 11-28-2017, 12:26 PM   #10
statmanhal
Pooh-Bah
 
Join Date: Jan 2009
Posts: 4,215
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
Continuing with a simplistic example, let's put villain on following range: 66,55,44.

Is prob hero wins (39/45) x (39/44) = .768 ?

If so, what about the fact it's really only 2 outs that are applicable to each hand in the range. Villain has either 66 OR 55 OR 44. So not ALL six outs will actually help. Do we apply any discounting or adjustments to calculation to account for this?
Your equation isn't quite right and it's a little more complicated.

Hero wins if villain completely misses or villain can hit one of his 2 outs on one street but hero hits a queen on the other.

P(H wins) = P(V doesnít hit his outs on turn and river) + P(V hits an out on one street and H hits a Q on the other)

= (43/45)*(42/44) + 2*(2/45)*(2/44) = 0.916

This checks with what Equilab calculates.
statmanhal is offline   Reply With Quote
Old 11-28-2017, 12:43 PM   #11
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Re: Postflop probabilities

Understood, so since each scenario has 2 outs we use (43/45 * 43/44).

What if villain's range contains hands with differing numbers of outs?

For example, if we add KJ to villain's range then we have:

66 --> 2 outs
55 --> 2 outs
44 --> 2 outs
KJ --> 5 outs (3K, 2J)

Would we use 5 outs in prob calculation, i.e. (40/45)*(40/44), or apply some kind of weighting to each of the hands in his range to determine the number of outs we use in calculation.
Sandman is offline   Reply With Quote
Old 11-28-2017, 12:57 PM   #12
SpewingIsMyMove
veteran
 
SpewingIsMyMove's Avatar
 
Join Date: Jun 2015
Posts: 2,285
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
Continuing with a simplistic example, let's put villain on following range: 66,55,44.

Is prob hero wins (39/45) x (39/44) = .768 ?

If so, what about the fact it's really only 2 outs that are applicable to each hand in the range. Villain has either 66 OR 55 OR 44. So not ALL six outs will actually help. Do we apply any discounting or adjustments to calculation to account for this?

You are on the right track. When you calculate your likelihood of winning against a range, you do a weighted average. In your example above, if you think his range as 66, 55, and 44 (and only those hands), you multply the likelihood of winning against each hand (91%) times the likelihood of having that hand (33.3%), and then add them up.

Let's take a much more meaningful example, a common preflop situation. You have raised with QQ., and a tight player has three bet all in. You believe that he would only do that with AK, AA, KK. You want to figure your likelhood of winning.

First,you look at your percentages against each hand
AK - 57%
AA - 18%
KK - 18%

Then you need to weight them by their frequency. We know there are 16 combos to make AK, 6 combos to make AA, and 6 combos to make KK

So, you will end up with the hand the following pecentage of time
AK -57%
AA - 21.5%
KK - 21.5%

to figure your percentage of win against the range, you now take a weighted average of the win percentage of each hand in the range

probability against the range = (57%)*(57%) + (18%)*(21.5%)+(18%)*(21.5%)= 40.2%

Your equity for QQ versus a range of AK, AA, KK is around 40%
SpewingIsMyMove is offline   Reply With Quote
Old 11-28-2017, 01:18 PM   #13
statmanhal
Pooh-Bah
 
Join Date: Jan 2009
Posts: 4,215
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
Understood, so since each scenario has 2 outs we use (43/45 * 43/44).

What if villain's range contains hands with differing numbers of outs?

For example, if we add KJ to villain's range then we have:

66 --> 2 outs
55 --> 2 outs
44 --> 2 outs
KJ --> 5 outs (3K, 2J)

Would we use 5 outs in prob calculation, i.e. (40/45)*(40/44), or apply some kind of weighting to each of the hands in his range to determine the number of outs we use in calculation.
You would have 2 different equations, one with 2 outs and one with 5 outs for a villain win. Yes, then you would weight the results by the occurrence frequencies.

For the pairs, there are 3 *6 = 18 combos and for KJ, there are 4*3=12 combos.

The KJ equation is P(H wins) = (40/45)*(39/44) = 0.788

Overall, H wins with probability (18*0.916 +12*0.788 )/30 = 0.864

Since the KJ combo, if suited, can give villain a win with a flush, this result differs in the third place from Equilab depending on what suit interactions you allow. You can actually model that, but we should not worry about such a small difference.
statmanhal is offline   Reply With Quote
Old 11-29-2017, 06:42 PM   #14
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Club Re: Postflop probabilities

So, essentially, the steps for determining prob of winning are as follows?

1) Establish villainís range
2) Group different hole-card combinations by number of outs and tally count in each group
3) Multiple each count by applicable weight, where weight = 1 - prob(villain does not win)
4) Sum products.

Is that correct?


And to clarify,

For the pairs: 3 x 6 = 18 is derived from (4 cards choose 2) = 6 then 6 x 3 pairs = 18, yes?

And for KJ: 4 x 3 = 12 is derived from (4 kings choose 1) = 4 and (3 jacks remaining choose 1) = 3 then 4 x 3 = 12, yes?
Sandman is offline   Reply With Quote
Old 11-29-2017, 07:00 PM   #15
SpewingIsMyMove
veteran
 
SpewingIsMyMove's Avatar
 
Join Date: Jun 2015
Posts: 2,285
Re: Postflop probabilities

Quote:
Originally Posted by Sandman View Post
So, essentially, the steps for determining prob of winning are as follows?

1) Establish villainís range
2) Group different hole-card combinations by number of outs and tally count in each group
3) Multiple each count by applicable weight, where weight = 1 - prob(villain does not win)
4) Sum products.

Is that correct?


And to clarify,

For the pairs: 3 x 6 = 18 is derived from (4 cards choose 2) = 6 then 6 x 3 pairs = 18, yes?

And for KJ: 4 x 3 = 12 is derived from (4 kings choose 1) = 4 and (3 jacks remaining choose 1) = 3 then 4 x 3 = 12, yes?
This is correct. To be honest, very rarely are you going to be calculating this during play. Work with an equity calculator to memorize the equity in common scenerios. You are rarely going to need to be exact, so being able to estimate your equity against villain's probable range is good enough.
SpewingIsMyMove is offline   Reply With Quote
Old 12-05-2017, 03:30 PM   #16
Sandman
newbie
 
Join Date: Mar 2017
Location: Hangin' out south of profit street
Posts: 41
Club Re: Postflop probabilities

Here is another scenario where Iíve tried to work out the probability of winning to help crystallize my understanding. My probability math skills are not exactly top notch which is why Iím working on them.

Despite there being apps out there to calculate these probabilities, Iím attempting to understand the actual core calculations.

Kindly have a look.

Hero: 99
Board after flop: 234
Villain Range TT+, ATs+, AJo+, KJs+

Probabilities for hero winning are,

Subrange 1: AA/KK/QQ/JJ/TT
Hero lands 9, no villain set = (2/45)*(42/44) + (43/45)*(2/44) = .0424 + .0434 = .086

Subrange 2: AKo/AQo/AJo/AKd/AQd/AJd/ATd/KJd/KQd
No villain pair = (39/45)*(38/44)=.748

Subrange 3: AKc/AKs/AKh/AQc/AQs/AQh/AQh/AJc/AJs/AJh/ATc/ATs/ATh/ KQc/KQs/KQh/KJc/KJs/KJh
No villain pair, no villain flush draw = (30/45)*(29/44) = .439
No villain pair, busted villain flush = (9/45)*(30/44) + (30/45)*(9/44) = .136 + .136 = .272
Total = .439 + .272 = .711

Combos:
Subrange 1: (4c2)*5 = 30
Subrange 2: (4c1)*(4c1)*3 + 6 = 54
Subrange 3: (3c1)(3c1)*6 = 54
Total combos = 138

Prob(Hero wins) = (30/138 * .086) + (54/138 * .748) + (54/138 * .711) = .019 + .293 + .278 = .59

59% hero wins? Feels high, no?
Sandman is offline   Reply With Quote
Old 12-05-2017, 04:43 PM   #17
statmanhal
Pooh-Bah
 
Join Date: Jan 2009
Posts: 4,215
Re: Postflop probabilities

Equilab shows 45.4%, so you have some mistakes.

I did a quick look and note that your combo counts are wrong for non-pairs. Off suit is 12 combos each and you have 16. Suited is 4 combos each and you have 9. Also you didn’t consider the possibility of villain hitting a wheel straight. I didn’t look further.
statmanhal is offline   Reply With Quote

Reply
      

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


Forum Jump


All times are GMT -4. The time now is 06:07 AM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
Copyright © 2008-2017, Two Plus Two Interactive
 
 
Poker Players - Streaming Live Online