# Poker Video: No Limit Hold'Em by WiltOnTilt (Micro/Small Stakes)

## Mathematics of NL Hold'em: Episode Four

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### Mathematics of NL Hold'em: Episode Four by WiltOnTilt

This episode of Mathematics of No Limit Holdem focuses on EV Calculations which are set up using examples of preflop, flop and turn play. The reliability of the EV Calculations is dependent on our ability to put our opponents on accurate hand ranges so handreading is also addressed. In addition, this episode introduces the TUPAC method of estimating equity against a handrange without the use of software.

#### About Mathematics of NL Hold'em

WiltOnTilt will discuss key concepts related to the mathematics of No-Limit play using Powerpoint. Begin with the basics: probability and pot odds. Then follow Wilt to more advanced arenas: implied odds and reverse implied odds, software tools and mental shortcuts for equity calculations, complex EV calculations, and an exploration of fold equity. And watch this series conclude with a discourse on the ultimate in professional poker math: hand frequencies, valuebetting, and G-bucks.

### Video Details

• Game:
• Stakes: Micro/Small Stakes
• 54 minutes long
• Posted over 5 years ago

## Comments for Mathematics of NL Hold'em: Episode Four

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#### Jonnolimit

29 posts
Joined 07/2011

but it s true that when you apply the 2 and 4 rule it makes it around 18% you win and 82% lose, so it s like a little less than 4:1

#### numjaw

164 posts
Joined 11/2011

I might be missing something here but.....

In section 2 of the TUPAC method, the pairing combos to known equities section, you match the crushing hands to the flips but you left out 98s.
Was this done as you knew in advance that you could "cancel out" 98s with JTs in section 3, analyze unpaired combos?

Surely in a real scenario we would pair off as many hands as possible in section 2 as we wouldn't have the prior knowledge of "canceling out" in section 3. Or maybe "cancel out" hands first?

It's also possible I'm suffering the effects of trying to do this at 3 in the morning.

#### WiltOnTilt

2402 posts
Joined 10/2007

I might be missing something here but.....

In section 2 of the TUPAC method, the pairing combos to known equities section, you match the crushing hands to the flips but you left out 98s.
Was this done as you knew in advance that you could "cancel out" 98s with JTs in section 3, analyze unpaired combos?

Surely in a real scenario we would pair off as many hands as possible in section 2 as we wouldn't have the prior knowledge of "canceling out" in section 3. Or maybe "cancel out" hands first?

It's also possible I'm suffering the effects of trying to do this at 3 in the morning.

probably an oversight. generally you should be putting the hands in their respective buckets and then figuring out how many of each you can cancel out

#### Chewey89

12 posts
Joined 07/2011

I think I understand everything except for the final part regarding the JTs+ 89s , there are five combos overall, and we are 2:1 favourite and dog respectively. When I work the two % out separately I get 7% for my JTs(1/10 range multiplied by my 70% equity) + 1.98% for the 98s ( 1/15 of 33%equity) . Obviously this is wrong but I am having trouble understanding what the problem is. How do they just cancel each other out? Thanks in advance.

#### WiltOnTilt

2402 posts
Joined 10/2007

pokenum -h 8s 9s - ks qs -- kc 9c 8d
Holdem Hi: 990 enumerated boards containing Kc 9c 8d
cards win %win lose %lose tie %tie EV
9s 8s 722 72.93 268 27.07 0 0.00 0.729
Ks Qs 268 27.07 722 72.93 0 0.00 0.271

pokenum -h js ts - ks qs -- kc 9c 8d
Holdem Hi: 990 enumerated boards containing Kc 9c 8d
cards win %win lose %lose tie %tie EV
Js Ts 284 28.69 706 71.31 0 0.00 0.287
Ks Qs 706 71.31 284 28.69 0 0.00 0.713

In these cases, the equity is about the same. For the example, I should have made the board Kc 9s 8s so there would be a closer number of combinations, but for this particular example with Kc 9c 8x that means there's only 2 combos of 98s and 4 combos of JTs, so in reality only 2 of the 98s "cancel out" 2 of the JTs, and we're left with a couple JTs left over, but this falls into the idea that it's supposed to be a rough estimation to begin with, so as long as we can get a close approximation, we're doing fine.

#### Chewey89

12 posts
Joined 07/2011

I think I'm getting it now, the reason I think I got mixed up was because I had been taking all their individual % but you are just rounding up. So would it be correct if

The 18 flips and crushes are taken as 60% of the range of hands ( 13crushes+9flips+8unmatched combos) which would be .6x 28%(our avg equity with flips +crushes) = 16.8

Then we take the 4 combos . which is 13% of the total range and multiply that times our equity which would be about 20% , .13x20= 2.4%

Now we have 8 unmatched combos left, we take the JTs vs our hand, this sum done the same as the previous examples, end up as .1x66% = 6.6%
Then we take 98s- sum ends up being- .15x33=4.95%
Last we take the 67s hands , this sum ends up as .1x60%=6%

Lastly I added all these together, making up 16.8+2.4+4.95+6 = 36.75

Apologies for writing so much, I hope it makes some sense, I just want to know is that the correct way to do it outright?
That was the reason I got mixed up with the JTs and 89s cancelling out, I know you are getting a rough estimate by counting the crushed and flipped hands as 27% but how come those others just cancel out, any help at all would be great. Thanks for your previous reply sorry if this is a stupid question.

#### runners23

129 posts
Joined 01/2011

Thank you, This helps alot! BTW 2Pac has been my fav rapper over 16 years now, so that helps too! THANK YOU for the hard work you put in this vid. Very well explained.

#### runners23

129 posts
Joined 01/2011

So lets say were vs a fishier villian who has say a total of 15 FD combos, and out of those 6 extra I have added for this fishier villian how would I go about getting a estimated equity. Cleary our equity would be higher I just dont know how much higher, and how to go about finding that number out. Id really appreciate some help on this. THX!

#### WiltOnTilt

2402 posts
Joined 10/2007

So lets say were vs a fishier villian who has say a total of 15 FD combos, and out of those 6 extra I have added for this fishier villian how would I go about getting a estimated equity. Cleary our equity would be higher I just dont know how much higher, and how to go about finding that number out. Id really appreciate some help on this. THX!

of the combos that are leftover (they dont pair up with something else) you'd want to see what your equity is (roughly 2:1 favorite for extra flush draws) and then see how many of those leftover combos there are compared to the total number. So if it's 6 extra combos out of 100, that extra 67% will help push you up a few points but probably not drastically. If it's 6 extra combos out of 15 total then yea that extra 67% for each of those will weigh a lot more.

Since it's at the table math, it will be hard to do the weighted average in your head, but just try to think about a) how big your edge is in those unpaired combos and b) how many of those exist relative to the entire range and then move your estimate up and down accordingly

#### WiltOnTilt

2402 posts
Joined 10/2007

I think I'm getting it now, the reason I think I got mixed up was because I had been taking all their individual % but you are just rounding up. So would it be correct if

The 18 flips and crushes are taken as 60% of the range of hands ( 13crushes+9flips+8unmatched combos) which would be .6x 28%(our avg equity with flips +crushes) = 16.8

Then we take the 4 combos . which is 13% of the total range and multiply that times our equity which would be about 20% , .13x20= 2.4%

Now we have 8 unmatched combos left, we take the JTs vs our hand, this sum done the same as the previous examples, end up as .1x66% = 6.6%
Then we take 98s- sum ends up being- .15x33=4.95%
Last we take the 67s hands , this sum ends up as .1x60%=6%

Lastly I added all these together, making up 16.8+2.4+4.95+6 = 36.75

Apologies for writing so much, I hope it makes some sense, I just want to know is that the correct way to do it outright?
That was the reason I got mixed up with the JTs and 89s cancelling out, I know you are getting a rough estimate by counting the crushed and flipped hands as 27% but how come those others just cancel out, any help at all would be great. Thanks for your previous reply sorry if this is a stupid question.

So the terms "cancel out" might be a bit confusing. It isn't canceling out to zero but to 50%. So think of a simple example where there are 2 combos. We are either 80/20 favorite or 80/20 dog. If you average those, we are 50%. So it's possible a lot of those "canceling out" combos could actually raise your overall equity if you have tons and tons of them and a few combos that crush you where you are a big dog. Make sense?

But yea to answer your question it looks like you are correctly weighting these equities by their share of the range, which is definitely one of the goals of the exercise. You're taking the hand equity times the share of the range they make up and then putting it all together at the end, which is a good way to think about what we are doing in steps 3 and 4.

#### muddymurphys

8 posts
Joined 05/2012

Hey, i've been learning poker for about a 2 days now. I knew the hand ranks, and how to bet and call before this but thts about it. Your videos are great man, i've learned a lot of faster than i would have without them.

I have a few qs though. Firstly, i'm a bit confused with regards to how you put the opponent on a range.

here's what i'm guessing:
pre-flop you narrowed it down to roughly
AA, KK, QQ, JJ, TT, 99, 88 (pocket pairs)
AQ, AJ, AT, A9, A8 (A and another card)
KQs, QJs, JTs, 98s, 87s (suited connectors)
Left out AK because he would have 4 bet that.

after flop:
AA, KK, 99, 88, AcQc, AcJc, AcTc, Ac8c, QcJc, QcTc, JcTc, 98s, 8c7c, JTs, 76s

Questions
1) I assume that QQ, JJ and TT are out because he would have folded that hand, is that correct ? So, due to the fact that he chose not to fold his connectors (76, JT) because hes drawing to an open ended straight draw. i'm guessing roughly that a open ended straight draw is a better hand to have in this situation than a high pocket pair ? How then are we a decent favourite with KQ when compared to his JT and 76. Unless KQ is a better hand than QQ, JJ, and TT in this situation ? what are we hoping to draw to ? 1 king is on the board, we have one, so thats 2 outs, 3 queens so 3 more outs, thats 5 outs ? an open ended straight draw has 8 outs ? any help is much appreciated.

2) Also, pre-flop you didnt really narrow it down to QcJc. You said maybe AQ. I assume QJ is worse off than an AQ or is this wrong. So is it right to assume that he would have gone in before the flop with just a QJ, QT and even a JT)

4) also , what about KJ. would he have gone in on the flop with that ? in which case that would be a threat now too post-flop wouldn't it ?

Secondly,
i've made a lot of inferences from your tupac (awsome name for your method btw) method. I just wanted to get some sort of affirmation that what i've got in my head is right. Most of these are things that i inferred so not exactly what you were talking about but i just wanted to check if this conclusions i'm drawing are correct.

I learnt that equity is basically the percentage chance that you will win the game with your hand.
I also learnt that if you have a draw, we basically kind of assume that it will be the winning hand and as a result of that, we don't really need to know our opponents hand, making it really one of 2 situations that we can calculate equity easily. And that would be by finding out the draw odds to the river, which basically can be translated to odds of winning, which is equity, because we assume we will win with that hand. Then later we use reverse implied odds to take care of the scenario that we might actually lose even with the winning hand.
I also learnt that there is another situation that we can calculate equity easily and that is if we know our opponents hand, and it is a drawing hand. In which case we just reverse his drawing odds to become our winning odds. So if he has an OESD, his odds are roughly 4.8:1 and we are a 4.8:1 favourite.

so basically to work out our equity we put him on a range, match up crushing and flipping and that gives us a rough equity of 25 to 30 percent based on some sort of trial and error you have done on poker stove. Then we try and tackle the rest of the hands (combinations specifically) by using whatever tools we have such as working our drawing odds (to the river) of his drawing hands.

Are these statements correct so far ?

The only thing missing is how you got your equity for his hand of 2 pairs with 98. Which is my last question.You put us as a 3:1 dog. how did u estimate that ?

Thanks a lot for the help, i know its a long post and i'm only half way through the video, but thanks !!!

8 posts
Joined 05/2012

#### muddymurphys

8 posts
Joined 05/2012

saw the last bit on your thought process. dont come to my table mate

#### WiltOnTilt

2402 posts
Joined 10/2007

Hey, i've been learning poker for about a 2 days now. I knew the hand ranks, and how to bet and call before this but thts about it. Your videos are great man, i've learned a lot of faster than i would have without them.

I have a few qs though. Firstly, i'm a bit confused with regards to how you put the opponent on a range.

here's what i'm guessing:
pre-flop you narrowed it down to roughly
AA, KK, QQ, JJ, TT, 99, 88 (pocket pairs)
AQ, AJ, AT, A9, A8 (A and another card)
KQs, QJs, JTs, 98s, 87s (suited connectors)
Left out AK because he would have 4 bet that.

after flop:
AA, KK, 99, 88, AcQc, AcJc, AcTc, Ac8c, QcJc, QcTc, JcTc, 98s, 8c7c, JTs, 76s

Questions
1) I assume that QQ, JJ and TT are out because he would have folded that hand, is that correct ?

QQ-TT probably either check and call or 4bet preflop or check and fold.

So, due to the fact that he chose not to fold his connectors (76, JT) because hes drawing to an open ended straight draw. i'm guessing roughly that a open ended straight draw is a better hand to have in this situation than a high pocket pair ?

The open end straight draws are better for him to checkraise the flop with compared to something like QQ because when he's called the draws have 8 outs usually whereas QQ has 2 outs if he's behind. If he's winning with QQ on the flop then all he does is make us fold our bluffs, so he's better to either check and call or check and fold depending on how strong he thinks our range is.

How then are we a decent favourite with KQ when compared to his JT and 76. Unless KQ is a better hand than QQ, JJ, and TT in this situation ?

KQ is a better hand than QQ/JJ/TT because when it's behind it will have more outs against 2 pair (well, depending on which 2 pair he has). Also KQ is a decent favorite against the straight draws because they only have 2 opportunities (turn/river) to hit one of their 8 outs, which ends up being about 32% if you remember the rule of 4 from the earlier videos. So our 68% is a decent favorite, it's no hammerlock on the hand, but we're making good money here long term against the straight draws all in on the flop.

what are we hoping to draw to ? 1 king is on the board, we have one, so thats 2 outs, 3 queens so 3 more outs, thats 5 outs ? an open ended straight draw has 8 outs ? any help is much appreciated.

Remember we're already being the straight draws, so it's up to them to hit. Most of the time the turn and river will miss the JT so our pair of kings will win.

2) Also, pre-flop you didnt really narrow it down to QcJc. You said maybe AQ. I assume QJ is worse off than an AQ or is this wrong. So is it right to assume that he would have gone in before the flop with just a QJ, QT and even a JT)

I think I mentioned QJ suited preflop, if not I mentioned it on the flop. I don't think he would checkraise all in on the flop with QJ of hearts, but certainly he might with QJ of clubs since he has the flush draw there. You are right QJ is worse off than AQ. He would fold QJ more often preflop than AQ (almost never folding AQ preflop here, maybe he 4bets it if the dynamic is aggressive enough, but he at least calls it). Some people will fold hands like QJ QT JT (especially the offsuit ones) because when they hit a pair they are in big danger of having the second best hand since the hands we would reraise him with preflop are usually dominating those hands (think like JJ QQ KK AA AK AQ KQ etc, those all crush QJ QT JT - however the suited versions have some chance to flop a draw he can try to bluff us with)

4) also , what about KJ. would he have gone in on the flop with that ? in which case that would be a threat now too post-flop wouldn't it ?

KJ he would usually either fold preflop or just call the flop. The reason he shouldn't really checkraise the flop with KJ is similar to reasons above why he wouldnt want to checkraise flop with QQ. If he's ahead on the flop, there's not much reason to raise and make us fold his air. If he does raise and gets called, he's probably in trouble!

Secondly,
i've made a lot of inferences from your tupac (awsome name for your method btw) method. I just wanted to get some sort of affirmation that what i've got in my head is right. Most of these are things that i inferred so not exactly what you were talking about but i just wanted to check if this conclusions i'm drawing are correct.

I learnt that equity is basically the percentage chance that you will win the game with your hand.
I also learnt that if you have a draw, we basically kind of assume that it will be the winning hand and as a result of that, we don't really need to know our opponents hand, making it really one of 2 situations that we can calculate equity easily. And that would be by finding out the draw odds to the river, which basically can be translated to odds of winning, which is equity, because we assume we will win with that hand. Then later we use reverse implied odds to take care of the scenario that we might actually lose even with the winning hand.
I also learnt that there is another situation that we can calculate equity easily and that is if we know our opponents hand, and it is a drawing hand. In which case we just reverse his drawing odds to become our winning odds. So if he has an OESD, his odds are roughly 4.8:1 and we are a 4.8:1 favourite.

so basically to work out our equity we put him on a range, match up crushing and flipping and that gives us a rough equity of 25 to 30 percent based on some sort of trial and error you have done on poker stove. Then we try and tackle the rest of the hands (combinations specifically) by using whatever tools we have such as working our drawing odds (to the river) of his drawing hands.

Are these statements correct so far ?

The only thing missing is how you got your equity for his hand of 2 pairs with 98. Which is my last question.You put us as a 3:1 dog. how did u estimate that ?

Thanks a lot for the help, i know its a long post and i'm only half way through the video, but thanks !!!

It looks like your assumptions and restatement of what we are doing here is very good! Remember the more time you spend in poker stove to see which hands are beating other hands (and by how much %) the easier this stuff will be to estimate in your head.

To find out our equity against 2pair, we can also use pokerstove and put in our hand against that hand. We can also think about our hand as a drawing hand against that one. We would have 5 outs on the flop but we get extra outs on the turn (2 kings, 3 queens, and 3 more of whatever the turn is, unless it's a 9 or 8). You can also see by putting this hand into poker stove. I went ahead and did this for you:

Board: Kc 9c 8d

equity win tie pots won pots tied
Hand 0: 27.071% 27.07% 00.00% 268 0.00 { KsQs }
Hand 1: 72.929% 72.93% 00.00% 722 0.00 { 9h8h }

You can see 27% is roughly 3:1 dog. Keep in mind, the whole thing is about estimating, so it doesn't have to be exact. Theoretically we're supposed to be able to do this at the table

#### WiltOnTilt

2402 posts
Joined 10/2007

Hehehe you are right, my friend It is not easy to do. I think more important than being able to do this at the table, is understanding each part of the range and how it weights the end result of the chance of winning. So you can see that when we break down his range into parts that are all about the same %, then we look at those parts individually and then combine them, it is easier to visualize just why we have the chance of winning we do against his entire range.

You will find that the more you try to think through this, the easier it will become. None of us can do this for every hand we play at the table every time, but the more you start thinking about "roughly how many combos of hands does he have that crushes me?" will help you get an overall idea of what your downside risk might be. Then when you get that down you can start thinking "how many hands does he have that are drawing?" etc etc

#### muddymurphys

8 posts
Joined 05/2012

Hey Wilt, thanks for the reply. I read through what you said and its been really useful. I have a few more questions.

Why are all the clubs under the flipping category. I know odds of a flush draw with 2 cards to come is around 2 : 1. Flipping would be 1 : 1. Did you count some other outs ? in which case it would be different for each hand? Example (first hand in flipping category) AcQc : 9 outs from flush draw plus 3 outs for another ace, and 2 outs for the remaining queen ? Is that how you managed to categorize it as "flipping" ?

Also, i was wondering what should i do if there a lot more combo's, say because the hand range is a lot wider. Say maybe 70 combos of crushing hands, and 50 combos of flipping hands. Can i say around 30% equity but bump it down around 5% for the 20 crushing hands (a bit more than 1/3 of the total crushing hands) unaccounted for ?

Also, i was thinking about pairing crushing hands with hands that we are decent favourites (or are crushing the villain) .. I did an example of my own and put it in poker stove. I managed to categorize villains hand into crushing and being crushed. And paired them and it worked out to around 50%. I tried it in poker stove and it was quite accurate. There were a few more crushing hands than hands that were being crushed (i was a favourite) and so i bumped my equity down about 5% which was correct. What do you think ? i was just thinking that not all sitiuations have so many categories under "flipping", esepcially if there are not many draws. Do you have any other tricks for estimating equity. I know matching flipping with crushing gives me around 30%. Then bump up here and there depending on how many more flipping vs crushing.

#### WiltOnTilt

2402 posts
Joined 10/2007

Hey Wilt, thanks for the reply. I read through what you said and its been really useful. I have a few more questions.

Why are all the clubs under the flipping category. I know odds of a flush draw with 2 cards to come is around 2 : 1. Flipping would be 1 : 1. Did you count some other outs ? in which case it would be different for each hand? Example (first hand in flipping category) AcQc : 9 outs from flush draw plus 3 outs for another ace, and 2 outs for the remaining queen ? Is that how you managed to categorize it as "flipping" ?

Also, i was wondering what should i do if there a lot more combo's, say because the hand range is a lot wider. Say maybe 70 combos of crushing hands, and 50 combos of flipping hands. Can i say around 30% equity but bump it down around 5% for the 20 crushing hands (a bit more than 1/3 of the total crushing hands) unaccounted for ?

Also, i was thinking about pairing crushing hands with hands that we are decent favourites (or are crushing the villain) .. I did an example of my own and put it in poker stove. I managed to categorize villains hand into crushing and being crushed. And paired them and it worked out to around 50%. I tried it in poker stove and it was quite accurate. There were a few more crushing hands than hands that were being crushed (i was a favourite) and so i bumped my equity down about 5% which was correct. What do you think ? i was just thinking that not all sitiuations have so many categories under "flipping", esepcially if there are not many draws. Do you have any other tricks for estimating equity. I know matching flipping with crushing gives me around 30%. Then bump up here and there depending on how many more flipping vs crushing.

right, many of those flush draws have extra outs which get them closer to 1:1 than 2:1 so we can just fudge it a little bit.

Similar to what you are describing. Sometimes things dont match up as nicely as they did in this example. You trying things out in pokerstove is exactly the right path to take, see how the pieces fit together and then you can better estimate in the future, just like you did in your examples. You are definitely on the right track

#### 13Strike

198 posts
Joined 07/2012

Hey man,

Really like this video. The only thing I would have done differently would have been to included some more visuals as you explain the TOPAC method. I think it might have worked well if you had a graphic or even an excel spreadsheet where you visually breakdown the ranges and then cancel them out. Still, as you said its all about trying it out for your self and you definetly gave us enough information to work with.

CHeers,

#### WiltOnTilt

2402 posts
Joined 10/2007

Hey man,

Really like this video. The only thing I would have done differently would have been to included some more visuals as you explain the TOPAC method. I think it might have worked well if you had a graphic or even an excel spreadsheet where you visually breakdown the ranges and then cancel them out. Still, as you said its all about trying it out for your self and you definetly gave us enough information to work with.

CHeers,

Thanks, and I agree, that would be better. These were the first videos I ever made so they definitely aren't as polished as they could be. Perhaps someday I will redo them.

#### wego2valuetown

2 posts
Joined 09/2012

Hey Wilt,lets assume that there are 9 combos that crush us and 9 combos which we are flipping against.
Our equity against crushing combos is 10% and vs flipping combos is 50%. So the our total equity is 50+10/2=30% right? Great series by the way.

And another question because my math sucks. Lets say that there are 12 crushing combos that gives us approximately 10% equity and 9 combos that gives us 50%. If we say that 9 combos out of 12 are 75% of the combos. Can we than not weigh the 9 combos with.75 and 12 combos with 1 to count our total equity? So: 50%X.75 = 37.5 and 10%X1= 10%. Than add the two numbers and divide by two? 47.5/2 = 23.75% equity

#### WiltOnTilt

2402 posts
Joined 10/2007

Hey Wilt,lets assume that there are 9 combos that crush us and 9 combos which we are flipping against.
Our equity against crushing combos is 10% and vs flipping combos is 50%. So the our total equity is 50+10/2=30% right? Great series by the way.

Right! Said another way, half the time we have 50% equity, the other half of the time we have 10% equity, so we can average them out to have 30% equity.

And another question because my math sucks. Lets say that there are 12 crushing combos that gives us approximately 10% equity and 9 combos that gives us 50%. If we say that 9 combos out of 12 are 75% of the combos. Can we than not weigh the 9 combos with.75 and 12 combos with 1 to count our total equity? So: 50%X.75 = 37.5 and 10%X1= 10%. Than add the two numbers and divide by two? 47.5/2 = 23.75% equity

I think the way to do it would be like this.

21 total combos, 9/21 give us 50% equity. 12/21 give us 10% equity.

(9/21 * .5) + (12/21 * .10) = .214 + .057 = .271 = about 27%

This way we are weighting each portion compared to the total and adding them together. I don't think you can do your method because you're saying 9 out of 12 but really it's 9 out of 21.

If you try this method with your first question, you'll see it works too... (9/18 * .5) + (9/18 * .10)

#### wego2valuetown

2 posts
Joined 09/2012

I get it, thanks for the reply

#### OranRai

59 posts
Joined 02/2010

Hi
Demonstration of alternate method :
our Equity = 1 - Villain's equity
Bet = Villain's bet = Our bet
Pot = flop pot + Bet /* pot after the villain's bet
Total pot = flop pot + villain's bet + our bet = flop pot + Bet + Bet = flop pot + 2*Bet
EV = our Equity * (flop pot + Bet) - Villain's Equity * Bet
EV = our Equity * (flop pot + Bet ) - (1-our equity)* Bet
EV = our Equity * (flop pot + Bet ) - Bet + our equity* Bet
EV = our Equity * (flop pot + Bet + Bet ) - Bet
Alternate method :

EV = our Equity * Total pot - Bet

regards

Alternate method looks easier and we have only one multiplication to make.

#### WiltOnTilt

2402 posts
Joined 10/2007

Good post, thanks

#### EnriqueP

3 posts
Joined 12/2012

thanks wilt, got it down to about 1/10 of a percent difference from the stove

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