# 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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#### demo79

108 posts
Joined 01/2008

Another great video Wot, it help me a lot with my thought process on the table.
I use something similar on these kind of situations (better than nothing i guess )but not as accurate as the real math, i list all of the possible hands in his range and see what hands im winning vs hands im losing or flipping and if hands i am winning are smaller number than the other side i would know im not getting even 30% percent equity (again this is mostly just based on feel and experience with pokerstove), but the way i do it doesnt account weighted possibilites of combos and the cards in my hand that block some of the villains out, and etc . Ill start using this method more and practice with it till i get a good feel of it.

Keep it coming.

Demo.

#### MickeyWins

1526 posts
Joined 07/2007

Wiltontilt....I wanna give this video like a 9!!! Its one of the best videos ever on DC.
granted it fits very well with were my NL game is, which is not that advanced.
however, I want to encourage all the admins making videos to use your "my thought process" example.
Getting a new poker tool(or in my case receipy for my cookbook) is great.
But you showing how this new tool fits into your decision, while perhaps seeming simple for you, is exactly what the student needs for a better understanding of the given principal.
I am hoping I can get DD or Entity and/or Danzasmack to do this "my thought process" kinda thing with hand/flop reading in limit. I will go post a request form them to watch or re-watch this technigue of yours.
ty so much....keep up the good work. I can't wait for the next one!

#### WiltOnTilt

2402 posts
Joined 10/2007

Thanks for the kind words guys :-)

#### tapped_out

52 posts
Joined 01/2008

This is some crazy stuff WOT...I'm trying to digest it right now but I really don't see how I could go through that process and come up with an estimation in the amount of time we have online.

The tupac method might work live though, I could simply pop in his CD and let the table know I'll be ready in about 2 songs...after I get done calculating of course

#### WiltOnTilt

2402 posts
Joined 10/2007

haha... yea man I understand the concern. Trust me, with practice you can get pretty good at it. Listen again to my "thought process" section at the end of the video. That thought process essentially follows TUPAC w/o explicitly saying "step 1", "step 2" etc.

You're right though, it would be tough to go through on a site that does not have the time-bank feature online. In a live game it should be doable. Hell everyone loves to pretend like they are on the WPT at the final table anyway, right? At least this will give you something to think about when everyone else assumes you're just "hollywooding" :-)

Good luck

363 posts
Joined 01/2008

<3 <3 <3

#### TheProdigy

23 posts
Joined 01/2008

I cannot find episode Three?

Edit: it just showed up when I did another filter? Some kind've bug or something because it wasn't on my filters at first(I just filtered videos for Mathematics, it wasn't there, then I took it off and filtered for Wilt videos and it didn't show up. Now it is there though)

#### theRabidDoG

53 posts
Joined 01/2008

ya this must be the best tip ive ever gotten in a poker video(!), and ive watched way over 100 vids on CR and deucescracked combined...

thx, cant w8 to watch the next one (and until i get better at estimating my eq quicker).

#### entelechy

1244 posts
Joined 02/2007

Really compelling, interesting stuff. Great videos, Aaron. I'm not a real math guy, so these have been very illuminating for me and very helpful to my thought processes at the table.

#### reMAX21

1 posts
Joined 02/2008

WOT, intense is an understatement. I think though that I came away an understanding of how an average math guy (myself) might be able to apply TUPAC. Please let me know if my simplification still works:

1) Using Pokerstove, memorize common post flop equities before playing (TP vs FD, TP vs OESD, OESD vs set). At least have them taped on your monitor or tattooed on your arm for live play.
2) Estimate (taking into account combos) the % of villain holding each range (50% he has FD, 25% he has set, 25% he has 2 pair)
3) Multiply equity by % of range for each range and add to get overall equity. (50% FD at 66% equity, 25% set at 2% equity, 25% 2 pair at 25% equity; when added together: .5*.66 + .25*.02 + .25*.25 which is 40% equity)

Am I using TUPAC right here? If so, I think that I could do this quickly after MUCH experience.

As an afterthought, I was laughing uncontrollably that 2 minutes prior to introducing TUPAC you were concerned that we would need to round 675 up to 700 and 325 down to 300 to add them up to get 1000. Steep learning curve in that 2 minutes.

Great video. That 45 minutes alone is worth an entire year subscription to DC!

#### WiltOnTilt

2402 posts
Joined 10/2007

remax, that's basically it!

We're essentially trying to determine his range, (step 1), group up all the different hand types and think about their equities (step 2), consider any outlier hands and their likely equity (step 3) then do a weighted average based on how 'likely' (ie how many combos) each grouping has... and there's your estimate.

It takes a lot of work, and isn't a trivial process, but with work and time in pokerstove you can get pretty good at it.

WoT

#### theRabidDoG

53 posts
Joined 01/2008

maybe im too tired and missing something here. either way its not that important i just wanna make sure im not misunderstanding something. u said there are 3 ways to make 2 pair with 98s Wilt but since the 9c and the 8d is out there 98cc and 98dd is not a part of his range, so there are actually only 2 combos of 98s (98hh 98ss) riiiiiight?

#### WiltOnTilt

2402 posts
Joined 10/2007

ya you're right, when i did that part i must have thought the board was Kd 9c 8c instead of Kc 9c 8d

Sorry about that. The oversight shouldn't change anything as far as the math/estimations go, but you're right that is a mistake. My apologies, and thanks for pointing that out.

WoT

#### shark_fishin

265 posts
Joined 03/2008

best vid iv ever seen(seen tons), thanks very much

#### chill

3 posts
Joined 04/2008

Great series WOT. Been stupidly playing for about a year without really emersing myself in the math behind the game. Now im learning from u, i feel ive been playing blind all this time. And although some of the theory is hard to get my head around, (not really a maths kinda guy), i see the huge importance of knowing these fundamentals of poker. Look forward to watching the rest of the series, many many thanks dude.

#### Ms.Bungle

823 posts
Joined 06/2008

This is THE video I have been looking for on Combinations for MONTHS!! Awesome. On my all time list of favourite videos...and I've watched quite a few videos!

I finally feel optimistic that I will be able to start moving my game to a next level, that I knew was out there, but felt I lacked the formal education, or that I was missing a few concepts to fully grasp. This video has given me my "missing links!" Thanks so much!!!!

#### c_hoop

3 posts
Joined 06/2008

wow what a great video. i'm embarrassed to admit but i've been playing poker for a living for over 2 years now and have been half-assing my way through equity calculations this whole time. this is the exact video i've been looking for, for some time now. thanks for taking the time WoT to make this series of videos. they aren't easy to get through but i can't wait to get to the next one. amazing

#### WiltOnTilt

2402 posts
Joined 10/2007

wow what a great video. i'm embarrassed to admit but i've been playing poker for a living for over 2 years now and have been half-assing my way through equity calculations this whole time. this is the exact video i've been looking for, for some time now. thanks for taking the time WoT to make this series of videos. they aren't easy to get through but i can't wait to get to the next one. amazing

Thanks man. Really appreciate the kind words.

Hope you "enjoy" (read: dont fall asleep) through the rest of the series

Aaron

#### jimike

8 posts
Joined 05/2008

Another good video.Loving this series.Put off learning the fundamental math for poker with stale equations for quite a while now.Overawed by it all,but the way you explain the concepts are much easier to absorb.Well done.

#### okepropertiesinc

6 posts
Joined 10/2008

im completely lost in this tupac method. So all we are doing is combining all the combinations of hands that could beat us, that we could beat decently, and those we're we are a slight favorite. We put them in 3 seperate categories and get the combinations. Combine the crushes us combos with the slight favorie combos and avg the equity from each bucket range out. Then we do that with the ones we are a decent favorite against. Now we combine all the equity calcs out for our total equity approx against that range? Is that all? if it is thats not hard at all. Maybe im making it harder then it seems. But what i dont understand is two things. Number one, the range we are using for opponent is it the potential draws on the board or a bayesian inference of the preflop holdings adjusted for card removel effects from the board and our the cards in our hand? And what are we doing with pokerstove? thats what im confused about most.

#### LowWaterMark

287 posts
Joined 01/2009

So I know if I'm getting the basics - the answer to your mini-homework assignment in the beginning of #4 (where you remove the three marginal hands from your opponent's range): is the EV = -\$200 or am I lost?

I have a procedural question. Would a valid derivative of your plan be to simply eliminate, pair for pair, a combo where you are crushed along with a combo where you crush. If I say "I crush" am I not stating:
(1 - equity of the villain)?
Given:
{[x + (1-x)]/2}=0.50
the equity of one or one thousand "I crush" averaged with the same number of "I'm crushed" is always 0.50 assuming equal crushing. If I have 50% equity than so must the villain. As such can't we ignore it?

I guessing you've thought of this as it would be easier but dispensed with it anyway, so I assume I'm wrong, but I don't see how.

Let's say my pair vs villain's range is:
I crush: 13 combos
I am crushed: 15 combos

Isn't there an equation that reduces from the above to:
I am crushed: 2 combos

#### WiltOnTilt

2402 posts
Joined 10/2007

you can't exactly ignore/reduce combo-for-combo crushing vs crushed combos because remember the weight of the 50% will also effect the overall equity. so think of it in the extreme.... say you had 1000 combos where we crush them and 1000 combos where they crush us, that will average out to 50% as you say, but we can't simply ignore it because then let's say we have 10 combos where we're slightly ahead at say 60/40 favorite... well those 10 combos at 60% will also average in to the other 2000 combos, but not so much that we can simply cancel out and ignore the other 2000 combos. In other words, if we do the averaging, the answer will still be close to 50% because of the sheer weight they hold with so many combos.

So you're right, the crushing and crushed combos will average out to 50%, and if there are only a few of those combos, you can sort of ignore them, but you can't completely ignore them as the number of crushing/crushed combos increases, the closer to 50% your overall equity will become.

I crush: 13 combos
I am crushed: 15 combos

you can't cancel out and ignore the 13 "i crush" and 13 of the 15 "i am crushed" combos as they will average out to 50%, and those 26 combos will pull up the equity of the 2 extra "i am crushed" combos and weight down the equity of the 2 "slight advantage me" combos.

Try it out in pokerstove real quick. Here's a super simple example:

Player 1: 9c9d
Player 2: 8c8d

Stove this and see 9c9d has 82.628% and 8c8d has 17.372%

Now what if we added canceling out combos of AJ and KJ suited?

Player 1: 9c9d,AhJh,KsJs
Player 2: 8c8d,AsJs,KhJh

Even though the 2 AJ and KJ combos of each player would be lumped in the buckets and seemingly "cancel out" in reality they don't as you can see by the new equities (try it out).

So what you've done is shown that TUPAC method isn't fool proof for every example (I believe I stated that in the vid, i hope so lol)... but the important thing is that IN PRACTICE, with many more combos, the inaccuracy we've shown here with very contrived examples doesn't tend to hurt you to this degree. Basically what happens is that the more combos you're canceling out (as a % of the total # of combos we're looking at) the more this inaccuracy will effect the estimate. That makes sense right? ... in the 99,AJ,KJ vs 88,AJ,KJ case we were looking at 2 combos out of 3 combos for each player that were being "canceled" and we noticed a dramatic effect. In the first example I gave with 2000 combos being canceled, that represented a high % of the total number of combos, and therefore a huge inaccuracy occurs. In practice, it tends to not be so dramatic (as shown in the vid).

I hope that makes sense.
WoT

846 posts
Joined 06/2008

Wow , no wonder you made it onto your local news station they must of seen this series hehe , this is awesome stuff , really opened my mind to how to go about thinkin of the game, i mean not only the math side but as a whole
id imagine mastering this side of the game alone would make someone a huge favourite at the table
i plan to work alot with the notes ive taken from this series , would it be possible for you to make a homework video where we can test ourselves ? maybe play a hand and tell us the information avalible then say pause the video , we work it out on paper and then you work it out so we can compair and find out where we mit be goin wrong ? id love to practise this stuff while also been shown if im thinking and goin about it in the right way , along with coming up with the right answers
Cheers

#### TheGeek

1478 posts
Joined 01/2009

I think there are a couple of slight mistakes towards the end of the TUPAC section of this video. First of all, the 98s hand is part of the "Crushing Us" section when we break up the hands in his range. Then when we analyse it later we put it in the same section as the JTs/67s and use it to average out the JTs combos. This confused me for a little bit as I was watching the video so I thought I would point it out.

Also, when we consider the 67s part of Villains range, it says on WoTs slide that 67 is about 1/6th of his range but then shows the hand combs as (3 combos of 67s / 13+9+3 of other combos). If I'm not mistaken or missing something that comes to 3 over 25 or roughly 1/8th. If we have 66% equity vs this 12.5% (1/8th) of his range, this would work out to be around 8% equity. This 8% when added to the 27% we got earlier from combing the crushing and flipping hands gives us 35% equity vs the entire range, which was the equity Pokerstove gave us. This little mistake makes our end answer a little less accurate. I hope I'm not wrong in pointing this out!

Thanks for doing this series Wilt, it's absolutely brilliant!

#### Kamisei

13 posts
Joined 07/2009

WoT, thanks for the great series.
I have a question though. At 18 minutes in this video thereÃ‚Â´s 700 in the pot in this example. LetÃ‚Â´s say for convenience that 350 of it is the playerÃ‚Â´s. With 290 expected to lose by playing, the result of calling is -EV you say.

But if you look at it long term, isn't folding even more -EV? Since you'll always be 'losing' the 350, even though it's not yours anymore. It still is if you look at it long-term?

So since losing 290 is less then 350, wouldn't it be better to call with this amount of money behind?

Another question: What if calling was -10\$ EV, would calling be a better option then since the 350 is in the pot already even though it's -EV?

#### WiltOnTilt

2402 posts
Joined 10/2007

WoT, thanks for the great series.
I have a question though. At 18 minutes in this video thereÃ‚Â´s 700 in the pot in this example. LetÃ‚Â´s say for convenience that 350 of it is the playerÃ‚Â´s. With 290 expected to lose by playing, the result of calling is -EV you say.

But if you look at it long term, isn't folding even more -EV? Since you'll always be 'losing' the 350, even though it's not yours anymore. It still is if you look at it long-term?

So since losing 290 is less then 350, wouldn't it be better to call with this amount of money behind?

Another question: What if calling was -10\$ EV, would calling be a better option then since the 350 is in the pot already even though it's -EV?

once the money is in the pot, it's already lost. i'm pretty sure it's faulty logic to look at folding as "losing" that money, because the calculation on the EV of putting that money into the pot should have already been considered. Once the action is made, the money is no longer yours, which is why we define folding as 0 ev. This is how Sklansky looks at it, so i'll default to him.

Thanks for watching
WoT

#### WiltOnTilt

2402 posts
Joined 10/2007

TheGeek, TUPAC method is a methodology of estimation. You're correct it's not perfect, but it will usually get us closer to the answer than just pure guessing, which is sort of the idea. It gives us an idea of how we can mentally analyze hand ranges and assign equity and weights to them, which is the key to mentally figuring out our equity when we're at the table and can't use pokerstove.

It's definitely an imperfect strategy, but it's close, and that's all we need is to be close when making table decisions because the tie breaker in closer decisions will be in game reads.

Thanks for the comment and thanks for watching!
WoT

#### TheGeek

1478 posts
Joined 01/2009

TheGeek, TUPAC method is a methodology of estimation. You're correct it's not perfect, but it will usually get us closer to the answer than just pure guessing, which is sort of the idea. It gives us an idea of how we can mentally analyze hand ranges and assign equity and weights to them, which is the key to mentally figuring out our equity when we're at the table and can't use pokerstove.

It's definitely an imperfect strategy, but it's close, and that's all we need is to be close when making table decisions because the tie breaker in closer decisions will be in game reads.

Thanks for the comment and thanks for watching!
WoT

No, I understand that. I don't think I explained myself clearly enough.

If you look at the slide at about 39 minutes into the video, I think there's a mistake with the hand combos that you use in the TUPAC method. The slide says "Our 3 unaccounted hands make up about 1/6th of our range: 3/(13+9+3)" But 3/25 is about 1/8th not 1/6th as it says in the slide, which makes the end estimate a little less accurate than it could be. When we use the correct figures in the TUPAC method for this hand it turns out to be very, very accurate. It's only a little nitpicky mistake but I wanted to point it out because a) I want to make sure I'm right and aren't missing something obvious and b) You're selling your awesome TUPAC method a little short by having a little error throw off it's accuracy!

The TUPAC method, and this series are absolutely fantastic, thanks so much for doing it!

#### WiltOnTilt

2402 posts
Joined 10/2007

Ahh I see what you mean. Thanks for pointing that out.

#### tmmoss

48 posts
Joined 05/2009

WiltOnTilt -

Just finished episode 5. I am new to the forums and fairly new to the game. Thanks for the detailed breakdowns - as I was listening to the method, it brought to mind the old "cancelling method" we used to reduce fractions when I was a kid. No jokes about my age showing! Thanks for vids. Very good.

#### PygmyHero

4246 posts
Joined 08/2007

Homework: ~ negative \$200

#### st3v3k4hn

3 posts
Joined 01/2010

Great series. Trying to get a handle on Tupac but my first thought was that I would put my opponent on a very different range so the resulting equity and EV calcs would also be very different. I am playing very low stakes NL (6-max) and at this level I would never leave AA or KK or AK in his range (he would 4-bet those preflop). And, if he is frustrated (as you said) I would include all pairs in his range preflop and include TT, JJ & QQ in his pushing range on the flop. That small change is enough to make this a positive equity situation against his range (mostly due to the 18 combinations of QQ, JJ & TT with which he might push). So I guess my point here is I would like to see more info about putting someone on a range of hands and how that varies by stakes. Maybe I am crazy thinking that a TAG would push TT here - but I see it every day at the stakes I am playing... Anyway, this video is pretty old so probably no one will even read this. But Wilt if you do read it thanks and keep up the good work...

#### killer108

258 posts
Joined 03/2010

very nice video, but when i am playing on 4/6 tables, very dificult to do that...BUT I THINK CAN GET EXPERIENCE IN THAT CASE
but i thnk to see whole serie 4-5 times to understand better, but i also think the most player go not calculate that, because he also can makes bluf , when somebody shoove me and i have one pair only with straight and flushdraw on the board i will fold without thinking is that wrong?

because i am beat lot of times i guess

#### Bean Box

75 posts
Joined 03/2010

Any MAC equivalents to pokerstove?

#### Dr. Loiselle

10 posts
Joined 03/2010

Homework: ~ negative \$200

Homework assignment: [24m34s]

our equity = 26%
total pot = \$2015
cost of call = \$675

[.26 * 2015] - 675 = negative \$151

LowWaterMark and PygmyHero say negative \$200
What did I do wrong?

#### briocheMC

1 posts
Joined 07/2010

Isn't there a mistake ? 3 ways of making 2 pairs with 89s when the flop has got Kc9c8d ? I'd say only hearts and diamonds left for that... So that's 2 ways.

#### Entity

8045 posts
Joined 11/2006

Isn't there a mistake ? 3 ways of making 2 pairs with 89s when the flop has got Kc9c8d ? I'd say only hearts and diamonds left for that... So that's 2 ways.

Yeah, you're definitely right there, nice catch.

Rob

#### DOMSTER

42 posts
Joined 02/2010

Poker at its best - the RE of R.E.M. broken down in its essentials. Havent seen a better piece of work on hand ranges and equity than that.

Great Job Aron

#### kgbmiked

192 posts
Joined 11/2010

Here are my notes on this episode, I tried to correct everything that was wrong in the video and be more accurate with my rounding. thanks WoT, best series ever. If anyone see's any errors feel free to correct me.

Notes on Mathematics of NL HoldÃ¢â‚¬â„¢em episode4 by WiltonTilt
By KGBMIKED

Video # 4 is all about EV Calculations.

Basic EV calculation setup:

EV = (Result of win) Ã¢â‚¬â€œ (Result of loss)

EV=(Our Equity) * (What we win) Ã¢â‚¬â€œ (VillainÃ¢â‚¬â„¢s Equity) * (What we lose).

Basic Example:

WeÃ¢â‚¬â„¢re in the big blind with AsAc. The UTG player shoves with KhKd and folds to you. ItÃ¢â‚¬â„¢s \$900 to call to win 1015 (stack+blinds) 5/10, \$1000 stacks

Ev = (our Equity) * (What we win) Ã¢â‚¬â€œ VillainÃ¢â‚¬â„¢s equity) * (What we lose)

Ev = .81*1015 - .19 * 990

Ev = 822.15 Ã¢â‚¬â€œ 188.1

Ev = +634.05

Thus, every time this situation occurs we expect to profit \$634.05

ALTERNATE METHOD

Ev = (Our Equity) * (Total pot) Ã¢â‚¬â€œ cost of our call
Ev = (.81) * 2005 -990
Ev 634.05

Both methods work, choose the one that seems to make the most sense to you. He prefers the first method because he thinks itÃ¢â‚¬â„¢s easier to build on, but itÃ¢â‚¬â„¢s essentially the same thing just a different way of thinking.

EV Calcs Vs Hand Ranges:

We have KsQc We have 3 bet this guy a lot, we are in position we 3 bet pf again he calls.
AK is not in his range because he would have 4bet. He checks the flop We bet 200 he jams for 875. There is 265 in the pot. The board is Kc9c8d
We assume he is check jamming here with at least 8 outs.

His range is KK+; 99,88, AcQc, AcJc , AcTc, Ac8c, QcJc,JcTc, 98s, 7c8c, JTs, 67s

.35(1075+265) - .65(675) = +30.25

#4 has how to do Tupac method at the table

This is not in the video but very valuable math.

One concern for me in NL HÃ¢â‚¬â„¢E math is that most people finding Equity do it through poker stove which gives you your equity for seeing all 5 cards. This article can help you find your equity PFR to Flop and then you can recalculate for turn and river. I think knowing your equity based on the 3 flop cards and not just all 5 cards is one of the most under rated math concepts in poker.
Chance Of Overcards Hitting
Question: dear poker master,
i've been thinking a lot about this situation as it pertains to tourneys. what are the odds for the overcards hitting again? and how do you figure them out before the flop. i know that there is a 6 out of 47 and 6 out of 46 percent chance of hitting on the turn and river but how do you calculate for all three cards of the flrop?
thanks
andrew
Answer: To calculate the odds of hitting them on the flop you use a similar equation like you do for the turn and river. Let's do an example with KQ. You have 2 cards in your hand and that leaves 50 unseen cards for the first flop card. You have 6 outs for the flop cards (3 Kings and 3 queens). The next card you have the same 6 outs but this time only out of 49 cards. The last flop card gives us 6 outs out of 48. That looks like this:
6/50 6/49 6/48
Here is the tricky part. Whenever you have a situation when an event, hitting your card, can happen on more then one chance you figure out the odds of it NOT hitting and then subract it by one.
1 - [ ((Cards - Outs) / Cards) * ((Cards - Outs) / Cards) ... ]
Let's try that with our numbers:
1 - [(44/50) * (43/49) * (42/48)]
1 - [.88 * .8775 * .875]
1 - [.675] ----- this basically shows there's a 68% chance of us NOT getting our cards.
32% ---- this means that there is a 32% chance we WILL get our cards.
That seems like a high percentage until you think of it compared to the flush draw which seems like it never gets there. If you want to figure out how often AK will hit by the river then just add the turn and river cards to the equation:
6/50 6/49 6/48 6/47 6/46
Flip these again to cards that won't help us:
44/50 * 43/49 * 42/48 * 41/47 * 40/46
.88 * .8775 * .875 * .872 * .869
= 51% of the time it not getting there.
= 49% of the time it will hit by the river.

#### Bonobo11

4 posts
Joined 03/2011

Here are my notes on this episode, I tried to correct everything that was wrong in the video and be more accurate with my rounding. thanks WoT, best series ever. If anyone see's any errors feel free to correct me.

Notes on Mathematics of NL HoldÃ¢â‚¬â„¢em episode4 by WiltonTilt
By KGBMIKED

this post is Winning!

#### Rodney Mullen

6 posts
Joined 04/2011

The matching up of combos was pretty confusing to me. Wouldn't this be an easier way to estimate?

13 combos of hands that crush us
9 combos of flips
6 combos of hands we are favorites over

drop all 9 flips
13 losses : 6 wins (round it down to 12:6, reduce to get 2:1)
So we are a 2:1 dog

Does this just work in this example? And if it doesn't maybe you have come up with an easier way of matching combos in the last 3 years?

#### WiltOnTilt

2402 posts
Joined 10/2007

You can't exactly drop the 50/50 combos because they do hold weight. Think of an extreme example. 100 flip combos. 2 big favorites. 1 big dog. Overall this would still end up
being a "flip" in terms of us estimating, not 2:1 favorite.

#### brainfreeze0

68 posts
Joined 05/2011

you can't exactly ignore/reduce combo-for-combo crushing vs crushed combos because remember the weight of the 50% will also effect the overall equity. so think of it in the extreme.... say you had 1000 combos where we crush them and 1000 combos where they crush us, that will average out to 50% as you say, but we can't simply ignore it because then let's say we have 10 combos where we're slightly ahead at say 60/40 favorite... well those 10 combos at 60% will also average in to the other 2000 combos, but not so much that we can simply cancel out and ignore the other 2000 combos. In other words, if we do the averaging, the answer will still be close to 50% because of the sheer weight they hold with so many combos.

So you're right, the crushing and crushed combos will average out to 50%, and if there are only a few of those combos, you can sort of ignore them, but you can't completely ignore them as the number of crushing/crushed combos increases, the closer to 50% your overall equity will become.

This will probably sound like a dumb comparison but your explanation reminds me a lot of it. At my job (10 hour work day) our positions are all computer calculated with random job assignments where X amount of time is assigned to complete these task. If we are assigned 1 hour to do the assignment and we do it in an hour we are at 100%. If I do it in an hour and 10 min I'm at like a 90%. So if I'm at a 90% for that hour assignment and the next one I get is only 10 minutes and I do it in 5 minutes I'd get 200%, but since it was such a short assignment combined with my former hour long assignment I'll only go up to around 100%.Similarly if I'm 9 hours into my day with an 85% (that's 9 hours strong) and I get an hour long assignment and do it in 35 minutes and get like 175% it only raises me up to like 89%. Hope that made sense.

Guess I've been doing this job so long your explanation makes complete sense to me.

#### WiltOnTilt

2402 posts
Joined 10/2007

This will probably sound like a dumb comparison but your explanation reminds me a lot of it. At my job (10 hour work day) our positions are all computer calculated with random job assignments where X amount of time is assigned to complete these task. If we are assigned 1 hour to do the assignment and we do it in an hour we are at 100%. If I do it in an hour and 10 min I'm at like a 90%. So if I'm at a 90% for that hour assignment and the next one I get is only 10 minutes and I do it in 5 minutes I'd get 200%, but since it was such a short assignment combined with my former hour long assignment I'll only go up to around 100%.Similarly if I'm 9 hours into my day with an 85% (that's 9 hours strong) and I get an hour long assignment and do it in 35 minutes and get like 175% it only raises me up to like 89%. Hope that made sense.

Guess I've been doing this job so long your explanation makes complete sense to me.

yup thats the exact type of thing that is going on here.

#### onehundred47

400 posts
Joined 10/2009

here you say that there are 3 unaccounted hands make up to 1/6 of our range: 3/ (13+9+3).

But our range is 6-AA; 1-KK; 3-88; 3-99; 2-98s ; 9-clubhands; 3-67s; 3-JTs =6+1+3+3+2+9+3+3=30

so isn't it 3/30 = 1/10 ?

#### DJSirMatthew

1 posts
Joined 09/2009

here you say that there are 3 unaccounted hands make up to 1/6 of our range: 3/ (13+9+3).

But our range is 6-AA; 1-KK; 3-88; 3-99; 2-98s ; 9-clubhands; 3-67s; 3-JTs =6+1+3+3+2+9+3+3=30

so isn't it 3/30 = 1/10 ?

You're right in my opinion. Even further so, if we take the 27% from step 2, add 6.6% from step 3 (1/10th of range with 66% equity vs that range 76s) we get 33.6%. Add 1 to 2 points for the JTs averaging out the 98s hands (more like 2 points since in reality there are only 2 combos of 98s and not 3 which gives 1 extra combo in his range of JTs where we are 3:1 fav against) we end up with a result of 35,6% which is indeed very close to the mathematical calculation.

Bottom line: TUPAC gives a nice estimation but being able to do it at the table is very hard to do and errors seem to slip in easily seeing that an "expert" as WiltOnTilt mades some mistakes here. But all we need is to get to the thought process explained at the end which leads to the real conclusion.

#### Pinko Panther

371 posts
Joined 04/2011

Edit: nevermind, i'm retarded lol.

Great series!

#### Prologion

2079 posts
Joined 03/2010

Great episode^^
The Tipac-Method is rly nice:

Only one thing:
@ Min. 38.30, you are saying that the 3 uncounted combos (76s) are making ~1/6th of Villain`s range:
3/(13+9+3) - wouldn`t it be actually ~1/8th?

edit: Wouldn`t it be actually even only 1/10th?
B/c to stiamte how large of a part the 3 combos are of his whole range, you actually also should include them into his range ? -> 3 : (13+9+3+3)

#### Jonnolimit

29 posts
Joined 07/2011

a bit less than 4:1 on our money? Isn t it suppose to be around 4.7:1 since 52 cards - 6 = 46 which 8 makes you win and 38 lose 38:8 or 4.7:1

#### 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

162 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

196 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

#### akramak

13 posts
Joined 01/2013

I agree 100% that folding is 0 EV, but money saved is money earned which makes it +EV. Just a different way to look at it

#### akramak

13 posts
Joined 01/2013

Shouldnt it be 2 ways to make 98s, board has 9c and 8d so 9c8c and 9d8d is out of villians range leaving only 9h8h and 9s8s.

#### WiltOnTilt

2402 posts
Joined 10/2007

Shouldnt it be 2 ways to make 98s, board has 9c and 8d so 9c8c and 9d8d is out of villians range leaving only 9h8h and 9s8s.

yes you are right. There are a few of these types of mistakes sprinkled out throughout these vids (which i apologize for) but usually it doesn't change the outcome or the actual mechanical process of finding the answer.

Good catch!

#### Carolingian

5 posts
Joined 05/2013

Did you forget to also calculate the 98s? Or am I just missing something?

#### WiltOnTilt

2402 posts
Joined 10/2007

Did you forget to also calculate the 98s? Or am I just missing something?

there are a few oversights like this in the series, sorry about that

If you find something that looks weird, you might just pause and check the thread as someone else probably noticed it too in the past 5 years. (wow... hard to believe it's been 5 years!)

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