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

Mathematics of NL Hold'em: Episode Three

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Mathematics of NL Hold'em: Episode Three by WiltOnTilt

This episode of Mathematics of No Limit Holdem again addresses Pot odds and Implied Odds, and this time introduces Reverse Implied Odds. These concepts are illustrated using hand examples examining preflop, flop and turn play. This video also gives an overview of some valuable software to help determine our pot equity - twodimes.net and pokerstove - and finishes off with some mental shortcuts to help you figure out math at the table.

About Mathematics of NL Hold'em Subscribe to

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.

Tags

aaron wilt wiltontilt math nl hold'em math equity pot equity pot odds math tools poker software ipod friendly

Video Details

  • Game: nlhe
  • Stakes: Micro/Small Stakes
  • 68 minutes long
  • Posted about 4 years ago

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Comments for Mathematics of NL Hold'em: Episode Three

Partytime11

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23 posts
Joined 01/2008

This series needs more love imo. My only complaint besides the pages on pages of notes I wrote down is the fact that this wasn't done before I read NLHE:TAP about 800 times and some things still don't make sense lol. Thank you for doing this.

Posted about 4 years ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Hi partytime, thanks for the comments. Hopefully after you watch my videos some of those concepts in NLHE:TAP will make some more sense. If not, please be sure to post any questions in these threads if I'm not explaining something well enough in the video.

Regards,
WoT

Posted about 4 years ago

HaiaN

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79 posts
Joined 01/2008

fizzleboink

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22 posts
Joined 01/2008

I really liked the example with the reverse implied odds. I aways struggle on how best to take that into account.

Posted about 4 years ago

Sugar Nut

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859 posts
Joined 03/2008

This is my first post here on DC and I guess you and this wonderful series deserve it. Thanks for this, I'm learning/refreshing/getting misunderstod concepts corrected a lot.

One thing just caught my eye though:

In the multiway pot example (we have TSpade9spade: in the BB on a ten handed table) where you threw us a "curveball".

First I can proudly say that I got it once you said that there are 36 ways to make overpairs that this cannot be true as we are holding a T and a 9.

So now there's only 30 ways he can make an overpair and 16 ways he can have AK, meaning he will raise 30 out of 46 times as you explain.

However I think it is even slightly worse for us as there is one AK combo (Aspade:KspadeSmile which he will most likely raise aswell making the hands he reises 31.

Alright, I might be nitpicking here and by no means am I critisizing your work. Like I said: great series!!

just caught my eye.

Sugar Nut

Posted almost 4 years ago

SixgunSam

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2 posts
Joined 03/2008

I understood the basics of poker math before, but not as clearly or completely as I do after watching this series. Now I feel confident in my hand analysis where prior to this series it was a struggle for me to "do the math" and feel certain I hadn't made a mistake. Great Video, Wilt! It has inspired me to go back and re-read NL:TAP and ToP armed with my clearer understanding of the concepts.

Posted almost 4 years ago

Gotcha

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9 posts
Joined 03/2008

Great series, this is stuff I kinda knew but now I know it properly.

I don't have the "winning %" button on PT though? I have a check box "Win %" and if I check it, it displays the % chance of winning underneath the players' names.

Posted almost 4 years ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Gotcha, it's possible you have a different version of PT than i had when making the video series. Either way as long as you can get a hold of he win % that's the important thing.

WoT

Posted almost 4 years ago

shipitldo

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2 posts
Joined 03/2008

For these Math-oriented series', which are basically lecture-style with power-point slides, would it be possible to upload files other than video? Powerpoint, .txt, etc? To go along with the video, not replace it. Thanks.

Posted almost 4 years ago

froggy

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1 posts
Joined 03/2008

For these Math-oriented series', which are basically lecture-style with power-point slides, would it be possible to upload files other than video? Powerpoint, .txt, etc? To go along with the video, not replace it. Thanks.

Posted almost 4 years ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Covered this in a few other threads, but there's no plan to release the powerpoint file I used to make the series. Sorry guys.

WoT

Posted almost 4 years ago

omaha

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61 posts
Joined 03/2008

Covered this in a few other threads, but there's no plan to release the powerpoint file I used to make the series. Sorry guys.

WoT



Bugger. I was hoping that the WoTs answer would be the opposite for us ducklings!

Omaha

Posted almost 4 years ago

Agentus

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3 posts
Joined 02/2008

The Reverse Impled Odds calculation is incorrect. It should be
EV(TT-AA)=(1/2*[-279.23]-61.13+86.59+86.59+86.59)/4.5

or

EV(TT-AA)=(3*[-279.23]+6*[-61.13]+18*86.59)/27

which is about EV(TT-AA)=13.12

Posted over 3 years ago

EpErOn

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134 posts
Joined 08/2008

The Reverse Impled Odds calculation is incorrect. It should be
EV(TT-AA)=(1/2*[-279.23]-61.13+86.59+86.59+86.59)/4.5

or

EV(TT-AA)=(3*[-279.23]+6*[-61.13]+18*86.59)/27

which is about EV(TT-AA)=13.12



good point!

what i am struggeling with:
on the flop you calculate with the *8 rule (2 streets). However, that assumes that you are gonna call the turn as well. You can often expect villain to bet on the turn as well. Lets say 50% of the time. Shouldn't you then use a *6 rule instead of *8 for calculating if you want to continue on the flop with a draw?

Posted over 3 years ago

BigEd157

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20 posts
Joined 10/2008

i feel like im in a college physics lecture. i dont know maybe its me but i immediately get sleepy within 3 minutes no make that 2 minutes.this is extrememly dry material which i think could use some simplification into lay mans terms . i think its to "mathy". i know u put a lot of work into it and i like the series but i cant stay awake why listening to it. thank u though i just am trying to be constructive, have u seen some of royalflush clubs videos. they keep it simple . they probably dont make as much cash as u guys at the tables but they keep it simple. and i find it to be pretty easy viewing. thye basically tell u your pant and hand odds and why they r playing the hand. thats it.
ed
didnt mean to sound ungrateful. i have an engineering degree and cant fathom the interest to follow along

Posted over 3 years ago

Entity

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Founder
7149 posts
Joined 11/2006

If you can't follow along with it, it may not be the series for you (it's already complete and was recorded in our first season). MoNLH is one of the more popular series we have on DeucesCracked but is generally considered to a series that you get back what you put in -- it's not for everyone. Basically -- it's definitely dense, definitely dry, but will definitely pay off if you work your way through it.

All that said, you may want to check out some more live play and more basic videos if you felt it was too mathy, given that the title really says it all here. Smile

Rob

Posted over 3 years ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Hi Ed, Thanks for the feedback.

If you found episodes 1-3 too complex, you'll definitely want to steer clear of episodes 4-8 as the intensity level raises a few notches.

WoT

Posted over 3 years ago

Tomtah

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5 posts
Joined 10/2008

Loved the 5,5 hand. Before I was 3-betting that hand more randomly but now I got a good foundation to understand when it's correct to 3-bet and when it's correct to call.

Posted about 3 years ago

crossboyke

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3 posts
Joined 02/2009

The Reverse Impled Odds calculation is incorrect. It should be
EV(TT-AA)=(1/2*[-279.23]-61.13+86.59+86.59+86.59)/4.5

or

EV(TT-AA)=(3*[-279.23]+6*[-61.13]+18*86.59)/27

which is about EV(TT-AA)=13.12



This makes kinda sense. Anyone can approve this?
Especially your second explanation makes me think this should be right, but I'm not sure and I don't want to start off with the wrong theory.

Thx in advance

Posted almost 3 years ago

ExaMeter

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1 posts
Joined 08/2009

This makes kinda sense. Anyone can approve this?
Especially your second explanation makes me think this should be right, but I'm not sure and I don't want to start off with the wrong theory.

Thx in advance



i just started watching the series and came here to post about this very mistake but agentus beat me to it.

agentus way using the combos leaves no room for mistakes like this (which can easily occur and im not bling WoT).
one could also go by the fractions using EV(TT-AA)=(1*[-279.23]+2*[-61.13]+6*86.59)/9 since TT is 1/9th of villains range, JJ is 2/9th and QQ+ is 6/9th, but thats pretty much the same thing as the combomethod.

Posted over 2 years ago

TecmoSuperBowl

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4875 posts
Joined 01/2009

Time Link to 01:06:06

I realize no one is ever going to check this thread, but I'm just now watching this series and I'm throwing out my equation and guess as for the final example.

The equation I used was -220 = .46x - .54x

x being his bet. 46% of the time we win what he bets, then 54% we lose so we have to figure out for what X makes the equation equal 220.

.46 - .54 = -.08

-220 = -.08x

220/.08 = 2750

If he bets more than 2750, we will be making less than the dead money in the pot offers us in the long run.

Now I'm going to watch the next eps to see if I'm right lol.

Posted over 2 years ago

PygmyHero

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4276 posts
Joined 08/2007

Hi Tecmo,

Your setup is incorrect because it doesn't account for us winning the $220 already in the pot when we make the best hand. I set the problem up as:

0 = 0.54 * (-x) + 0.46 * (220 + x)

Where 0 is the breakeven point (our EV is 0)
0.54 is the chance we lose
x is villain's bet size (note that we lose it 54% of the time so the first one is negative)
0.46 is the chance we win
220 is the money already in the pot

Solving the equation:

0 = -0.54x + 101.2 + 0.46x
0 = -0.08x + 101.2
0.08x = 101.2
x = 1265

We can also check this. Let's assume villain bets 1265.

54% of the time we lose our 1265 call
0.54 * (-1265) ~ -683.10 (N.B. NEGATIVE 683.10)

46% of the time we win villain's 1265 bet plus the 220 already in the pot
0.46 * (1265 + 220) ~ 683.10

So calling here when villain bets 1265 is neutral EV.

Posted about 2 years ago

PygmyHero

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4276 posts
Joined 08/2007

Time Link to 00:56:35

FWIW I think you made this problem WAY too hard.

We have to call 365, which I will define as one unit.

There is 725 in the pot, which is conveniently approximately two units (365*2 = 730).

Therefore when the action is on use there are ~3 units in the pot (the two already in there and the villain's bet). Again, we are looking at calling one unit (because of the way I set the problem up), so it's easy to see we're getting ~3:1 here.

I realize your point was to explore easy mental math tricks for approximating these types of situations, and I'm fine with the methods you used in general. But I also think it's important to recognize situations where we can use an even easier method.

Posted about 2 years ago

TecmoSuperBowl

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4875 posts
Joined 01/2009

Hi Tecmo,

Your setup is incorrect because it doesn't account for us winning the $220 already in the pot when we make the best hand. I set the problem up as:

0 = 0.54 * (-x) + 0.46 * (220 + x)

Where 0 is the breakeven point (our EV is 0)
0.54 is the chance we lose
x is villain's bet size (note that we lose it 54% of the time so the first one is negative)
0.46 is the chance we win
220 is the money already in the pot

Solving the equation:

0 = -0.54x + 101.2 + 0.46x
0 = -0.08x + 101.2
0.08x = 101.2
x = 1265

We can also check this. Let's assume villain bets 1265.

54% of the time we lose our 1265 call
0.54 * (-1265) ~ -683.10 (N.B. NEGATIVE 683.10)

46% of the time we win villain's 1265 bet plus the 220 already in the pot
0.46 * (1265 + 220) ~ 683.10

So calling here when villain bets 1265 is neutral EV.



Thanks for the help Pygmy. Will have to rewatch this later just to drill it into my head.

Posted about 2 years ago

TecmoSuperBowl

Avatar for TecmoSuperBowl

4875 posts
Joined 01/2009

Hi Tecmo,

Your setup is incorrect because it doesn't account for us winning the $220 already in the pot when we make the best hand. I set the problem up as:

0 = 0.54 * (-x) + 0.46 * (220 + x)

Where 0 is the breakeven point (our EV is 0)
0.54 is the chance we lose
x is villain's bet size (note that we lose it 54% of the time so the first one is negative)
0.46 is the chance we win
220 is the money already in the pot

Solving the equation:

0 = -0.54x + 101.2 + 0.46x
0 = -0.08x + 101.2
0.08x = 101.2
x = 1265

We can also check this. Let's assume villain bets 1265.

54% of the time we lose our 1265 call
0.54 * (-1265) ~ -683.10 (N.B. NEGATIVE 683.10)

46% of the time we win villain's 1265 bet plus the 220 already in the pot
0.46 * (1265 + 220) ~ 683.10

So calling here when villain bets 1265 is neutral EV.



y = money already in pot.

Ok, so my equation was 0 = y + .46x - .54x.

Your equation was 0 = (y + x).46 - .54x.

I was close! In my equation, I am adding y as if we win that amount no matter what happens (win or lose). In your equation, it accounts for the fact that we only win y 46% of the time (when we win). That makes sense now. Is this correct?

Posted about 2 years ago

PygmyHero

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4276 posts
Joined 08/2007

I was close! In my equation, I am adding y as if we win that amount no matter what happens (win or lose). In your equation, it accounts for the fact that we only win y 46% of the time (when we win). That makes sense now. Is this correct?


Yeah, that's right. Basically I think of your equation as:

0 = 100% * 220 + 46% * x - 54% * x

In that setup we win the money in the pot 100% of the time.

Posted about 2 years ago

Texas Donald

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7 posts
Joined 09/2009

HI WOT,

been working through this series really like it, however when looking at reverse implied odds on the hand where we have the OESD on x4T 4 facing a turn bet, you have done some calculations and in each one you say we are 18.2% to hit our OESD, but on your chart in episode one it said 8 outs on the turn is 17.4% to hit?

also when we have just 4 clean outs to the straight you say we are 9.1% to hit our hand, yet in week 1 you said 4 outs has an 8.7% chance hit by the turn?

Is there something I am missing or doing wrong?

thanks

Posted about 2 years ago

Rockhoe14er

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349 posts
Joined 12/2009

FWIW I think you made this problem WAY too hard.

We have to call 365, which I will define as one unit.

There is 725 in the pot, which is conveniently approximately two units (365*2 = 730).

Therefore when the action is on use there are ~3 units in the pot (the two already in there and the villain's bet). Again, we are looking at calling one unit (because of the way I set the problem up), so it's easy to see we're getting ~3:1 here.

I realize your point was to explore easy mental math tricks for approximating these types of situations, and I'm fine with the methods you used in general. But I also think it's important to recognize situations where we can use an even easier method.



wow this is an awesome trick and makes it much easier to calculate the math. Thanks, a lot pygmy

Posted almost 2 years ago

MayContainNuts

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235 posts
Joined 03/2010

Texas Donald,
Stuggled with this a bit too - you've probably now worked this out but for anyone else who gets stuck - it's because he's counting the two cards the opponent has as 'seen'.

So there are 52 in the deck, we've seen our 2 hole cards, 4 on the board and the opponent's 2 (say QQ).

52-8 = 44.

There are 8 cards which will help our hand (8 to make the OESD)and 36 unseen that won't. So 36/8, which means we're 4.5:1 to improve.

Convert to percentage: 1/5.5 = 0.181818181 or 18.2%.

Without knowing (or estimating) the opponent's holding, it's 17.4%.

Think this is right but then again I couldn't convert a ratio to percentage or back before I started this series yesterday, so it could be nonsense Smile

Thanks Wilt btw - it's brilliant and fascinating.

Posted almost 2 years ago

crypkilla@gmail.com

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2 posts
Joined 05/2010

maybe im confused but...
i downloaded all the videos for this series in regular and ipod versions.
in other series the ipod versions are smaller in file size than their corresponding regular versions (this makes sense.)

In this series all of my ipod versions are BIGGER that the regular versions. I double checked that i didnt mix them up. sure enough the ipod versions are of lower resolution/quality whatever but they're still bigger than the regular versions. did someone encode them wrong or something?

Posted over 1 year ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

maybe im confused but...
i downloaded all the videos for this series in regular and ipod versions.
in other series the ipod versions are smaller in file size than their corresponding regular versions (this makes sense.)

In this series all of my ipod versions are BIGGER that the regular versions. I double checked that i didnt mix them up. sure enough the ipod versions are of lower resolution/quality whatever but they're still bigger than the regular versions. did someone encode them wrong or something?



might want to email support about this... i dont think others have had this problem but I'm not sure on the tech aspects of this stuff.

Posted over 1 year ago

RiverdogAVFC

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7 posts
Joined 09/2010

Time Link to 01:01:57

I'm way too bad at remembering math calculations WoT.Information exits my head quicker than it enters it.So please believe me WoT when i say this has been the easiest way EVER to make sure it stays in my head & for that i'm eternally grateful!! Smile

Posted over 1 year ago

johnyraku

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2 posts
Joined 01/2011

according to 1:06

hey, I made this stuff:

1.
x-the unkown size bet
P-pot not including the bet
Eq- equity in % (%chance to win)

x=Eq*P/(1-2Eq)


2.
Same but in ratio data:
x- the unkown size bet we are looking for
P-pot not including the bet
F- (F:1 Under DOG, so if we are 3:1 dog, F=3)

x=P/(F-1)

Seems ok but good if some1 would recheck it if its all right.

great videos WiltOnTilt, really enjoying them Smile
cheers

Posted about 1 year ago

Hyronimous

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15 posts
Joined 04/2010

great series,

really a session that makes you work, but it's worth it.

Posted 12 months ago

Tiazas

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1 posts
Joined 03/2011



1.
x-the unkown size bet
P-pot not including the bet
Eq- equity in % (%chance to win)

x=Eq*P/(1-2Eq)



johnyraku, I checked your solution and it is correct.
Here's how i did it:

Eq * (P+x) = (1-Eq) * x => Eq*P + Eq*x = x - Eq*x => Eq*P = x - Eq*x - Eq*x => Eq*P = x * (1-2Eq)
x = Eq*P / (1 - 2Eq)


Great series WoT

Posted 11 months ago

bhall2323

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1 posts
Joined 01/2009

Time Link to 00:29:11

Your reasoning to fold here is very thorough, what i don't quite get is why you would even call in the first place given your not likely to flop a better hand with 10 9s than a flush draw. Is it because the villian UTG you described is raising here and some others would just flat SB's lead?

Posted 9 months ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Your reasoning to fold here is very thorough, what i don't quite get is why you would even call in the first place given your not likely to flop a better hand with 10 9s than a flush draw. Is it because the villian UTG you described is raising here and some others would just flat SB's lead?



I wouldn't expect the small blind to lead into the field all that often.

If we thought that UTG wasn't going to play overpairs fast here, I would likely call the flop lead. Given the read of this guy fast playing overpairs, our pot odds are hurt.

Posted 9 months ago

odahikaru1

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10 posts
Joined 02/2011

I have a question for Wilt, or anyone who can answer me otherwise. When he is doing the EV calc for reverse implied odds when opponent has pocket JJ (at about 15m49sec), he mentions that 9.1% of the time (on turn) we will hit one of our four dity outs and get stacked ( easy to understand). HOWEVER, in the next part of the equation he says that 4.5 % of the time we will hit one of our good outs and win his stack... my question is....

if in an 8 out draw 4 of our outs being bad gives us 9.2 % chance... why would the other 4 good outs not also give us a 9.2 % chance to hit our good outs...

Was this just a mistake or am I seeing things wrong. seems like both ends of the draw should have the same % chance of occurrence.


Thanks!

Posted 8 months ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

I have a question for Wilt, or anyone who can answer me otherwise. When he is doing the EV calc for reverse implied odds when opponent has pocket JJ (at about 15m49sec), he mentions that 9.1% of the time (on turn) we will hit one of our four dity outs and get stacked ( easy to understand). HOWEVER, in the next part of the equation he says that 4.5 % of the time we will hit one of our good outs and win his stack... my question is....

if in an 8 out draw 4 of our outs being bad gives us 9.2 % chance... why would the other 4 good outs not also give us a 9.2 % chance to hit our good outs...

Was this just a mistake or am I seeing things wrong. seems like both ends of the draw should have the same % chance of occurrence.


Thanks!



there are only 2 jacks left in the deck yet there are 4 sixes. remember, he has 2 of the jacks in his hand!

Posted 8 months ago

brainfreeze0

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68 posts
Joined 05/2011

I loved this one. Stuck with it like you encouraged me to. I must have watched and rewatched the reverse implied odds part for like an hour trying to figure out how to get the specific %'s and playing with Pokerstove to do the math until it finally started clicking.

It took me some time to figure out how to come up with the JJ = 4.5% until I remembered you saying last video that when you want to come up with the EV for making the hand just on the turn only do it for one street like the turn to the river. So I stoved QQ vs JJ on the same Flop and turn to get the % for hitting a J on the river and voila, 4.5%. (For those who are wondering why I'm so happy to figure this out math is a pretty weak subject for me and Wilt told me to keep at it and not give up so it's kind of exciting that I actually did manage to finally understand what comes fairly easy to a lot of ppl)

If I did it correctly (?) then if you take out QQ-AA and only leave a specific range of 10 10 and JJ for that same hand you would have a -EV of -$100.38. Is that correct?

Posted 8 months ago

odahikaru1

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10 posts
Joined 02/2011

Pinko Panther

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264 posts
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Liquid Cash

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126 posts
Joined 07/2011

Time Link to 00:15:15

I am a little confused about how you plug the pocket tens ev calc into the calculator. I know if it was 20% I would multiply 1629 (-140 + -765)by .2 right? would I do .18 for 18%? + 140 x.8 correct? Also the final -269 or whatever it is seems really low to me given that 18% of the time you lose over 1k. Please help me to understand this. Thanks for making this video.

Posted 6 months ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

I am a little confused about how you plug the pocket tens ev calc into the calculator. I know if it was 20% I would multiply 1629 (-140 + -765)by .2 right? would I do .18 for 18%? + 140 x.8 correct? Also the final -269 or whatever it is seems really low to me given that 18% of the time you lose over 1k. Please help me to understand this. Thanks for making this video.



Got your PM saying you figured it out

Posted 6 months ago

numjaw

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29 posts
Joined 11/2011

Did we ever get an answer to the problem at the end of this video?

Posted 9 days ago

WiltOnTilt

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Exec Producer
2098 posts
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Did we ever get an answer to the problem at the end of this video?



if you watch ep 4 and 5 you should be able to do it no problem Smile

Posted 8 days ago

KamikazeMan1

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7 posts
Joined 04/2011

Time Link to 00:06:01

Hey WoT,

I'm a little bit confused on the first pot odds example. What I'm confused about is where are you getting the 4.9:1 odds amount with the OESD. If you base it off of pot odds alone we only require pot odds of 2.2:1 or better to break even or to profit. Even if this was based on just seeing the turn card only, we would need 4.7:1 or better. I'm just wondering where you came up with 4.9:1...

Posted 8 days ago

WiltOnTilt

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Exec Producer
2098 posts
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ya weird, must have been a mistype when i made the powerpoint and then when I was talking about it I just didn't catch it. you are right about 4.7:1

Posted 8 days ago

KamikazeMan1

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7 posts
Joined 04/2011

ya weird, must have been a mistype when i made the powerpoint and then when I was talking about it I just didn't catch it. you are right about 4.7:1



Okay, thanks for clarifying Wilt, this series is so freaking badass and you put so much work into it, just wanted to say great job man.

Posted 7 days ago

WiltOnTilt

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Exec Producer
2098 posts
Joined 10/2007

Okay, thanks for clarifying Wilt, this series is so freaking badass and you put so much work into it, just wanted to say great job man.



Really appreciate it, thanks!

Posted 6 days ago



HomePoker Videos → Mathematics of NL Hold'em → Episode Three