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

## Mathematics of NL Hold'em: Episode 5

Get the Flash Player to see this player.

### Mathematics of NL Hold'em: Episode 5 by WiltOnTilt

In episode 5, WiltOnTilt presents a formula to estimate a villain's open-raising range and compares the EV of calling vs 3-betting preflop. Also, the concept of Fold Equity is introduced into the EV calculations. WiltOnTilt shows us a method of determining the fold equity required when bluffing or semi bluffing without the use of software by thinking in terms of pot units.

#### 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
• 81 minutes long
• Posted over 5 years ago

## Comments for Mathematics of NL Hold'em: Episode 5

or track by Email or RSS

#### WiltOnTilt

2409 posts
Joined 10/2007

min 26 - isnÂ´t our EV only 12.73?

can you elaborate on why you think this? i just redid the math and it seems right?

WoT

#### Luzhin64

2 posts
Joined 03/2008

min 26 - isnÂ´t our EV only 12.73?

can you elaborate on why you think this? i just redid the math and it seems right?

WoT

EV=(our equity) * (what we win)- (villainÂ´s equity) * (what we loose)
EV= 55.5% * (40+15) - 44.5% * 40
EV= 0.555 * 55 - 0.445 * 40
EV= 30.525 - 17.8
EV= 12.725

or

EV= (our equity)*(total pot) - cost of our call
EV= 0.555*95 - 40
EV= 52.725 - 40
EV= 12.725

to me seems wrong to count our call in "what we win"

Anyway "Math of NLH" are best poker videos I have ever seen. Thx a lot for them.

#### SevenNineSuited

4 posts
Joined 03/2008

Wilt - First, great series. Really gets the critical thinking juices flowing.

My question is a bit on theoretic side. In the video you discussed how when the EV(Call) and EV(3-Bet) are close, you should go with 3-Bet because of the very real and accurate issue of either not getting to see all 5 cards or folding the best hand on the river. Makes perfect sense but from a contrarian standpoint can it be said that when evaluating EV(Call) and assuming you have > 50% equity that there exists "implied money" which will go into the pot postflop that would not exist in 3-betting since 3-betting derives most of it's overall EV from villain folding? I guess what I am trying to say is that wouldnt it be more correct to make estimates or even adjust the equity to account for the fact that some % of the time more money will go into the pot postflop when you call and that hero has a > then 50% claim to this "future money" since he is ahead of villain's range?

I am also curious to hear the response to Luzhin64's post above because I thought the same thing when I was watching the video.

#### WiltOnTilt

2409 posts
Joined 10/2007

SugarNut made me aware of an algebraic error I made in this episode around the 45 minute mark. it doesn't drastically change the result or spirit of the calculation, but it is wrong.

So here's how it is in the slide:

EV(total) = 370x â€“ 12.85(1-x)
EV(total) = 370x â€“ 12.85 + 12.85x
EV(total) = 382.85x â€“ 12.85
12.85 = 382.85x
x = 12.85 / 382.85
x = 3.4%

Here's how it should be:

EV(total) = 370x â€“ 12.85(1-x)
EV(total) = 370x â€“ 12.85 - 12.85x
EV(total) = 357.15x - 12.85
12.85 = 357.15x
12.85 / 357.15 = x

x =~ 3.6%

The error occured on line 2 where i distributed 12.85(1-x) incorrectly. Sorry about that guys.

Also, Luzhin64 above who posted back in march, it looks like he is correct as in the video I somehow added in an additional \$40 to my equation. So around the 26 minute mark the incorrect equation is:

EV = [Our Equity] * [what we win] â€“ [Villainâ€™s equity] * [what we lose]
EV(call) = 55.5% * (40 + 40 + 15) â€“ 44.5% * (40)
EV(call) = 52.73 - 17.8
EV(call) = 34.93

and the correct way is is how Luzhin64 wrote it above:

EV=(our equity) * (what we win)- (villainÂ´s equity) * (what we lose)
EV= 55.5% * (40+15) - 44.5% * 40
EV= 0.555 * 55 - 0.445 * 40
EV= 30.525 - 17.8
EV= 12.725

I'm not sure how that extra \$40 crept into the equation. Must have been a typo or absentmindedness. How embarassing, sorry guys! At least the faithful DC'ers found my mistake and got it corrected for everyone else. Also at least it didn't hose up the process, just slight errors in calculation... so as long as you've learned the process you'll probably calculate correctly :-)

Thanks
WoT

#### WiltOnTilt

2409 posts
Joined 10/2007

Wilt - First, great series. Really gets the critical thinking juices flowing.

My question is a bit on theoretic side. In the video you discussed how when the EV(Call) and EV(3-Bet) are close, you should go with 3-Bet because of the very real and accurate issue of either not getting to see all 5 cards or folding the best hand on the river. Makes perfect sense but from a contrarian standpoint can it be said that when evaluating EV(Call) and assuming you have > 50% equity that there exists "implied money" which will go into the pot postflop that would not exist in 3-betting since 3-betting derives most of it's overall EV from villain folding? I guess what I am trying to say is that wouldnt it be more correct to make estimates or even adjust the equity to account for the fact that some % of the time more money will go into the pot postflop when you call and that hero has a > then 50% claim to this "future money" since he is ahead of villain's range?

I am also curious to hear the response to Luzhin64's post above because I thought the same thing when I was watching the video.

79s, yes there's merit to what you're saying. It becomes a lot more difficult to calculate though, but certainly there are situations that can arise where that would be a very real concern. One type of situation that comes to mind immediately is a spot where you are playing against an aggressive bluffy player and you've got a strong hand on the turn where many draws are present and based on how the hand went down you suspect your opponent is on a draw. Raising might be correct on paper from an EV perspective, but there's also some "hidden" value in just calling the turn and snapping off river bluffs on a blank since you can (hopefully) accurately determine which river cards helped him and which didn't, and because of our read we have reason to believe he will bluff no matter what, so we can make more correct calls and folds. The problem is that becomes pretty difficult to quantify, but on the other side of the coin is that it's also tough to quantify the benefit of our "aggressive image" by constantly choosing the more aggressive option when the EV of a passive action vs aggressive action are close.

You bring up a good and valid point though, thanks for posting.

WoT

#### SpiralSpikes

1 posts
Joined 06/2008

At 28 minutes you are determining villains' range for a call of our 3bet, deciding that such a range would be TT+ and AK. You go on to say that this accounts for 3.5% of all holdings. What confuses me is that in all previous episodes you have taken pains to point out that we should remove from our opponents range any possibilities that involve either the community cards or our own pockets. Here we have AsKs, so surely we should remove options involving these cards from his range: If we do that then his calling range is more like 2.5%.

This in turn means that we will collect the pot 77.7% of the time, not the 69% stated in the video. Our EV is then \$40.65, not \$34.89.

Of course I could be the gibbering idiot so I'm a little confused as to what I should be doing. Please enlighten.

#### WiltOnTilt

2409 posts
Joined 10/2007

spiral, nice catch

#### Cueballmania

1 posts
Joined 08/2008

Around the 48 minute mark, you list the combinations of hands. If you hold the As, there is only 9 ways to make AKo, AQo, AJo. Also, there are only 12 combinations of KQo regardless.

#### EpErOn

134 posts
Joined 08/2008

i like the video, however i think the formula of PFR% is still somewhat wrong...?

isn't it missing out on the percentage villain raises when there are limpers in front of him?

i think the formula should be:

PFR% = 3betting + open raising + raising limpers!

1 posts
Joined 10/2008

Thank you a lot WiltOnTilt. I thought I knew pretty much about maths and so on but these videos have been a good eyeopener. I believe that my view of certain opponents acts are now more clear to me. Hopefully I can turn my play from break even to winning.

#### wems

12 posts
Joined 06/2008

I really enjoy the series... however i hate math and suck at it... but here is a hand where I am trying to find out my FE... and I would really appreciate it if someone could check my math and make sure im doing things right...
http://www.pokerhand.org/?3384820
ev(fold)=60
ev(call)=.40 * 204 - 83 = -1.4
ev(total)= 2.3% which is how often he needs to fold... is this right???

Now I'm not certain if the number of combos he has/is calling with is correct I was more concerned with getting the whole math aspect of this correct than figuring out approximate ranges, however I do feel the ranges are fairly close... I was more focused on getting a number of combos to work with and ive already spent an hour on this problem so i might have taken a shortcut
AKo, AQo, A8s, K8s, T9s, T8s, 86s which is ~45 combos.
then his call combos i believe are:
22, 66, 88, 99, TT, JJ, QQ (im going to say he 3bets KK, AA preflop)
so thats 23 call combos
So he calls 51% of te time and folds 49% of the time... and so this is a +EV play because he is folding > 1.4% ?!?? for some reason that just doesn't seem right... the 1.4% needed for him to fold that is...

so now we plug that into our formula etc
ev(total)= 60x - 1.4(1-x)
ev(total)= 60(.49)-1.4(1-.49)
ev(total)= 60 * .49 - 1.4 * .51
ev(total)= 29.4 - 0.714
ev(total)= \$28.69

So that means by shoving this turn we are making \$28.69 in ev?

Thanks,
wems

127 posts
Joined 06/2008

SugarNut made me aware of an algebraic error I made in this episode around the 45 minute mark. it doesn't drastically change the result or spirit of the calculation, but it is wrong.

So here's how it is in the slide:

EV(total) = 370x â€“ 12.85(1-x)
EV(total) = 370x â€“ 12.85 + 12.85x
EV(total) = 382.85x â€“ 12.85
12.85 = 382.85x
x = 12.85 / 382.85
x = 3.4%

Here's how it should be:

EV(total) = 370x â€“ 12.85(1-x)
EV(total) = 370x â€“ 12.85 - 12.85x
EV(total) = 357.15x - 12.85
12.85 = 357.15x
12.85 / 357.15 = x

x =~ 3.6%

The error occured on line 2 where i distributed 12.85(1-x) incorrectly. Sorry about that guys.

You distributed correctly in the video.

The check works out....

0 = 370(12.85 / 382.85) + (-12.85)(1 - (12.85 / 382.85))
0 = 370 * 0.033564059030952070001305994514823 + -12.85 * 0.96643594096904792999869400548518
0 = 12.4187018414522 - 12.4187018414522
0 = 0

if your ev calculation is EV = [EV(fold)] * x + [EV(call)] * (1 - x)
Then distributing -12.85 would yield a calc that looks like this ..
EV = 370x + [(-12.85)(1 - x)]
= 370x + (-12.85 + 12.85x)
= 370x + 12.85x - 12.85
= 382.85x - 12.85
x = 12.85/382.85
x = 0.033564059030952070001305994514823

Someone correct me if I'm wrong.

I can see how SugarNut came to his conclusion somewhat.
Maybe he changed around the origincal Fold Equity equation to...
EV = [EV(fold)] * x - [EV(call)] * (1 - x)
In that case x would be -.0359793.
But even then the answer seems erroneous being negative and all that. But i can see the correlation between 3.6%.

Anyone want to clear that up?

#### WiltOnTilt

2409 posts
Joined 10/2007

I guess the mistake I made was thinking that I made a mistake.

WoT

#### wems

12 posts
Joined 06/2008

anyone have some input on my math like 2-3 posts up? im uncertain if that is right or not

was arguing with someone on irc they said i needed him to fold like 30% ?!?

im so bad at math... lol

3 posts
Joined 02/2009