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

## Mathematics of NL Hold'em: Episode 5

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### 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

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#### brainfreeze0

68 posts
Joined 05/2011

Here your talking about villains cbetting range. Maybe it's different at the higher stakes, but in my experience at 50NL and 100NL most villains cbet almost 100% of the time on hands they opend with pf. Their cbet range being their entire opening range preflop. It seems common which is why so many float the flop with air and even the turn waiting for pf raisers to check it seems. Are we being opponent specific in the example to nits? Am I wrong or missing something? Their range could be anything inside of their opening range including sc's and one gappers and they cbet whether they hit or not. Maybe I misconstrued.

#### WiltOnTilt

2411 posts
Joined 10/2007

Here your talking about villains cbetting range. Maybe it's different at the higher stakes, but in my experience at 50NL and 100NL most villains cbet almost 100% of the time on hands they opend with pf. Their cbet range being their entire opening range preflop. It seems common which is why so many float the flop with air and even the turn waiting for pf raisers to check it seems. Are we being opponent specific in the example to nits? Am I wrong or missing something? Their range could be anything inside of their opening range including sc's and one gappers and they cbet whether they hit or not. Maybe I misconstrued.

are you using a hud? All you have to do is look at the cbet stat to see that people aren't really cbetting 100%. Sure many are 70-80 (and at ssnl it's probably correct to cbet a very high %), so just use what you know about each player to tailor their range.

Also, it's a 3bet pot so the range is going to be tighter, but I still have some air in there. As long as you know the process you can flex the range as you see fit.

#### brainfreeze0

68 posts
Joined 05/2011

Good plan sir ty!

#### JKitok

3 posts
Joined 08/2010

First, I would like to thank you for the wonderful series that you've given us beginners of poker! 3 years after release (maybe even longer) there are still people recommending and watching your videos.

Second, I'm wondering a bit about the calculations made in around the 45 minute mark in the vid. It's when you calculate the minimum of times he needs to fold for the shove to be +EV with the Fold EQ formula.

When you calculate the EV for the fold respectively for the call, you are already making the assumption that he is folding a certain percent of the hands. If we would change the percentage of hands he is calling with, our EV for when villain is actually calling are shove will change.

Therefore, when you estimate that he would only need to fold 3%-ish of his hands, you are calculating that with the EV when villain is actually calling with 32,5% (39/120). Thus, your not regarding the fact that the EV for call will change depending on the percentage of him calling. Your equity and hence your EV for calling is certainly different if he is calling the bet with all of his hands.

For example, let's use the most obscure example when villain is only calling with his 3 combos of TT, or 1/40=2,5%. Putting that into the formula without changing the EV for call would give the following:

EV = 370*0.975+(-12,85)*0.025 = 360,43\$

However, our equity if he's calling range is TT+ is certainly not 43%-ish. Pokerstove calculates our equity to about 25,55%. Hence, the EV(call) is: =0.2555*(2005)-875 or -362,7\$

This gives the Fold eq EV according to the formula:

EV= 370*0.975+(-362,7)*0.025 = 351,68\$

Which is not a big difference, but there is one. There will also be bigger differences when you use other percentages.

Also, against his cbet-range, we're actually a favorite (not 43% as mentioned in the movie. I think it's a mistake, since you say that we have 43% equity against both his c-betrange and his c-bet&call range. Therefore, we wouldn't mind him calling 100% of his hands. And again, with him calling all of his hands, we cannot use the calculated EV that was made on an assumption from what his calling range was.

How to calculate how much he will need to fold for our shove to be -EV. Since we have +EV even if he folds 100% or 0% there must be something in between. Otherwise, we are always expecting +EV regarding his foldpercentage. How to set up this calculation I won't think about more since it's almost midnight here in sweden and I have work tomorrow.

I might look like a big fool writing this wall of text if it turns out that I am mistaken, but aren't the things mentioned above correct?

#### WiltOnTilt

2411 posts
Joined 10/2007

Your EV when he calls will differ based on how often he's calling only if hands are being taken out/added of the bet/calling range....so to restate it, if you change his bet/calling range, then our equity when called will change.

That doesn't necessarily mean that the EV of him calling will change based on the % of him calling. Maybe his original 3bet-cbet range is wider than I was assuming, therefore there are more hands he's bet/folding and our shove is move profitable but our equity vs his bet/calling range is the same, etc.

Does that make sense?

#### JKitok

3 posts
Joined 08/2010

That make sense, and it never occurred to me. I was all thinking about just changing the cbet/calling-range and entirely forgot that it's also possible to change his 3-betrange.

Thanks for the really fast answer. I guess it's by these questions we improve our thinking about the game aswell. Also, thanks again for the wonderful series. Going to watch the rest ASAP.

#### JKitok

3 posts
Joined 08/2010

Thinking about it even more, the following should be true:

- We've given villain an calling range.

- For our play to be +EV he needs to have ~3% more hands in his c-betrange.

- Now, thinking about his range, we'll see that he is folding even more than 3%, which makes our play good.

Changing the steps a little, first figuring the calling range, then calculating the equity and the Fold eq. Then, after this, trying to figure out his c-betrange. This makes it more clear for me.

#### WiltOnTilt

2411 posts
Joined 10/2007

Changing the steps a little, first figuring the calling range, then calculating the equity and the Fold eq. Then, after this, trying to figure out his c-betrange. This makes it more clear for me.

Yep exactly, just make sure you go back to the beginning to make sure the cbetting and calling range hands are also in their actual 3bet and cbet range

#### whatwonder

53 posts
Joined 03/2010

Aaron, do you still believe that 3-betting AKs against a 15/10 is more +EV than calling in this kind of situation, given the current state of the games? It seems like a) a lot of players go into 4bet or fold mode when facing a 3-bet OOP, and b) by just flatting and then calling/floating most flops, it seems like we can get more value from most of his range, especially Ax, by just flatting preflop than we gain from fold-equity by 3-betting.

(edit: I'm referring to the hand discussed around the 30-minute mark)

#### WiltOnTilt

2411 posts
Joined 10/2007

Aaron, do you still believe that 3-betting AKs against a 15/10 is more +EV than calling in this kind of situation, given the current state of the games? It seems like a) a lot of players go into 4bet or fold mode when facing a 3-bet OOP, and b) by just flatting and then calling/floating most flops, it seems like we can get more value from most of his range, especially Ax, by just flatting preflop than we gain from fold-equity by 3-betting.

(edit: I'm referring to the hand discussed around the 30-minute mark)

Depends on whether you think your history is enough to get him to 4bet/fold a good amount. Generally speaking, if the guy is so tight that I don't feel like I can profitably 3bet/get it in with some value hand, I shy away from 3betting it to begin with...but if we feel like we can't 3bet/get it in with AK then maybe that indicates we aren't playing aggressively enough against the guy (ie, not inducing him to open up his 4b bluff range).

Certainly flatting some of these hands, especially in full ring games, has more merit...but just be sure to think about what it means about our perceived 3bet range if we feel like we can't 3bet/felt a hand as strong as AK (in addition to thinking about what his opening range is).

9 posts
Joined 08/2010

if i want to know his openraisefreq from utg i look at my hud ?!....

#### whatwonder

53 posts
Joined 03/2010

I don't know if that stat was on HUDs 3 years ago.

#### WiltOnTilt

2411 posts
Joined 10/2007

if i want to know his openraisefreq from utg i look at my hud ?!....

as whatwonder mentioned, this series was made in late 07/early 08. we have evolved quite a lot since then in terms of stats/hud

#### Allermand_DK

794 posts
Joined 11/2008

Hi Aron.
Thanks for the this great series In timeline: I don't get how you the total pot of 1720? 1:05 isn't 1860?

#### WiltOnTilt

2411 posts
Joined 10/2007

Hi Aron.
Thanks for the this great series In timeline: I don't get how you the total pot of 1720? 1:05 isn't 1860?

Keep in mind that i can only win/lose based on what is in the effective stacks. Villain has more money... so its our \$800 + his \$800 + \$120 in the middle = \$1720

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