# 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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#### Claymangs07

1 posts
Joined 07/2009

Hey WoT,
At 1:17:26, you're talking about Grunch's method to determine how much FE we need to make a turn shove breakeven.

When villain calls, we're a 3:1 dog. So when called, we lose approx. 8P. After this point, I think there's a mistake. We gain 1P every time villain folds and we expect to lose 8P when called. So we need villain to fold 8 times as often as he calls for this to be breakeven. So villain must fold 8/9 times or ~88% of the time.

Let me know if I'm wrong because I could easily be overlooking something.

Thanks for the great series,
Ben

#### WiltOnTilt

2404 posts
Joined 10/2007

Re-watch the part where I talk about viewing the situation in 12 total instances. The green and the red numbers are the first 4 instances, because we're a 3:1 dog, we lose 3 times and win 1 time, so we can see how far we are in the hole. We have to use the fold equity to get us out of the hole and we need 8 more instances of him folding in order to get out of that hole.

We don't need him to fold 8/9 times because the times he doesn't fold we'll sometimes win the whole pot... in order to take into consideration the times we win the whole pot, we break out those win/loss instances as shown in the red and green numbers. What you're doing is counting the -4 -4 -4 +4.5 and saying that's -8 and counting it as one instance instead of counting it as 4 different instances... so that's effecting the divisor (your 9, my 12), which effects the division (8/9 vs 8/12).

Thanks for watching!
WoT

#### husker

27 posts
Joined 07/2008

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.

I don't think you're figures are correct here. It looks as though you have removed all AK hands from his range, which has dropped his range from 3.5% to 2.5%. If we put in a specific suited hand for ourselves, such as A K and then take this hand out of the villains range then his total range only drops to 3.4%

#### lekarz20

20 posts
Joined 08/2009

Hi

That R(1) = raise first in holdem manager?

raise first- Raise First is similar to Pre Flop Raise except it doesnâ€™t include 3bets as its only the 1st person to raise that has their Raise First stat effected and it doesnt include raising limpers.

#### WiltOnTilt

2404 posts
Joined 10/2007

Hi

That R(1) = raise first in holdem manager?

raise first- Raise First is similar to Pre Flop Raise except it doesnâ€™t include 3bets as its only the 1st person to raise that has their Raise First stat effected and it doesnt include raising limpers.

ya seems reasonable.

this series was made before HEM is the beast that it is now

#### supsis

146 posts
Joined 05/2009

Here we are determining the EV if villain calls. If our equity in the pot vs. his calling range is 43% wouldn't that make his equity 57%? He has to call \$760 to win \$1245 and if he does call within our defined range on average he would have that 57% and would be making a +\$382.90 EV play. Wouldn't that make it -\$382.90 each time he calls within his range? I also have villain needing 38% equity to make an +EV call. 1.6:1. Still if we thin him by 66% we 'earn' 2x 370 per 1x -382.90.

Where have I gone wrong?

Mind blowing series.

#### Synchronicity

6 posts
Joined 09/2009

Dude, at about 23:08 my head asploded, for real. You said "and so we go ahead and do the algebra...do the subtraction...do the division here and we find that R(1) equals 11.2%" It was right there that it went wait, what!? POP!!!!

You might as well have said click your heels, snap your fingers, and say "Magically Delicious" and we find out that R(1) = 11.2%

Please, for a guy who hasn't had to do algebra in over 25 years....how do you do you get to 11.2%?

The series has been great and well explained in detail, right up to that moment. I have no idea where to go with that.

#### Synchronicity

6 posts
Joined 09/2009

Never mind, figured it out. Please don't scare me like that again. JC!

LOL

#### PygmyHero

4246 posts
Joined 08/2007

I'm somewhat interested in the derivation of this formula if there's a thread you can point me to.

That said, I'd be interested to know if you think this information is now obsolete given all the data HEM makes available to us.

#### PygmyHero

4246 posts
Joined 08/2007

There are a few errors in the combo listings here.

AKo = 9 combos (you double counted the AKs hands)
AQo = 9 combos (same as AK - you double counted the AQs hands)
AJo = 9 combos (but maybe you meant AJo and AJs here, in which case 12 is correct)
KQo = 12 combos

So that would lower the total number of combos a bit, but ultimately the answer of how often we need villain to fold is relatively unaffected (we still need very little FE for this to be +EV).

By the way I generally find this a lot easier to just look at in Stove. For example in this problem we could just have:

Enter the villain's PF 3-bet plus cbet range into Stove. IIRC this was ~10% of all hands.

Then enter the villain's PF 3-bet plus cbet plus call shove range into Stove. I think this was about 3.8% of all hands.

In other words, he's calling off 3.8%/10% ~38% of hands and folding the other 62% of the time.

#### PygmyHero

4246 posts
Joined 08/2007

Homework:

If villain folds 69% of the time I calculated our EV as ~\$17.97

The play might be too high variance to be palatable for some, but that's still a play with more than a 2% edge.

#### Chris MintZ

556 posts
Joined 07/2009

So basically if the UTG+1 3bets that is calculated into his PFR? Is that why we use (UTG+1) 3bet% in this equation?

#### cocktails

14 posts
Joined 10/2008

Grabbed by Holdem Manager
NL Holdem \$1(BB) Replayer
SB (\$176)
BB (\$101)
UTG (\$182)
UTG+1 (\$100)
Hero (\$129)
BTN (\$159)

Dealt to Hero J A

fold, UTG+1 raises to \$4, Hero calls \$4, fold, SB raises to \$19, fold, fold, Hero calls \$15

FLOP (\$43) 7 2 2

SB bets \$27, Hero raises to \$110 (AI), SB calls \$83.05

TURN (\$263) 7 2 2 8

RIVER (\$263) 7 2 2 8 8

Villains Betting range
3.7%
Villains Bet/call range
2.5%

2.5/3.7 = .67
Villain calls 67% and folds 33%

I calculated we have 45.5% equity
Evcall 263 *0.455 - 110
Evcall 119.70 - 110
Evcall 9.70

EVCALL 9.7
EVFOLD 70

PushEV = [ev(fold)] * x + [ev(call)] * (1-x)
PushEv (total ) = 70x - 9.7(1-x)
PushEV = 70(.33) - 9.70(1-.67)
PUSHEV = 70 * .33 - 9.7 * .67
PUSHEV = 23.1 - 6.5
PUSHEV = 16.6

Did i do this correct?

#### Chazb0t

1816 posts
Joined 01/2009

Boba Fett Picture

2 posts
Joined 05/2009