# 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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#### 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

178 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

2411 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

2411 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

2411 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

2411 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.

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