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

## Mathematics of NL Hold'em: Episode Four

Get the Flash Player to see this player.

### 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

or track by Email or RSS

#### tmmoss

48 posts
Joined 05/2009

WiltOnTilt -

Just finished episode 5. I am new to the forums and fairly new to the game. Thanks for the detailed breakdowns - as I was listening to the method, it brought to mind the old "cancelling method" we used to reduce fractions when I was a kid. No jokes about my age showing! Thanks for vids. Very good.

#### PygmyHero

4246 posts
Joined 08/2007

Homework: ~ negative \$200

#### st3v3k4hn

3 posts
Joined 01/2010

Great series. Trying to get a handle on Tupac but my first thought was that I would put my opponent on a very different range so the resulting equity and EV calcs would also be very different. I am playing very low stakes NL (6-max) and at this level I would never leave AA or KK or AK in his range (he would 4-bet those preflop). And, if he is frustrated (as you said) I would include all pairs in his range preflop and include TT, JJ & QQ in his pushing range on the flop. That small change is enough to make this a positive equity situation against his range (mostly due to the 18 combinations of QQ, JJ & TT with which he might push). So I guess my point here is I would like to see more info about putting someone on a range of hands and how that varies by stakes. Maybe I am crazy thinking that a TAG would push TT here - but I see it every day at the stakes I am playing... Anyway, this video is pretty old so probably no one will even read this. But Wilt if you do read it thanks and keep up the good work...

#### killer108

258 posts
Joined 03/2010

very nice video, but when i am playing on 4/6 tables, very dificult to do that...BUT I THINK CAN GET EXPERIENCE IN THAT CASE
but i thnk to see whole serie 4-5 times to understand better, but i also think the most player go not calculate that, because he also can makes bluf , when somebody shoove me and i have one pair only with straight and flushdraw on the board i will fold without thinking is that wrong?

because i am beat lot of times i guess

#### Bean Box

75 posts
Joined 03/2010

Any MAC equivalents to pokerstove?

#### Dr. Loiselle

10 posts
Joined 03/2010

Homework: ~ negative \$200

Homework assignment: [24m34s]

our equity = 26%
total pot = \$2015
cost of call = \$675

[.26 * 2015] - 675 = negative \$151

LowWaterMark and PygmyHero say negative \$200
What did I do wrong?

#### briocheMC

1 posts
Joined 07/2010

Isn't there a mistake ? 3 ways of making 2 pairs with 89s when the flop has got Kc9c8d ? I'd say only hearts and diamonds left for that... So that's 2 ways.

#### Entity

8021 posts
Joined 11/2006

Isn't there a mistake ? 3 ways of making 2 pairs with 89s when the flop has got Kc9c8d ? I'd say only hearts and diamonds left for that... So that's 2 ways.

Yeah, you're definitely right there, nice catch.

Rob

#### DOMSTER

42 posts
Joined 02/2010

Poker at its best - the RE of R.E.M. broken down in its essentials. Havent seen a better piece of work on hand ranges and equity than that.

Great Job Aron

#### kgbmiked

192 posts
Joined 11/2010

Here are my notes on this episode, I tried to correct everything that was wrong in the video and be more accurate with my rounding. thanks WoT, best series ever. If anyone see's any errors feel free to correct me.

Notes on Mathematics of NL Holdâ€™em episode4 by WiltonTilt
By KGBMIKED

Video # 4 is all about EV Calculations.

Basic EV calculation setup:

EV = (Result of win) â€“ (Result of loss)

EV=(Our Equity) * (What we win) â€“ (Villainâ€™s Equity) * (What we lose).

Basic Example:

Weâ€™re in the big blind with AsAc. The UTG player shoves with KhKd and folds to you. Itâ€™s \$900 to call to win 1015 (stack+blinds) 5/10, \$1000 stacks

Ev = (our Equity) * (What we win) â€“ Villainâ€™s equity) * (What we lose)

Ev = .81*1015 - .19 * 990

Ev = 822.15 â€“ 188.1

Ev = +634.05

Thus, every time this situation occurs we expect to profit \$634.05

ALTERNATE METHOD

Ev = (Our Equity) * (Total pot) â€“ cost of our call
Ev = (.81) * 2005 -990
Ev 634.05

Both methods work, choose the one that seems to make the most sense to you. He prefers the first method because he thinks itâ€™s easier to build on, but itâ€™s essentially the same thing just a different way of thinking.

EV Calcs Vs Hand Ranges:

We have KsQc We have 3 bet this guy a lot, we are in position we 3 bet pf again he calls.
AK is not in his range because he would have 4bet. He checks the flop We bet 200 he jams for 875. There is 265 in the pot. The board is Kc9c8d
We assume he is check jamming here with at least 8 outs.

His range is KK+; 99,88, AcQc, AcJc , AcTc, Ac8c, QcJc,JcTc, 98s, 7c8c, JTs, 67s

.35(1075+265) - .65(675) = +30.25

#4 has how to do Tupac method at the table

This is not in the video but very valuable math.

One concern for me in NL Hâ€™E math is that most people finding Equity do it through poker stove which gives you your equity for seeing all 5 cards. This article can help you find your equity PFR to Flop and then you can recalculate for turn and river. I think knowing your equity based on the 3 flop cards and not just all 5 cards is one of the most under rated math concepts in poker.
Chance Of Overcards Hitting
Question: dear poker master,
i've been thinking a lot about this situation as it pertains to tourneys. what are the odds for the overcards hitting again? and how do you figure them out before the flop. i know that there is a 6 out of 47 and 6 out of 46 percent chance of hitting on the turn and river but how do you calculate for all three cards of the flrop?
thanks
andrew
Answer: To calculate the odds of hitting them on the flop you use a similar equation like you do for the turn and river. Let's do an example with KQ. You have 2 cards in your hand and that leaves 50 unseen cards for the first flop card. You have 6 outs for the flop cards (3 Kings and 3 queens). The next card you have the same 6 outs but this time only out of 49 cards. The last flop card gives us 6 outs out of 48. That looks like this:
6/50 6/49 6/48
Here is the tricky part. Whenever you have a situation when an event, hitting your card, can happen on more then one chance you figure out the odds of it NOT hitting and then subract it by one.
1 - [ ((Cards - Outs) / Cards) * ((Cards - Outs) / Cards) ... ]
Let's try that with our numbers:
1 - [(44/50) * (43/49) * (42/48)]
1 - [.88 * .8775 * .875]
1 - [.675] ----- this basically shows there's a 68% chance of us NOT getting our cards.
32% ---- this means that there is a 32% chance we WILL get our cards.
That seems like a high percentage until you think of it compared to the flush draw which seems like it never gets there. If you want to figure out how often AK will hit by the river then just add the turn and river cards to the equation:
6/50 6/49 6/48 6/47 6/46
Flip these again to cards that won't help us:
44/50 * 43/49 * 42/48 * 41/47 * 40/46
.88 * .8775 * .875 * .872 * .869
= 51% of the time it not getting there.
= 49% of the time it will hit by the river.

#### Bonobo11

4 posts
Joined 03/2011

Here are my notes on this episode, I tried to correct everything that was wrong in the video and be more accurate with my rounding. thanks WoT, best series ever. If anyone see's any errors feel free to correct me.

Notes on Mathematics of NL Holdâ€™em episode4 by WiltonTilt
By KGBMIKED

this post is Winning!

#### Rodney Mullen

6 posts
Joined 04/2011

The matching up of combos was pretty confusing to me. Wouldn't this be an easier way to estimate?

13 combos of hands that crush us
9 combos of flips
6 combos of hands we are favorites over

drop all 9 flips
13 losses : 6 wins (round it down to 12:6, reduce to get 2:1)
So we are a 2:1 dog

Does this just work in this example? And if it doesn't maybe you have come up with an easier way of matching combos in the last 3 years?

#### WiltOnTilt

2402 posts
Joined 10/2007

You can't exactly drop the 50/50 combos because they do hold weight. Think of an extreme example. 100 flip combos. 2 big favorites. 1 big dog. Overall this would still end up
being a "flip" in terms of us estimating, not 2:1 favorite.

#### brainfreeze0

68 posts
Joined 05/2011

you can't exactly ignore/reduce combo-for-combo crushing vs crushed combos because remember the weight of the 50% will also effect the overall equity. so think of it in the extreme.... say you had 1000 combos where we crush them and 1000 combos where they crush us, that will average out to 50% as you say, but we can't simply ignore it because then let's say we have 10 combos where we're slightly ahead at say 60/40 favorite... well those 10 combos at 60% will also average in to the other 2000 combos, but not so much that we can simply cancel out and ignore the other 2000 combos. In other words, if we do the averaging, the answer will still be close to 50% because of the sheer weight they hold with so many combos.

So you're right, the crushing and crushed combos will average out to 50%, and if there are only a few of those combos, you can sort of ignore them, but you can't completely ignore them as the number of crushing/crushed combos increases, the closer to 50% your overall equity will become.

This will probably sound like a dumb comparison but your explanation reminds me a lot of it. At my job (10 hour work day) our positions are all computer calculated with random job assignments where X amount of time is assigned to complete these task. If we are assigned 1 hour to do the assignment and we do it in an hour we are at 100%. If I do it in an hour and 10 min I'm at like a 90%. So if I'm at a 90% for that hour assignment and the next one I get is only 10 minutes and I do it in 5 minutes I'd get 200%, but since it was such a short assignment combined with my former hour long assignment I'll only go up to around 100%.Similarly if I'm 9 hours into my day with an 85% (that's 9 hours strong) and I get an hour long assignment and do it in 35 minutes and get like 175% it only raises me up to like 89%. Hope that made sense.

Guess I've been doing this job so long your explanation makes complete sense to me.

#### WiltOnTilt

2402 posts
Joined 10/2007

This will probably sound like a dumb comparison but your explanation reminds me a lot of it. At my job (10 hour work day) our positions are all computer calculated with random job assignments where X amount of time is assigned to complete these task. If we are assigned 1 hour to do the assignment and we do it in an hour we are at 100%. If I do it in an hour and 10 min I'm at like a 90%. So if I'm at a 90% for that hour assignment and the next one I get is only 10 minutes and I do it in 5 minutes I'd get 200%, but since it was such a short assignment combined with my former hour long assignment I'll only go up to around 100%.Similarly if I'm 9 hours into my day with an 85% (that's 9 hours strong) and I get an hour long assignment and do it in 35 minutes and get like 175% it only raises me up to like 89%. Hope that made sense.

Guess I've been doing this job so long your explanation makes complete sense to me.

yup thats the exact type of thing that is going on here.

HomePoker ForumsMicro Stakes Online NL → Mathematics of NL Hold'em: Episode Four