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

Mathematics of NL Hold'em: Episode Six

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Mathematics of NL Hold'em: Episode Six by WiltOnTilt

In this episode, WiltOnTilt examines how to produce weighted hand ranges by counting hand combinations and by examining frequencies. This concept is examined using a preflop hand example where we are playing out of position against an aggressive 3 bettor. A second example is given in which we are heads up with our opponent and we need to determine the number of combos required in villain's range to allow us to call a shove.

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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.

Tags

wiltontilt hand frequencies nl hold'em nlhe nl math mathematics of poker ipod friendly

Video Details

  • Game: nlhe
  • Stakes: Micro/Small Stakes
  • 43 minutes long
  • Posted almost 4 years ago

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Comments for Mathematics of NL Hold'em: Episode Six

HaiaN

Avatar for HaiaN

79 posts
Joined 01/2008

Squishee

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1374 posts
Joined 01/2008

good video !

next one gonna be very helpfull I guess Smile

Posted over 4 years ago

Philbet

Avatar for Philbet

2 posts
Joined 09/2007

Yes realy getting into the series now, found it all a bit laborious at first but the classroom style of instruction does give you plenty of time to take it all in and understand it better.
I am now enjoying the whole concept and looking forward to the next episode,
Well done Aaron and Deuces Cracked.
Phil.

Posted over 4 years ago

frenchfish

Avatar for frenchfish

6 posts
Joined 06/2008

You don t just hand out the fish ,you actually teach how to fish and that s what i like in the classroom format.

TY ,exelent series so far.5 stars!

Posted almost 4 years ago

chkmyrivr

Avatar for chkmyrivr

19 posts
Joined 03/2008

Good video.

Just wanted to point out a small flaw in your reasoning in the last hand : you say we can ignore the Ah combos because we average 50% equity against them, however given we already have money invested in the pot we need ~40% equity to call and therefore these combos actually give more EV to the calling option.

Posted almost 4 years ago

Route66

Avatar for Route66

17 posts
Joined 05/2008

This is a spectacular series. Question on the 88 hand example... around 20 min in when calculating EV(call), the amount we win is shown as $1050. That seems to be taking taking into account our $35 open twice. Should it be $1015 instead, making EV(call) -206.66 instead of -193.26? Not trying to nitpick, but I setup an EV calc spreadsheet and can't otherwise get the calculations to come out correctly (-206.66 is what I get using "method 2" of calculating EV(call).

Thanks.

Posted almost 4 years ago

quaddamage

Avatar for quaddamage

127 posts
Joined 06/2008

This is a spectacular series. Question on the 88 hand example... around 20 min in when calculating EV(call), the amount we win is shown as $1050. That seems to be taking taking into account our $35 open twice. Should it be $1015 instead, making EV(call) -206.66 instead of -193.26? Not trying to nitpick, but I setup an EV calc spreadsheet and can't otherwise get the calculations to come out correctly (-206.66 is what I get using "method 2" of calculating EV(call).

Thanks.



Once our 35 dollars goes in the pot it is no longer ours.
10(BB) + 5(SB) + 35(Our open) + 1000(Villain's 3-bet/call) = 1050

Posted over 3 years ago

PygmyHero

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4276 posts
Joined 08/2007

Time Link to 00:26:02

I know someone asked for homework in a prior thread. I would propose:

WoT showed examples of villain 3-betting ranges where our shove was -EV and +EV. How many total combos need to be in villain's 3-betting range for our shove to be 0EV? Assume villain's call off range always remains at the 59 combos listed in the video.

Posted over 2 years ago

PygmyHero

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4276 posts
Joined 08/2007

Time Link to 00:40:13

Possibly interestingly, we can use GrunchCan's trick you showed in Episode 6 to determine how often we need to be ahead.

When we lose it costs us 42,800
When we win we gain 17,200

Thus we need to win 42,800 / 17,200 times as often to be 0EV.

My mental math was as follows:
Divide all numbers by 1,000
Problem is now 42 / 17
17 * 2 = 34
Half of 17 is ~8 and if I add 8 to 34 that's 42
Thus 17 goes into 42 ~2.5 times

Depending on how you think here are a few ways to formulate the next step:
I need to win 2.5 times as often as I lose.
I need to win 2.5 times for every one time I lose.
I need to win 2.5 out of every 3.5 instances.

2.5 / 3.5 ~ 71%

So we need to be ahead here ~71% of the time, as the video showed.

Posted over 2 years ago

kgbmiked

Avatar for kgbmiked

192 posts
Joined 11/2010

Here are my notes on Episode 6 for anybody that doesn't want to have to constantly come back to the video for the equations and how to work them.



Notes on Mathematics of NL Hold’em episode6 by WiltonTilt
By KGBMIKED


This episode was about the concept of Frequency and had more about the information we can gain from doing Fold Equity Calcs.

Builds on the concept of How often a villain has a particular hand based on hand combinations. Example is the fact that there are 12 hand combinations for AA-KK (6forAA and 6forKK) and there are 16 combos for AK so it is more likely for a villain to have AK then AA or KK. And it is much for likely they have AK then just AA This helps when you are 4 bet pf with AK you know he is slightly more likely to have AK then AA or KK, don’t get me wrong we only have 40% Equity against his range if he is tight but there may be enough in the pot to still call,


We are playing 5/10 NL. We open the CO to $35 with 88 and get 3-bet by an aggressive regular on the button to $125. We think our hand is best right now so we jam in the rest of the 1k. Total blinds $15,

The question is how often does he have to have a hand that he 3-bet/folds with combined with the times he calls it off and we are either flipping or he has us crushed.

General 3 betting range here is 99+,AJ+KQ, some suited connectors, some suited aces.(We cant give the SC and SA the same weight as other hands because he is not doing it every time he gets this hand. So we need to take out some combos of the range we gave him so here are the adjusted combos based on frequency of play

99 50% = 3
TT 50%= 3
JJ+100% = 24
AJ,KQ 50% = 16
AQ,AK 100% = 32
AXs 25% = 8
SCs 50% = 16

TOTAL = 102

Now let’s find a range that he calls our 4 bet jam with. He’s an Aggressive regular so

TT+AQ,AK ( I don’t agree with the AQ but this is the example used in the video so I will keep it the same)

Combos based on Frequency
TT = 3
AQ+ = 32
JJ+ = 24

TOTAL = 59

So what is our Fold Equity

102-59 = 43 folding combos
43/102 = 42% Fold Equity
He is calling 58%
Now we need to find our Equity in Poker Stove against his range. Make sure to take out some combos based on the frequencies we gave him.
So against his calling range we have 38.3% Equity
Equity when he calls
Now lets set up our EV calc

EV(Total) = x*EV(fold)+ (1-x) *EV(call)

EV(fold) = 15+35+125 = $175

EV(Call) = 1050(.383) - 965(.617) = -193.26

Breakeven fold %

0 = 175x -193.26 – 193.26x
x = 52.5%

so he needs to fold 52.5% of the time for this to be breakeven. We had already found his fold equity to be 42% so we don’t have enough fold equity and it is a negative EV play.
If we make this play we can expect to lose
TotalEvShove = .42(175) + .58(-193.26)
= 73.5 – 112.09
= -$38.59 Every time we shove in this situation on average.

Knowing we need 52.5% fold equity we can go back to Poker Stove and add in combos and maybe more hands to until we get our 52.5% fold equity, we can then see what this VPIP looks like.

So lets make a new range of
55+(didn’t do 88) = 54 combos
78s-QJs+ = 24
ATs = 4
KQ = 16
AJ = 16
AQ = 16
AK = 16
TOTAL 146 combos

Calling combos stays the same at 59
So 146-59 = 87 folding combos
87/146 = 59.5 % Fold Equity.

This range is 10.7% in Poker Stove. So this means he needs a 3 bet range of just about 10.7% in order for this shove to be profitable here.

So if we plug this 59.5% fold equity back into our EV Calc we get

EV(Total) = x*EV(fold) + (1-x) *EV(Call)
EV(fold) = 175
Ev(call) = -193..26


SO
EV(Total) = .595(175) + .405(-193.26) = +$29.90 So this is a long haul gain of about 30 bucks. So this introduces a huge variance into your play for a very small gain. Also, since a small mistake in his range makes this negative EV it probably is not a good play. Even if his 3 bet% is over the required amount, unless you have a huge database with TONS of hands on him, we probably won’t have a large enough sample to ever have an accurate enough range for him to be sure this is a positive play.

Posted over 1 year ago

Dzikijohnny

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141 posts
Joined 12/2009

I used the trick for estimating fold equity for the 88 hand at the ~20 min mark. And it works!!!!!!

pu=225 675/225= 3pu

Shove/win: +4pu
Shove/folds: +1pu
Shove/lose: -4p
Odds: 62:38 31:19 1.63:1 dog

1.63*[-4pu] +[4]pu = -2.52pu

He needs to fold 2.52 times of [2.52+2.63] = 5.15 for us to be break even.
2.63/5.15= 51% is the Fold Equity that we need.

actually 52.5% calcs worked

Posted about 1 year ago

WiltOnTilt

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2185 posts
Joined 10/2007

I used the trick for estimating fold equity for the 88 hand at the ~20 min mark. And it works!!!!!!

pu=225 675/225= 3pu

Shove/win: +4pu
Shove/folds: +1pu
Shove/lose: -4p
Odds: 62:38 31:19 1.63:1 dog

1.63*[-4pu] +[4]pu = -2.52pu

He needs to fold 2.52 times of [2.52+2.63] = 5.15 for us to be break even.
2.63/5.15= 51% is the Fold Equity that we need.

actually 52.5% calcs worked




BOOOOM Smile

Posted about 1 year ago

pokerspravy

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0 posts
Joined 12/2008

Is there a mistake in counting all the A2s-A9s and 45s-JQs in the example with our 4-bet all-in with 8s8d in time of 24th minute of the video? In the video there are 32+32 combos counted for these groups, but we have 8s8d, so we block SCs 7s8s,8s9s,7d8d,8d9d and As8s, Ad8d fom Axs, so there should be 6 combos less.

Anyway his 3-betting range will then have 136 hands instead of 142. He will call 59 hands of those 136, so 136-59=77 hands he will fold, which is 77/136=56.5% and that is still over 52.5% needed for us to have that shove +EV. So the result is the same, although +EV is little bit lower then in the video, if I am right

Posted about 1 month ago

WiltOnTilt

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2185 posts
Joined 10/2007



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