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

Mathematics of NL Hold'em: Episode Seven

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Mathematics of NL Hold'em: Episode Seven by WiltOnTilt

In episode 7, WiltOnTilt examines EV calculations which take bet sizing into consideration by examining hand histories featuring preflop, flop, turn and river play. This video also examines how often a bluff needs to be successful to be plus EV given various bet sizes. Finally, the concept of Continuation Betting is addressed with a big focus on board texture and bet sizing.

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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.

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wiltontilt bet sizing nl hold'em nlhe nl math mathematics of poker ipod friendly

Video Details

  • Game: nlhe
  • Stakes: Micro/Small Stakes
  • 65 minutes long
  • Posted over 5 years ago

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Comments for Mathematics of NL Hold'em: Episode Seven

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Cblanks

Avatar for Cblanks

102 posts
Joined 03/2008

awesome video. i feel that the last 10 or 15 minutes is vital to getting some players out of the micro stakes. some people are trying to create/balance a range when playing exploytably is far from optimal down at .5-1$ and lower

Posted about 5 years ago

WiltOnTilt

Avatar for WiltOnTilt

2402 posts
Joined 10/2007

thanks for the reply cblanks.

I would venture to say that playing exploitably is far more optimal at stakes up to 5/10 and 10/20nl as well. It's just that as you move up people tend to read hands better.

WoT

Posted about 5 years ago

frenchfish

Avatar for frenchfish

8 posts
Joined 06/2008

This serie is simply amazing ,what a fantastic job!
TYTYTY !!

Posted over 4 years ago

tmmoss

Avatar for tmmoss

48 posts
Joined 05/2009

Hey WiltOnTilt, Just wanted to let you know that almost a year after you posted this vid, instructors are still referring us and we are still watching. I'm a beginner in micro stakes and your series is helping me turn around a big down swing.

I had the coolest thing happen right after this episode. I was playing two tables and got pocket aces on both at same time. One against a loose fish, the other against a tight aggro. Potted both of them playing the hands very differently. It could have been in a movie. Thanks!

Posted over 3 years ago

DarkApfelstrudel

Avatar for DarkApfelstrudel

55 posts
Joined 07/2008

@ about 42:00
I think you donot point out that this 7.5% bluffraise frequency is the total probability that is needed to be better than the 500$ valuebet.
But it would better to say that he has to bluff with a frequency of 75 / (0,7*1000) = ~11% everytime he has a hand that is not calling.

Posted over 3 years ago

boske

Avatar for boske

1 posts
Joined 06/2009

Time Link to 00:13:17

why are you including the pot in the EV of a bet?

It seems to me this would make a bet "+EV" when you lose 60% of the time when called if the pot is big enough. While the bet will be losing you 1/5th (60%-40%) of your betsize in the long run.
You are also adding the pot to your EV for the times when you lose?

I've skimmed through the previous parts of the series, so maybe i missed something, but this seems like a bad way of presenting the EV of a bet.

very nice analysis other than that Smile

Posted over 3 years ago

PygmyHero

Avatar for PygmyHero

4246 posts
Joined 08/2007

boske, I might not understand your question as I found your wording confusing, but

why are you including the pot in the EV of a bet?


Because when we have the best hand we win the bet our opponent calls AND the pot.

It seems to me this would make a bet "+EV" when you lose 60% of the time when called if the pot is big enough.


Yes, of course the pot size affects our decision and EV.

You are also adding the pot to your EV for the times when you lose?


No he's not - you think that because of the order the terms are in.

Posted over 3 years ago

PygmyHero

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4246 posts
Joined 08/2007

Time Link to 00:54:00

Algebraic error or typo:

EV($40 bluff) = 80 - 8 = $72

As for the question about maximizing, without doing any more math we can see that we should bet as little as possible while maintaining maximum FE. So the answer is $34 (or $33.34 if he will literally fold to anything > 1/3 pot). EV is $73.20

Once our bet size drops the money we save by betting less is overcome by the fact that villain callo more hands (try even a $1 bluff bet in the formula to see this - EV is $69.70).

Posted over 3 years ago

Crash

Avatar for Crash

3 posts
Joined 09/2009

Time Link to 00:24:14

This doesn't make any sense as when we shove he will either fold or call our raise, we won't just call the 100 meaning the EV(call) shouldnt have anything to do with the EV(shove)

Doesn't this make more sense?

EV(shove) = x * EV(raise when he folds) + (1-x) * EV(raise when he calls)

where x = the % of the time he folds when we raise

x can then be derived from us knowing what percent of the time we have the best hand after he raises which is 90% and what percent of the time he will call with a worse hand which is 30% and us assuming that he never folds a better hand to a shove. 30 / 10 = 3 70 / 3 = 23.333
10 + 23.333 = 1/3

So then we find out EV(raise when he folds)

EV(RWHF) = 466 + 100 + 200
EV(RWHF) = 766

and EV(raise when he calls)

EV(RWHC) = x * (582) - (1-x) * (582)

where x = the percent of the time that he calls with a worse hand

EV(RWHC) = 0.3 * (582) - (1-0.3) * (582)
EV(RWHC) = -232.8

Then plugging it in to the EV(shove) equation

EV(shove) = (2/3) * (766) + (1/3) * (-232.8)
EV(shove) = 433

Or am I wrong?

Also thank you for a great series Smile

Posted over 3 years ago

Slowjoe

Avatar for Slowjoe

1111 posts
Joined 01/2010

This doesn't make any sense as when we shove he will either fold or call our raise, we won't just call the 100 meaning the EV(call) shouldnt have anything to do with the EV(shove)



First, WiltonTilt is calculating EV(RWHC). 30% of the time, you are going to win the pot + the call. You calc ignores this.

I think that your calculation of the villain winning is also incorrect. At the time of the bet, p(winning) = 90%, so p(losing) = 10%.

We assume he always calls when he is winning. p(winning when shove is called) = 30%.
=> p(losing when shove is called) = 70%. This is equivalent to the 10% above.

So, p(shove is called) = 10%/70% = 14.28%

My calc of EV(shove) = p(fold)*pot - p(call)*EV(RWHC) - p(lose)*100
= 85.7% * 766 - 14.28% * (-232.80) - 10
= $613.31

Posted over 3 years ago

Crash

Avatar for Crash

3 posts
Joined 09/2009

First, WiltonTilt is calculating EV(RWHC). 30% of the time, you are going to win the pot + the call. You calc ignores this.

I think that your calculation of the villain winning is also incorrect. At the time of the bet, p(winning) = 90%, so p(losing) = 10%.

We assume he always calls when he is winning. p(winning when shove is called) = 30%.
=> p(losing when shove is called) = 70%. This is equivalent to the 10% above.

So, p(shove is called) = 10%/70% = 14.28%

My calc of EV(shove) = p(fold)*pot - p(call)*EV(RWHC) - p(lose)*100
= 85.7% * 766 - 14.28% * (-232.80) - 10
= $613.31




Ok I mixed up the percentages it should be 70/10 = 7 30/7 = 4.28 10 + 4.28 = 14.28%.

Now I'm confused you are telling me Wilt is calculating EV(RWHC) but in your equation you use the number I derived with what according to you is a faulty EV(RWHC) equation? But lets assume you ment to use Wilt's EV(shove) equation as your EV(RWHC) equation

This is how Wilt explains EV(raise) which is a part of his EV(shove) equation:

EV(raise) = 582x - 582(1-x) where x is how often he calls with a worse hand

Which means 1-x equals how often he calls with a better hand the key word is calls which is why I used this as my EV(RWHC) equation to just add the EV of a call doesnt make sense

Then if you are correct that the pot should be in the equation doesnt this make more sense for EV(RWHC)

EV(RWHC) = 0.3(466+100+200+582)-0.7(582)
EV(RWHC) = 404.4 - 407.4
EV(RWHC) = -3

And why did you add p(lose) * 100, we are never calling when we are shoving so cant see why it should be in there

Also why did you subtract p(fold) * pot with p(call) * EV(RWHC) they are both representing things we gain even though we gain a negative amount, they should be added together or?

EV(shove) = x * EV(RWHF) + (1-x) * EV(RWHC)

EV(shove) = (0.8572 * 766) + (0.1428 * -3)

EV(shove) = 656.62 + -0.43

EV(shove) = 656.19

This is what I got with the changes, thank you for the respons Slowjoe and I would appreciate some more feedback =)

Posted over 3 years ago

Slowjoe

Avatar for Slowjoe

1111 posts
Joined 01/2010

This is what I got with the changes, thank you for the respons Slowjoe and I would appreciate some more feedback =)



Feedback: jeez, that's a lot of questions! I'm no guru, so I may be wrong etc. etc.

Still, it's fun to look at your questions. Can't address them all now, it's late. Let's see (at random):

And why did you add p(lose) * 100, we are never calling when we are shoving so cant see why it should be in there



We need to add this, because it comes into play when the shove is called. That hundred isn't in the pot, and it isn't in the Ev(RWHC) if you check. Gotta be in the math somewhere Smile

Posted over 3 years ago

Crash

Avatar for Crash

3 posts
Joined 09/2009

Feedback: jeez, that's a lot of questions! I'm no guru, so I may be wrong etc. etc.

Still, it's fun to look at your questions. Can't address them all now, it's late. Let's see (at random):



We need to add this, because it comes into play when the shove is called. That hundred isn't in the pot, and it isn't in the Ev(RWHC) if you check. Gotta be in the math somewhere Smile



Oh, missed that one but I would just add it to the EV(RWHC) meaning

EV(RWHC) = 0.3(466+100+200+582) - 0.7(682)

Same thing though =) thanks

Posted over 3 years ago

gadget

Avatar for gadget

40 posts
Joined 08/2008

I've got the same problem as boske!
Here's an example the way I see it:

say we've got a strong hand and that the if we just get called we are good 100% and if we get raised we are beat by 10% of his total range.

Assume his hand range is distributed as follows for a given bet:

folds 20%
calls 50%
raises 30% (we are beat a 3rd of the time here)

Here are the results for the given scenarios:

1)He folds: we win the pot,
EV(fold) = pot

2)He calls: we win the pot plus our bet (not actually our bet but the bet we win off villain equal in value to our bet).
EV(Call) = pot + Bet

3)He raises: 2/3 of the time we win the pot plus a stack and 1/3 of the time we lose our stack,
EV(raised allin)= (2/3)*(pot + stack) - (1/3)*(stack)

which results in the overall EV equation:

equation 1
EV(bet)=(0.2)(pot)+(0.5)(pot +bet)+(0.3)*[(2/3)(pot +stack)-(1/3)(stack)]

The pot variable in all terms except the negative term when our opponent has the best hand. So if we expand and simplify we can create a unique term for the pot with a coefficient of (1-(fraction of the time we're behind)), which in the example I've given is 0.1 (10%) or (0.3)*(1/3) in equation 1.

The shortened equation (equation 1 expanded and simplified) then looks like:

F=fold %
C=call %
P=pot value
S=stack value
B=bet value
Ra=% of the time we're raised and ahead
Rb=% of time we're raised and behind

EV(bet) = C*B + Ra*S - Rb*S + (1-Rb)*P

In Wilts example we were only behind 1.5 % so the pot term coefficient is 98.5 % which is near enough to 1. But if we are behind a significant portion of villains range then this needs to be taken into consideration.

Posted over 3 years ago




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