# 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.

#### 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
• 65 minutes long
• Posted over 5 years ago

## Comments for Mathematics of NL Hold'em: Episode Seven

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61 posts
Joined 12/2011

I dont understand how this bluff calculation makes sense? Isnt it always the same as villains pot odds? And i can calc odds faster then this formula..!?

So for example if there is a 100 dollar pot and i bet 50 oponets odds for call are 1:3 he needs to win at least every 1 out of 3 to be 0 EV and the odds doesnt change when i make the bluff so I get same odds.
If i put it into formula its 100x - 50 + 50x = 1:3 !?
Are there any exceptions or is there a mistake in my thought process?

#### WiltOnTilt

2402 posts
Joined 10/2007

I dont understand how this bluff calculation makes sense? Isnt it always the same as villains pot odds? And i can calc odds faster then this formula..!?

So for example if there is a 100 dollar pot and i bet 50 oponets odds for call are 1:3 he needs to win at least every 1 out of 3 to be 0 EV and the odds doesnt change when i make the bluff so I get same odds.
If i put it into formula its 100x - 50 + 50x = 1:3 !?
Are there any exceptions or is there a mistake in my thought process?

It's not the same as villain's pot odds because of the risk reward. You risk some amount to win what's in the pot. From villain's perspective, the pot is now bigger because of your extra money.

The formula is meant to figure out how often your bluff needs to work to break even.

if you bet 50 into a 100\$ pot, your opponent is getting 3:1 (win 150, risk 50). That means he needs to win 1 time out of 4 to break even (not 1 time out of 3). Remember 3:1 means 3 instances for every 1 instance... so 4 total instances.

The formula is just for getting practice and showing the math behind it, but it's probably worth your while to commit some common bet sizes to memory, like 1/2 pot, 3/4 pot, pot bet, 2x pot, etc

If x is how often he folds and we want to find the break even point, we set to = 0, so for your half pot example:

0 = 100x - 50 (1 - x)
0 = 100x - 50 + 50x
0 = 150x - 50
50 = 150x
x = .333333 that means for us to show a profit, villain must fold 1/3 of the time when we risk half pot.

This is different than his pot odds. He has to call 50 to win 150, which means he can lose 50 three times for each one time he wins 150. That means out of 4 total instances, he must win 1. 1/4 = 25%.

Hope that helps!

61 posts
Joined 12/2011

Ah thx a lot i calculated the Pot Odds wrong my mistake -.-
Didnt add his call to the overall pot.

But i think i found a shortcut now, by calculating pot odds wrong by forgetting about his call...

If you take the

[amount villain needs to call (your betsize)] : [pot at the moment]+[your betsize]

for this example its 50 : 100 + 50
50:150
1:3

Lets try one more exmple if i got 100euro pot and i bluff 200euro

200 : 100 + 200
2:3

0 = 100x - 200 + 200x
0 = 300x -200
200 = 300x
2:3

I guess you can do your method also very fast and use it easy while you play.
you think this one is also correct?
Cause i can do it like that faster in my head...

EDIT: Ah i guess you dont calculate it at all cause you know it for 1/4 1/2 pot 2x pot anyways

#### WiltOnTilt

2402 posts
Joined 10/2007

I think you might be right but I think the way you are expressing what you mean could confuse you (or me lol) later. Keep in mind, pot odds isn't the same thing as calculating how much you risk in order to bluff. His pot odds will contain your bluff amount, but when you bluff you're only winning what is in the pot.

Also keep in mind that using the : to express 2 numbers is read as a ratio, not the same as dividing with /

0 = 100x - 200 + 200x
0 = 300x -200
200 = 300x
2:3

is a little misleading because odds ratio of 2:3 would convert to a 40/60 situation (in %) however what you're really calculating is how often he needs to fold, and to do that you'd say 2/3 or .66666

61 posts
Joined 12/2011

I just write 2:3 although i mean 2/3 cause im used to it from school we never wrote / for divide just always : thx for that advice though...in my head its correct but your right when its gettin more complicated later i guess i might make mistakes

I will keep that formula in mind not so complicated anyways.
Calculated it for some betsizes that i can think of it ingame very fast.
1/4 Pot = 16.6%
1/2 Pot = 33.3%
3/4 Pot = 42.85%
Pot = 50%
1 1/2 Pot = 60%
2x Pot = 66.6%

That should help =)

Thx a lot for that series rly helped me a lot, to get a understanding of the basic maths in the game.

Im grinding at nl50/nl100 at the moment with good winnings and 0 maths.
I play on a pretty small platform so i have over 10k hands with some players and pretty solid stats. So to max. exploit them and also to get more confidence in my game i decided to do a lot of maths the next 2-3 Month.

Finished your series now i think i will watch some Episodes again cause i guess its important to know the basics quick with no much thinking anymore...

Can you PLEASE give me Tips which series would good for me to continue to improve my maths. I want2be able to construct good solid ranges against those oponets i have so many stats against =)

I heard that running the streets by shuttle is very good but is pretty advance isnt it!?
Also heard that sthief09 and 2fouroffsuit have some good maths vids?

I hope i dont annoy you2much, thx 1 more time for your series and your answers your awesome man cant thank you enough!!!

#### WiltOnTilt

2402 posts
Joined 10/2007

Ya definitely check out josh's (sthief's) videos. He does great stuff. When you're done with that, and you want some more theoretical stuff, you can check out bellatrix's series that goes over the book Mathematics of Poker (which is pretty heavy stuff).

Best of luck!

#### Homelesscoin

7 posts
Joined 11/2011

I dont understand. I am a big beginner at this, so I only try to explain my taughtprocess, because I dont see where I am wrong.
The read is that for 90% of the time I have the best hand and for 10% of the time I have a worse hand.
If I shove I will always get called in the case of the 10%.
If I shove I will force him to make a decision in the other 90% of the hands that I beat him. In that case he will decide to fold 70% of the time and decide to call 30% of the time. He calls 30% of the time with a worse hand. So 70% of the time of the 90% of the time I have the best hand, he folds and I win the same amount as if I had called. 30% of the time of the 90% of the time I have the best hand, he calls and I win the shove-amount (pot + call amount + his remaining stack). In the shove situation I will still lose 10% of the time and lose in addition of the 100 call amount, the amount of his remaining stack.
So shoving is more +EV than calling because.
If you use WIlts formula you always in every pot situation come to the conclusion that he has to call more than 50% procent of the time with a worse hand??? Regardles of how many times you in fact have the best hand. THe percentage of the times you have the best hand is not considerated in the formula. If you use my logic above you win 63 of the time the pot, 27 of the time the shoveamount (the situations where you have best hand) and you lose 10% of the time the shoveamount. The difference is that you will lose more dollars because of losing more when your the dog (10%), but winning more (90%) when you are ahead. When you are ahead you can win 27 of the time the shoveamount. I my quick calculation I have a EV of +800 when shoving and more than the +600 when just calling.

#### Homelesscoin

7 posts
Joined 11/2011

Again I am probably awfullly complete not getting the point.

In a extreme example when I make a bad read and I fact he has the best hand 99% of the time. Regardless of my read he will call my shove 99% of the time.
If I shove I lose money, its easy to see.
In the 1% of the times I have the best hand. In this case if I follow Wilt formula and I make my opponent call 80%of the time with his worse hand (more as the required 50) and fold 20% of the time with the worse hand.
So with my shove I lose all my stack 99 procent of the times, I win 80% of the 1% of the time I have the best all the shoveamount and I only win pot 20% of 1% of the time I have te best hand.
So I made him call more than 50% of the time I have the best, what is good and wins me money. But my shove is hugely -EV in this case! And if I follow Wilts formula it is considerated a good shove???

#### Homelesscoin

7 posts
Joined 11/2011

Now I am getting pretty sure the formula is wrong. Another example:
If I know I win the hand 100% of the time, because 1) I have the nuts 2) I have a 100% solid read of even I saw his cards then everybody knows that the best move even if he maybe want call is to shove of to raise.
But in his formula if I shove, EVshove= EVcall+582X-582(1-x). My EVcall is better than in the example I have 90% best hand.the same, because I win the hand all the time. If you shove and the read is that d he will call 30% and fold 70% of the time, my EVcall would be the same because that is what I am winning no matter what and in addition I win the shoving amount if he makes the call.The more he calls the more I make money. The breakpoint isn't 50% it is 0%, I want to make him call as much as possible if I have the nuts. To fill in the amounts in formula.
EVcall(100%) is 766. EVshove when using formula with 0.3 is 533? Less then EVcall? impossible
I think the general formula should be (I made a shot ad it, I think my reasoning is correct, but my formula still may be not completely correct)
EVshove= 90% (30%EV(shovebesthandandvillaincall)+70%EV(shovebesthandandvillainfolds))+10%(100%EV(shoveworsehandsandvillaincalls)+0%EV(shoveworsehandsandvillainfolds))
That seems logic and explains bluffing as well. You can put variables in stead of the percentages, and then you can explain a lot. If you have 100% best hand you only the first part counts. If you have 0% the best hand only the second part counts, and you have -EV if villain calls, only +EV if you make him fold. If you have something in between, you EV will be a the best if you make him call when you have the best and make him fold when you have the worst.
Calculating the percantage you should shove in those situations is to difficult for me, but it is deffinetly NOT 50% every time, every pot as the Wilt formula in fact suggests!

#### Homelesscoin

7 posts
Joined 11/2011

EV(S)= X * [ Z EV(SBVC)+ (1-Z) EV(SBVF) ] + (1-X) * [ Z EV(SWVC) + (1-Z) EV(SWVF) ]

I am not sure to use Z in the second part or use another varialble.
I think the fold and call percentage stays the same for villain regardless if you have the best or worse. (so the example in my previous post could be corrected)

Can someone build on this new formula and try to know the percentage we have to shove or just saying I am awfully wrong so I stop wasting my time

#### WiltOnTilt

2402 posts
Joined 10/2007

The idea is that it doesn't matter what happens when you bet and he folds, the only thing that matters is what your EV is when he calls***. The reason for this is because if we have the best hand 99% and bet, and he folds, the result of the bet doesn't really matter, especially if we could play it a different way (such as check/call). So we only focus on the times where it goes we bet and he calls. We need him to call with a worse hand 50% of the time or more for our bet to be good.

The comparison isn't how often he calls vs how often he folds. The comparison is when he calls, how often do we win or lose.

*** The above is a bit of an oversimplification because there are times where you might think you have the best hand, yet you bet to prevent yourself from being bluffed, so you might make a -ev value bet (he calls you with worse < 50% of the time) however you are in a position where you cannot make a +EV river check/call, so instead you "block" bet to prevent yourself from being bluffed. This is outside of the scope of these videos though, i'm just including it here for completeness.

#### Homelesscoin

7 posts
Joined 11/2011

thank you, still not getting it completely, but I will get it eventualy. I saw the 8episodes and will watch them again. Its the only part I am not fully getting, but maybe is because of my english.

#### YongGook

177 posts
Joined 01/2012

7:00

Talking about what our bet size would be. For me it would depend heavily on what the action was before it got to the flop as to what I thought the villain would have. Without this information I found myself using an educated guess. Flop and turn information is really important in these kind of situations right?

#### WiltOnTilt

2402 posts
Joined 10/2007

7:00

Talking about what our bet size would be. For me it would depend heavily on what the action was before it got to the flop as to what I thought the villain would have. Without this information I found myself using an educated guess. Flop and turn information is really important in these kind of situations right?

Sure, but hopefully all of the info under the 'reads' section was enough to make a determination of how much we want to bet, given that we want to bet. Of course more information is always better, but sometimes I have to simplify the hands/situations in order to highlight how to do the math...so just assume that we are on the river and the reads are accurate.

#### YongGook

177 posts
Joined 01/2012

Thanks

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