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

im watching this series i love it WoT thankyou for taking time to do these videos! im grasping basic maths but im just sooooooooooooooooo lost im watching taking notes but in the back of my mind im thinking how the hell am i going to incorporate all this into my game! im also thinking even if i could do these calculations id never player a hand because i would time out all the time!

im watching this series i love it WoT thankyou for taking time to do these videos! im grasping basic maths but im just sooooooooooooooooo lost im watching taking notes but in the back of my mind im thinking how the hell am i going to incorporate all this into my game! im also thinking even if i could do these calculations id never player a hand because i would time out all the time!

The key is doing enough of the work outside of your time at the table that when you are at the table your brain will have a better grasp of estimating the right moves. While I outline some tricks for trying to do some quick calcs at the table, it's not a necessity, and doing as much work as you can in your post-game analysis is where the real benefits are gained.

Good luck!
WoT

funnily enough after that post i went back a few episodes and started again and went through the ev calcs again and it started to click after pausing and rewinding a few clips! long long way to go though!

thanks

Time Link to 00:23:10

"and so we go ahead and do the algebra...do the subtraction...do the division here and we find that R(1) equals 11.2%"

After over an hour later,a breath of fresh air & a cup of coffee i think i may have the way you worked it out??

Could you please give a complete rundown on how you came to 11.2%..especially the algebra,subtraction & division part because i suck at this!! Thanks

Time Link to 00:26:10

Why are u adding two times 40 in what we win? It shouldn t be 40+15? We are risking 40 to win 55 thats the pot we shouln d count our call in the equacion.Right? We are making a decision to call or no, so it shouldn t go to the midle or call. Or i m making a mistake? Could u pls explain to me.
EV=0.55(40+15)-0.445(40)
EV=30.25-17.8
Ev=12.45

Regards and sorry for my bad english

Sorry didn t notice u already had posted. My mistake.

Here are my notes on this episode. There are a few errors in the video that I tried to correct so the notes should be right. If anyone see's any mistakes let me know.


Notes on Mathematics of NL Hold’em episode5 by WiltonTilt
By KGBMIKED

This episode is about Fold Equity Calcs.

5/10nl, 1000 stack. He is 15/10 he opens to 40 UTG +1 we have AsKs. We 3 bet to $120. We are determining if 3 bet was correct here or if we should have just called. . Blinds in pot = $15 He bet $40 we 3 bet to $120
What is his pf opening % from UTG+1
Klyka’s formula: What we need.
1. PFR% of the villain in question
2. generalize the preflop raise % for the people in front of villan
3. Villan’s 3 betting range
4. 4-Bet% and 5-Bet% are negligible (mostly true, somewhat player dependent)


Formula is: PFR% = P(raise)*R(2) + (1-P(raise)) * R(1) We are solving for R(1)







1. PFR% of villain in question is 10% from poker tracker.


2. P(raise) = Average PFR% of people in front of villain put into 1-(1-PFR%)^n (n = number of players)

2. 1-P(raise) = Probablity that it has not been raised in front of villain. Calculated by (1-PFR%) ^ (n = number of players)

3. R(1) = The frequency villain open raises (This is what we’re going to solve for)

4. R(2) = The frequency villain 3-Bets.



1. PFR = 10%

2. In order to find 1 minus the probability of a raise we must first determine the probability of a raise which is P(raise) = 14% we got this from poker tracker by finding the average of PFR from UTG+1 from the top ten players of this player type with the biggest number of hand samples. We then find the probability of a raise by
So if probability of a raise in front of us is 14% we then find the probability if there is no raise in front of us by using 1-P(raise) this looks like
1-.14 = .86. So 1-P(raise) = .86

3. We then determine R(2) which is his 3 bet%. We assume players this tight will typically only 3-bet QQ+ and AK. We put this range into poker stove and find it makes up 2.6% of hands. So R(2) = 2.6% or .026. This is the old way of doing it because in poker tracker 2 there was no 3-bet %. Using PT3 we are told what his 3-bet% is. So R(2) = Villains 3-bet %. In this example we are going to use the 2.6%.

4. Now we solve for R(1) which gives us his open raising range from UTG + 1.
PFR% = P(raise) * R(2) + (1-P(raise) * R(1)
.10 = .14 * .026 + .86*R(1)
.10 = .00364 + .86 * R(1)
.09636 = .86 *R(1)
R(1) = .112 = 11.2%
Therefore his open raising range from this position is 11.2% of hands. We put 11.2% of hands in the slider on poker tracker and find his range is
77+,A9s+, KTs+,QTs+,ATo+,KQo.
We then revise the range based on the player type of a nit. We think he is probably not raising hands like K10 as much as he is raising hands like 66 that aren’t in the poker tracker range. So our revised range is
22+,AJs+,KJs+,QJs,AJo,KQo This equals 11.3% of hands also but is a more reasonable range for this player.

So now we need to determine our equity with AsKs against the new range as 55.5%
So now we do an EV calc
Ev = (Our Equity) * (What we win) – (Villain’s Equity) * (What we lose)
Ev(Call) = .555 ($15+$40) - .445(40)
30.53-17.8 = $12.73
Ev(Call) = +$12.73



So how does the EV of a call compare to the Ev of a 3 bet, keeping in mind that he is a nit we need to find his calling range. We figure TT+ and AK. This puts our equity at 43.4%. Remember too that his calling range of TT+ and AK is only 3.5% of hands But then we need to take out the cards he can’t have in that 3.5% because we hold the AsKs. Now his calling range is only 2.5% of hands

So lets again look at the EV if we 3 bet and he calls
EV(3-Bet/call) = (Our Equity) * (Total Pot) – our Cost
EV(3Bet/call) = .434(15+120+120) – 120
Ev(3Bet/call) = -$9.33

So what about the times we 3bet and he folds

Ev(3bet/fold) = 40+15 = $55 every time he folds

So what is the EV of the 3bet calculated based on how often he is folding?

EV(3bet) = Call% * EV(3bet/call) + Fold% * EV(3bet/fold)

Ev(3bet) = (2.5/11.3) * -9.33 + (8.7/11.3) * 55

Ev(3bet) = -2.06 + 42.35

Ev(3 bet) = $40.29



So: EV of a call is $12.73 and the Ev of a 3 bet is $40.29. So we are gaining an extra $27.56 by 3 betting.

So we should be 3 betting here.

If the EV of calling compared to 3 betting was a lot closer then we would be tempted to call because there are a lot of bad hands he can call with and maybe we can stack him. But, the problem with that is if we don’t flop a pair it is going to be hard to know what he has and we are going to have to fold a lot of flops where we are better with just A high and we are not taking advantage of our EV because the EV assumes we get to see all 5 cards. If we 3 bet and he calls he will have to fold any hand he doesn’t flop a pair or have a pair. A lot of times we both won’t flop anything, especially when we both have AK but we will still take it with a c bet. When we are in position it gives us the chance to c bet or bluff when appropriate and see a free card when appropriate.

So in conclusion 3 bet is the best option because the EV difference compared to a call is so large but even if the EV of calling was a little bit higher then the EV of a 3 bet, we would still 3 bet because a 3 bet sets us up for the flop so much better. It also makes our fold equity better on the flop compared to a call.




Here is another scenario. We have As9s on button we open to 35 sb folds bb 3 bets us we call. Flop comes 10s5c2s. Villain c bets $115 he has a wide 3 bet %. We jam for $875. How often does the aggressive reg have to fold for this to be a +EV move?

So we need to first find villains 3 betting range. We figure 55+,ATs+,KJs+,QJs+,JTs+,T9s+,98s+,87s+,76s+,AJo+,KQo

Against this range we have a PF Equity of 42.4%

Then we need to figure out his C betting range.
We figure TT+,55,ATs+,KJs+,QJs+,JTs,9Ts,89s,87s,67s,AJo+,KQo (I don’t agree with this range , I think he c bets all pairs but this is what is used for the example. The reasoning he checks 88,99 is because he says a lot of good players do this because if they are called they don’t really know where they are at) Against this C bet range we have Equity of 42.3%.


Now we need to figure out his bet calling jam range. We figure:
TT+,55,ATs,KsQs,KsJs,QsJs,JTs,T9s We have 43.4% Equity against this Bet/Call range.

Then we need to find our fold Equity
Here is the base formula

EV = (EV(Fold) * x +(EV(call)) * (1-x)

X = % of times he folds

1-X = % of times he calls

So now we need to find out the EV when he folds
EV(heFolds)= 255+115 = $370

Now we need our EV when he calls (we’re going to use method two) which is:

EV(heCalls) = Equity * (total pot) – our shove
EV(heCalls) = .434(2005) – 875
EV(heCalls) = -$4.83 so we know if he never folds this is a –EV move


Now we can plug these EV’s into our base formula to figure out how often he has to fold for this to be a +EV move.
0 = (EV(Fold)* x + (EV(call)) * (1-x)
0 = ($370) * x + (-$4.83) * (1-x)
0 = $370x - $4.83 + $4.83x
0 = $365.17x - $4.83
$4.83 = 357.15x
x = .0135
x = 1.35%

So now we know he only needs to fold 1.35% of the time for this to be a +EV play.

So now we need to determine if he will fold over 1.35% of the time. We do looking at combos of his c betting range and compare it to his calling range.






So we determined his C betting range to be TT+,55,ATs+,KJs+,QsJs+,JTs,9Ts,89s,87s,67s,AJo+,KQo

The combos are

TT = 3 78s = 4
JJ = 6 67s = 4
QQ = 6 KQs = 4
KK = 6 QJs = 4
AA = 3 AQs = 3
55 = 3 AKs = 3
ATs = 3 AKo = 9
AJs = 3 AQo=9 KJs= 4 AJ = 12
JTs = 3 KQo = 12
9Ts = 3
89s = 3

Total C bet combo’s = 110

Then we need to find the combos of calling combinations which we said was
TT+,55,ATs,KsQs,KsJs,QsJs,JsTs,T9s

AA = 3
AA-KK = 18
TT = 3
55 = 3
ATs = 3
JTs =3
9Ts = 3
QsKs = 1
QsJs = 1
KsJs = 1

Total = 39


So total Combos of calling = 39 and total combos of c betting = 110

So he is only calling 39/110 = 35%
He is folding 65%
We only needed 1.35% fold equity to be a +EV play. So we know this is +EV but just how + is it?



We find this by plugging these numbers back into our original base equation of
EV = (EV(Fold) * x +(EV(call)) * (1-x)
X of 1.35% is how much he has to fold but now we have x = 65%.
EV(heCalls) = -$4.83
EV(heFolds) = $370
He is only calling 39/110 = 35%
He is folding 65%

EV(Total) = 370(.65) – 4.83(.35)
EV(Total) = 240.5 – 1.69
EV(Total) = +$238.81

So this is a very good spot to Shuv because almost all of our Equity comes from fold Equity.

Here is something I found in the notes under this video that will be useful in the future:
“By the way I generally find this a lot easier to just look at in Stove. For example in this problem we could just have:

Enter the villain's PF 3-bet plus cbet range into Stove. IIRC this was ~10% of all hands.

Then enter the villain's PF 3-bet plus cbet plus call shove range into Stove. I think this was about 3.8% of all hands.
In other words, he's calling off 3.8%/10% ~38% of hands and folding the other 62% of the time.


Thanks go’s out to PygmyHero for this time saving trick



So here are some general rules about fold equity

1. The more money in the pot the less he needs to fold for your shove to be profitable. Also if you shuv half pot, it only needs to work about half the time.
2. The more money in the pot the less he will fold on average. So if you are only shuving half pot then he will call more
3. The more equity you have in the hand, the less often he needs to fold to reach profitability. This is why Semi bluffs can be so profitably
4. the wider his range, the fewer hands he has to continue with and the more fold equity you should have. If you tried this move against a tighter player this will not be as profitable because his range of hands he is c betting to what hands he is calling a shuv is much closer then someone who c bets a wide range and only calls a slim range.



Here is another Example


We are in the cutoff with Ah9h board on the turn is 10d6h2s5h pot is 120 villain bets 80 we are in position and we shuv for 800
How often does he need to fold in this situation to make the jam +EV
We have 12 outs and we are doing this like we were at a live game so we use the rule of 2 which gives us 24% Equity

Fold Equity Calc is EV = (EV(fold)* x + (EV(call)) * (1-x)

1. So EV of a fold is $200
2. EV of a call using method two is .24(1720) – 800 = -$387.20

Now we need to solve the Fold equity Calc set to break even point of 0

0 = 200x -387.20 -387x
X = 66% So he needs to fold a pretty large amount of the time. I did it again if he folds 69% of the time and it came out to +$17.97. So this is a pretty high variance play and we might want to consider another spot.

Lets see how often he will actually fold.

Lets say he is a 14/12 and he PFR and c bet the flop and is now c betting the turn

The c bet turn range of hands I put him on is.
TT+,66,55,22,7h8h,99,88, ATs. This is 3.9% of hands in pokerstove (I could add in more bluff hands but I didn’t because I’m doing this as a worst case scenario.) Also you need to take out combos that have Ah,9h,Td,6h,5h,2s. Because they are cards that can’t be in his hand and if you just click say 99 it will say there are 6 combos when there are really only 3.


His Cbet turn/call range is TT+66,55,22,7h8h,AT. This is 3.2% in pokerstove.(He may or may not call with AT but I left it in because we already took out 7 combos of AT because there are only 3 A’s and 3 T’s he can have. Not 4 of each. (16-9=7)




So he is calling 3.2%/3.9% of hands which means he is calling 82.1% of the time
He is folding 17.9% of the time. So he needs to fold 66.2% of the time and he is only folding 17.9% of the time. So how much are we losing by shoving


Now we plug in the numbers

Fold Equity Calc is EV = (EV(fold)* x + (EV(call)) * (1-x)
EV = $200(.179) - 387.20(.821)
EV = 35.8 – 317.89
EV = - $282.09

(I think this is right but not positive. Let me know if you see any errors.)

So we are losing -$282.09 every time he shove here on average.

great series, made me work to calculate things, but this is very benefitial for the future

I'm somewhat interested in the derivation of this formula if there's a thread you can point me to.

That said, I'd be interested to know if you think this information is now obsolete given all the data HEM makes available to us.

Could you answer this please.

Could you answer this please.

I looked back in my notes from 2008 when this series came out and I couldn't find any additional info on the derivation of the formula.

I suspect that it would be better to use the HEM "range" stats such as "3bet range" and "4bet range"

I have a question with regards to the [1-PFR%]^n part

In the example you use Jared's figure of 14% for an average UTG open raising range for his stake. If we were on the button in a 6max game, would we need to use a figure that is a mean of the avarage UTG,UTG+1,MP and CO ranges for the stake, or is that the function of the '^n' part?

I'm not mathematcally minded, so if this question isn't clear, please say.

I have a question with regards to the [1-PFR%]^n part

In the example you use Jared's figure of 14% for an average UTG open raising range for his stake. If we were on the button in a 6max game, would we need to use a figure that is a mean of the avarage UTG,UTG+1,MP and CO ranges for the stake, or is that the function of the '^n' part?

I'm not mathematcally minded, so if this question isn't clear, please say.

in 2008 we didn't have the nice positional stats we have now. The best thing now would be just to pull up your HEM and get the positional vpip/pfr/3bet.

TBH Its been so long since I've looked at or thought about his formula I don't think I can give you a meaningful answer to your question besides just using the positional stats now

That was quick, thanks Wilt.

In a previous post you mentioned that this video was pre HEM as it is now. Does that mean that I should focus more on the fold equity part of the video, and leave the first part to HEM?

That was quick, thanks Wilt.

In a previous post you mentioned that this video was pre HEM as it is now. Does that mean that I should focus more on the fold equity part of the video, and leave the first part to HEM?

yes definitely

Damn it was like living in mideival times before PT3 came out. I started watching the first 5 minutes before I just skipped past that part since PT3 does it now.