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

Wow,

I'm impressed with how you elaborate on the formula. I didn't realize myself how much there was to be said about it.

Two points that I would like to point out:

1) The PFR% to plug into the formula is his PFR% for that particular position. So if he's playing 15/10 in general, probably we should plug a slightly tighter PFR% into the formula.

2) The 1-[1-pfr%]^n formula for P(raise) assumes that all the n players in front have the same pfr%. That is a simplification that probably shouldn't cause too much inaccuracy. One could use the formula 1 - pfr%(1)*pfr%(2)*[...]*pfr%(n) as well.

Excellent video!

Klyka

Is it just me or is the whole "Determine Villain's Open Raising Range" formula completely and utterly pointless?

First of all it's not valuable or good for a better understanding of NLHE at all, mostly becuase it's incorrect, villain will change his openingrange depending on mood, tableconditions, precense of ratolher etc.

And the only difference between this and just taking the pfr percentage directly is that he will have somwhat lower pfr then openinraise because people will have opened in front some times and he will not 3bet all hands he would have opened with. So in that sense this formula will be more reliable, but that really doesn't mather at all since you made approximations about openraises in front and his 3-betting percentage anyway. And the formula doesnt take into account how the player responds to limps in front of him, he might tighten up or loosening up his raising percentage depending on that too.

And last but not least, you used his overall pfr, not the pfr in the UTG+1 seat. There's probably a significant difference between those, even bigger if he would have been in the cut-off or the button. This was probably just a misstake by your part but it changes the result dramaticly.

The fact that you used the overall pfr and not his pfr from utg+1, and the fact that you used approximations about the openingpercentages in front of him aswell as his 3-bet percentage makes the result vastly incorrect. You could aswell just filter PT for the amount of players at the table and look at his pfr from utg+1 and just add a percent or two and get a more reliable result. But that's not really the big problem with the formula. The big problem is that his openingrange range will not be consistent, it will change depending on many factors. Using PT stats and formulas for this is not the way to go. If you know the player and now how he plays, what mood he's in all the other variables you get a better result just using logic and put him on a range you think he's opening with and gow with that instead of that pointless formula.

This got quite long and sounded more harsh then I intended it to do. I haven't really followed your series but I like what I have seen (except said formula) and I actually think I will watch it all when I have time. You're doing a great job and I know that many pokerplayers out there really should take a look at your series for their own best. But I just reacted on that you spent the first 20 minutes on this video on such a pontless formula.

First of all it's not valuable or good for a better understanding of NLHE at all, mostly becuase it's incorrect, villain will change his openingrange depending on mood, tableconditions, precense of ratolher etc.

This does not make the formula incorrect. It's a general formula for a general figure, just like PFR% is a general figure in the first place.

The point is not that you should use this formula to come up with R(1) and stick with that number until death. The point is to show how PRF% is skewed by a few factors, and that it can, contrary to what many people believe, not be applied directly to a situation where the player open raises. The formula shows the relations between different factors and how they come together in the figure that we usually call PFR%.

This does not make the formula incorrect. It's a general formula for a general figure, just like PFR% is a general figure in the first place.

True, I might have used the word pointless" a little recklessly,, sry about that. But the truth is that you most likely get a much better number by looking at the opponent, his tendencies, his flow atm and the table and just use common sense to come up with a range. And use that range to determine if it's better to repop of flat AK.

Everything the forumla does is take into account that the pfr% from one possition will not be the same as the openingraise% from that position because of the fact that people can open in front, it doesn't even take limpers into account (even though it will make very little difference, but approximating pfr with openingraise from utg+1 or using this formula will make very little difference to). And spending 20 minutes or 1/4 of the video on it (and missapplying it) is, imo, pointless.

One could use the formula 1 - pfr%(1)*pfr%(2)*[...]*pfr%(n) as well.

No, I got this one wrong. The alternative formula is a bit trickier than that. Never mind though.

I agree I probably shouldn't have spent as much time as i did on the formula, but i don't think it's pointless. Once I got into explaining each part, I wanted to make sure it was fully understandable (at the cost of time/redundancy). A better approach might have been saving everyone's time and just explaining once through what each value of the formula represents and letting people plug-n-play. However in terms of the usefulness of the formula, like many of the poker math topics, the formula takes some estimation and guess work to plug in values. I don't think that makes it flawed, at least in comparison to other math topics like plugging in how often you think someone folds into the fold equity calculation... it's an educated guess, just how using the preflop raise% from PT is a (more accurate, imo) educated guess that gets refined through this formula to pull out a range.

You're right though I should have better explained about using his positional PFR%, but I do encourage you to go look at your PT DB and see how much a really tight player's opening range changes by position. I'll give you a hint... most do not(at least at 6max). However for purposes of completeness (and if someone wanted to do this formula for a more laggy player), you're right I should have mentioned using that particular figure.

One reason this series is very difficult to create is because I'm trying to not only make it accessible to a wide range of people (in terms of their Math backgrounds) but I'm also trying to use somewhat real life examples so even if people don't want to sit down with a pen and paper to figure this stuff out, they might learn something about situations they encounter. At least, that's the goal. Whether I succeed or fail in those things is ultimately up to all you guys.

Thank you klb for the feedback though, I do really appreciate hearing what everyone has to say -- good or bad.

Aaron

You're right though I should have better explained about using his positional PFR%, but I do encourage you to go look at your PT DB and see how much a really tight player's opening range changes by position. I'll give you a hint... most do not(at least at 6max).

Though, this is partially because of the factors that are incorporated in the formula. Even if a player in fact does loosen up in late position, this will not be entirely visible in his PF% stats. This is because P(raise) is bigger in later position, simply because there are more players who can raise in front (the n value is larger). A larger P(raise) means that the PFR% figure will be more dependent on R(2) - the 3-betting frequency - than on R(1). Since R(2) is smaller than R(1), for all sensible players at least, this means a smaller PFR%.

This means that a looser play in the late positions may yield the same PFR% figure as a tighter play in early positions.

So full of informations... my head is about to explode !

I think some homework/practique sheet could also help those who want to work on it. Do you think about putting some homework for peoples who wish to ? (I mean like 3-4 Questions with calcul to make on something like word.doc or straightforward in forum text.. and we discuss about the answer week later)

Will do my best to incorporate theses thing in my play, thanks

Squishee, perhaps at the end of the series i'll see what i can do... as it is making videos like this takes quite a long time... like this one took me 20+ hours from start to finish... so once I'm a bit less strapped for time I'll see what I can do to get you guys some homeworks.

WoT

wow, I didnt expected to take so long time to do a video like this.. (ok this one lasted 1h20min) then I clearly understand you

yea it takes a long time to not only draw up examples but make sure the examples you think up actually show something somewhat useful, then creating the screen shots, putting what i want to say on slides, then actually trying to say it in a way that will actually make some sense...and that doesn't even count all the time spent by Chuck (danzasmack) helping me check and recheck my math haha...

i like doing it, it just takes a looongggg time.

WoT

I was writing down your p calculations for fold equity and something came to me that seemed simpler to me.

In general if we are a 3:1, thet means we have 4 situations (3 negative and 1 positive).

Our 1 postive cancels out 1 of the negative, leaving of course 2 negatives out of the 3 negatives.

So we need him to fold to cancel out those negatives.

So if he folds 2 out of the 3 negatives the 3 negatives are cancelled out.

2/3 is 66%!

I'm a logical rather than mathematical person so this could be full of holes.

But it seems to be interesting at least.

If were a 4:1 dog we need him to fold 75% of the negative times.

If we're even money, 1:1 we don't need him to fold at all.

If he's a dog 1:2, we have to fold for him to win the pot.

Seems logical!

Now this doesn't take into consideration what's in the pot, only that we win it.

So if we only try to win it when we have the correct pot odds we should be ok!

Could you run some math on this idea and see what floats to the top?

May be my flash was a brain cramp.


Thanks!
sudic

Really fantastic series. That "shortcut" of Grunch's that you showed at the end was extremely helpful and powerful.

Thanks so much for this series, Wilt. It's really helped my thinking at the tables.

min 26 - isn´t our EV only 12.73?

min 26 - isn´t our EV only 12.73?

can you elaborate on why you think this? i just redid the math and it seems right?

WoT

min 26 - isn´t our EV only 12.73?

can you elaborate on why you think this? i just redid the math and it seems right?

WoT

EV=(our equity) * (what we win)- (villain´s equity) * (what we loose)
EV= 55.5% * (40+15) - 44.5% * 40
EV= 0.555 * 55 - 0.445 * 40
EV= 30.525 - 17.8
EV= 12.725

or

EV= (our equity)*(total pot) - cost of our call
EV= 0.555*95 - 40
EV= 52.725 - 40
EV= 12.725

to me seems wrong to count our call in "what we win"

Anyway "Math of NLH" are best poker videos I have ever seen. Thx a lot for them.

Wilt - First, great series. Really gets the critical thinking juices flowing.

My question is a bit on theoretic side. In the video you discussed how when the EV(Call) and EV(3-Bet) are close, you should go with 3-Bet because of the very real and accurate issue of either not getting to see all 5 cards or folding the best hand on the river. Makes perfect sense but from a contrarian standpoint can it be said that when evaluating EV(Call) and assuming you have > 50% equity that there exists "implied money" which will go into the pot postflop that would not exist in 3-betting since 3-betting derives most of it's overall EV from villain folding? I guess what I am trying to say is that wouldnt it be more correct to make estimates or even adjust the equity to account for the fact that some % of the time more money will go into the pot postflop when you call and that hero has a > then 50% claim to this "future money" since he is ahead of villain's range?

I am also curious to hear the response to Luzhin64's post above because I thought the same thing when I was watching the video.

SugarNut made me aware of an algebraic error I made in this episode around the 45 minute mark. it doesn't drastically change the result or spirit of the calculation, but it is wrong.

So here's how it is in the slide:

EV(total) = 370x – 12.85(1-x)
EV(total) = 370x – 12.85 + 12.85x
EV(total) = 382.85x – 12.85
12.85 = 382.85x
x = 12.85 / 382.85
x = 3.4%


Here's how it should be:

EV(total) = 370x – 12.85(1-x)
EV(total) = 370x – 12.85 - 12.85x
EV(total) = 357.15x - 12.85
12.85 = 357.15x
12.85 / 357.15 = x

x =~ 3.6%

The error occured on line 2 where i distributed 12.85(1-x) incorrectly. Sorry about that guys.

Also, Luzhin64 above who posted back in march, it looks like he is correct as in the video I somehow added in an additional $40 to my equation. So around the 26 minute mark the incorrect equation is:

EV = [Our Equity] * [what we win] – [Villain’s equity] * [what we lose]
EV(call) = 55.5% * (40 + 40 + 15) – 44.5% * (40)
EV(call) = 52.73 - 17.8
EV(call) = 34.93

and the correct way is is how Luzhin64 wrote it above:

EV=(our equity) * (what we win)- (villain´s equity) * (what we lose)
EV= 55.5% * (40+15) - 44.5% * 40
EV= 0.555 * 55 - 0.445 * 40
EV= 30.525 - 17.8
EV= 12.725

I'm not sure how that extra $40 crept into the equation. Must have been a typo or absentmindedness. How embarassing, sorry guys! At least the faithful DC'ers found my mistake and got it corrected for everyone else. Also at least it didn't hose up the process, just slight errors in calculation... so as long as you've learned the process you'll probably calculate correctly :-)

Thanks
WoT

Wilt - First, great series. Really gets the critical thinking juices flowing.

My question is a bit on theoretic side. In the video you discussed how when the EV(Call) and EV(3-Bet) are close, you should go with 3-Bet because of the very real and accurate issue of either not getting to see all 5 cards or folding the best hand on the river. Makes perfect sense but from a contrarian standpoint can it be said that when evaluating EV(Call) and assuming you have > 50% equity that there exists "implied money" which will go into the pot postflop that would not exist in 3-betting since 3-betting derives most of it's overall EV from villain folding? I guess what I am trying to say is that wouldnt it be more correct to make estimates or even adjust the equity to account for the fact that some % of the time more money will go into the pot postflop when you call and that hero has a > then 50% claim to this "future money" since he is ahead of villain's range?

I am also curious to hear the response to Luzhin64's post above because I thought the same thing when I was watching the video.

79s, yes there's merit to what you're saying. It becomes a lot more difficult to calculate though, but certainly there are situations that can arise where that would be a very real concern. One type of situation that comes to mind immediately is a spot where you are playing against an aggressive bluffy player and you've got a strong hand on the turn where many draws are present and based on how the hand went down you suspect your opponent is on a draw. Raising might be correct on paper from an EV perspective, but there's also some "hidden" value in just calling the turn and snapping off river bluffs on a blank since you can (hopefully) accurately determine which river cards helped him and which didn't, and because of our read we have reason to believe he will bluff no matter what, so we can make more correct calls and folds. The problem is that becomes pretty difficult to quantify, but on the other side of the coin is that it's also tough to quantify the benefit of our "aggressive image" by constantly choosing the more aggressive option when the EV of a passive action vs aggressive action are close.

You bring up a good and valid point though, thanks for posting.

WoT

At 28 minutes you are determining villains' range for a call of our 3bet, deciding that such a range would be TT+ and AK. You go on to say that this accounts for 3.5% of all holdings. What confuses me is that in all previous episodes you have taken pains to point out that we should remove from our opponents range any possibilities that involve either the community cards or our own pockets. Here we have AsKs, so surely we should remove options involving these cards from his range: If we do that then his calling range is more like 2.5%.

This in turn means that we will collect the pot 77.7% of the time, not the 69% stated in the video. Our EV is then $40.65, not $34.89.

Of course I could be the gibbering idiot so I'm a little confused as to what I should be doing. Please enlighten.

spiral, nice catch

Around the 48 minute mark, you list the combinations of hands. If you hold the As, there is only 9 ways to make AKo, AQo, AJo. Also, there are only 12 combinations of KQo regardless.

i like the video, however i think the formula of PFR% is still somewhat wrong...?

isn't it missing out on the percentage villain raises when there are limpers in front of him?

i think the formula should be:

PFR% = 3betting + open raising + raising limpers!

Thank you a lot WiltOnTilt. I thought I knew pretty much about maths and so on but these videos have been a good eyeopener. I believe that my view of certain opponents acts are now more clear to me. Hopefully I can turn my play from break even to winning.

Yours Madaa

I really enjoy the series... however i hate math and suck at it... but here is a hand where I am trying to find out my FE... and I would really appreciate it if someone could check my math and make sure im doing things right...
http://www.pokerhand.org/?3384820
ev(fold)=60
ev(call)=.40 * 204 - 83 = -1.4
ev(total)= 2.3% which is how often he needs to fold... is this right???

Now I'm not certain if the number of combos he has/is calling with is correct I was more concerned with getting the whole math aspect of this correct than figuring out approximate ranges, however I do feel the ranges are fairly close... I was more focused on getting a number of combos to work with and ive already spent an hour on this problem so i might have taken a shortcut
AKo, AQo, A8s, K8s, T9s, T8s, 86s which is ~45 combos.
then his call combos i believe are:
22, 66, 88, 99, TT, JJ, QQ (im going to say he 3bets KK, AA preflop)
so thats 23 call combos
So he calls 51% of te time and folds 49% of the time... and so this is a +EV play because he is folding > 1.4% ?!?? for some reason that just doesn't seem right... the 1.4% needed for him to fold that is...

so now we plug that into our formula etc
ev(total)= 60x - 1.4(1-x)
ev(total)= 60(.49)-1.4(1-.49)
ev(total)= 60 * .49 - 1.4 * .51
ev(total)= 29.4 - 0.714
ev(total)= $28.69

So that means by shoving this turn we are making $28.69 in ev?

Please help me I am uncertain how right/wrong this is and would love some advice...

Thanks,
wems

SugarNut made me aware of an algebraic error I made in this episode around the 45 minute mark. it doesn't drastically change the result or spirit of the calculation, but it is wrong.

So here's how it is in the slide:

EV(total) = 370x – 12.85(1-x)
EV(total) = 370x – 12.85 + 12.85x
EV(total) = 382.85x – 12.85
12.85 = 382.85x
x = 12.85 / 382.85
x = 3.4%


Here's how it should be:

EV(total) = 370x – 12.85(1-x)
EV(total) = 370x – 12.85 - 12.85x
EV(total) = 357.15x - 12.85
12.85 = 357.15x
12.85 / 357.15 = x

x =~ 3.6%

The error occured on line 2 where i distributed 12.85(1-x) incorrectly. Sorry about that guys.

You distributed correctly in the video.

The check works out....

0 = 370(12.85 / 382.85) + (-12.85)(1 - (12.85 / 382.85))
0 = 370 * 0.033564059030952070001305994514823 + -12.85 * 0.96643594096904792999869400548518
0 = 12.4187018414522 - 12.4187018414522
0 = 0

if your ev calculation is EV = [EV(fold)] * x + [EV(call)] * (1 - x)
Then distributing -12.85 would yield a calc that looks like this ..
EV = 370x + [(-12.85)(1 - x)]
= 370x + (-12.85 + 12.85x)
= 370x + 12.85x - 12.85
= 382.85x - 12.85
x = 12.85/382.85
x = 0.033564059030952070001305994514823

Someone correct me if I'm wrong.

I can see how SugarNut came to his conclusion somewhat.
Maybe he changed around the origincal Fold Equity equation to...
EV = [EV(fold)] * x - [EV(call)] * (1 - x)
In that case x would be -.0359793.
But even then the answer seems erroneous being negative and all that. But i can see the correlation between 3.6%.

Anyone want to clear that up?

I guess the mistake I made was thinking that I made a mistake.

Thanks quaddamage.

WoT

anyone have some input on my math like 2-3 posts up? im uncertain if that is right or not

was arguing with someone on irc they said i needed him to fold like 30% ?!?

im so bad at math... lol

About the openraisingrange formula.
Am I wrong or is this the stat that we can find in the HEM popup stats (raise 1st stat)

I know that this video was made while HEM wasn't probably even made.

Let's just say that i would be glad if I was able to somehow skip this part

Hey WoT,
At 1:17:26, you're talking about Grunch's method to determine how much FE we need to make a turn shove breakeven.

When villain calls, we're a 3:1 dog. So when called, we lose approx. 8P. After this point, I think there's a mistake. We gain 1P every time villain folds and we expect to lose 8P when called. So we need villain to fold 8 times as often as he calls for this to be breakeven. So villain must fold 8/9 times or ~88% of the time.

Let me know if I'm wrong because I could easily be overlooking something.

Thanks for the great series,
Ben

Re-watch the part where I talk about viewing the situation in 12 total instances. The green and the red numbers are the first 4 instances, because we're a 3:1 dog, we lose 3 times and win 1 time, so we can see how far we are in the hole. We have to use the fold equity to get us out of the hole and we need 8 more instances of him folding in order to get out of that hole.

We don't need him to fold 8/9 times because the times he doesn't fold we'll sometimes win the whole pot... in order to take into consideration the times we win the whole pot, we break out those win/loss instances as shown in the red and green numbers. What you're doing is counting the -4 -4 -4 +4.5 and saying that's -8 and counting it as one instance instead of counting it as 4 different instances... so that's effecting the divisor (your 9, my 12), which effects the division (8/9 vs 8/12).

Thanks for watching!
WoT

At 28 minutes you are determining villains' range for a call of our 3bet, deciding that such a range would be TT+ and AK. You go on to say that this accounts for 3.5% of all holdings. What confuses me is that in all previous episodes you have taken pains to point out that we should remove from our opponents range any possibilities that involve either the community cards or our own pockets. Here we have AsKs, so surely we should remove options involving these cards from his range: If we do that then his calling range is more like 2.5%.

This in turn means that we will collect the pot 77.7% of the time, not the 69% stated in the video. Our EV is then $40.65, not $34.89.

Of course I could be the gibbering idiot so I'm a little confused as to what I should be doing. Please enlighten.

I don't think you're figures are correct here. It looks as though you have removed all AK hands from his range, which has dropped his range from 3.5% to 2.5%. If we put in a specific suited hand for ourselves, such as A K and then take this hand out of the villains range then his total range only drops to 3.4%

Hi

That R(1) = raise first in holdem manager?

raise first- Raise First is similar to Pre Flop Raise except it doesn’t include 3bets as its only the 1st person to raise that has their Raise First stat effected and it doesnt include raising limpers.

Hi

That R(1) = raise first in holdem manager?

raise first- Raise First is similar to Pre Flop Raise except it doesn’t include 3bets as its only the 1st person to raise that has their Raise First stat effected and it doesnt include raising limpers.

ya seems reasonable.

this series was made before HEM is the beast that it is now

Time Link to 00:45:13

Here we are determining the EV if villain calls. If our equity in the pot vs. his calling range is 43% wouldn't that make his equity 57%? He has to call $760 to win $1245 and if he does call within our defined range on average he would have that 57% and would be making a +$382.90 EV play. Wouldn't that make it -$382.90 each time he calls within his range? I also have villain needing 38% equity to make an +EV call. 1.6:1. Still if we thin him by 66% we 'earn' 2x 370 per 1x -382.90.

Where have I gone wrong?

Mind blowing series.

Dude, at about 23:08 my head asploded, for real. You said "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%" It was right there that it went wait, what!? POP!!!!

You might as well have said click your heels, snap your fingers, and say "Magically Delicious" and we find out that R(1) = 11.2%

Please, for a guy who hasn't had to do algebra in over 25 years....how do you do you get to 11.2%?

The series has been great and well explained in detail, right up to that moment. I have no idea where to go with that.

Never mind, figured it out. Please don't scare me like that again. JC!

LOL

Time Link to 00:03:36

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.

Time Link to 00:48:15

There are a few errors in the combo listings here.

AKo = 9 combos (you double counted the AKs hands)
AQo = 9 combos (same as AK - you double counted the AQs hands)
AJo = 9 combos (but maybe you meant AJo and AJs here, in which case 12 is correct)
KQo = 12 combos

So that would lower the total number of combos a bit, but ultimately the answer of how often we need villain to fold is relatively unaffected (we still need very little FE for this to be +EV).

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.

Time Link to 01:07:29

Homework:

If villain folds 69% of the time I calculated our EV as ~$17.97

The play might be too high variance to be palatable for some, but that's still a play with more than a 2% edge.

Time Link to 00:12:41

So basically if the UTG+1 3bets that is calculated into his PFR? Is that why we use (UTG+1) 3bet% in this equation?

Grabbed by Holdem Manager
NL Holdem $1(BB) Replayer
SB ($176)
BB ($101)
UTG ($182)
UTG+1 ($100)
Hero ($129)
BTN ($159)

Dealt to Hero J A

fold, UTG+1 raises to $4, Hero calls $4, fold, SB raises to $19, fold, fold, Hero calls $15

FLOP ($43) 7 2 2

SB bets $27, Hero raises to $110 (AI), SB calls $83.05

TURN ($263) 7 2 2 8

RIVER ($263) 7 2 2 8 8



Villains Betting range
3.7%
Villains Bet/call range
2.5%

2.5/3.7 = .67
Villain calls 67% and folds 33%


I calculated we have 45.5% equity
Evcall 263 *0.455 - 110
Evcall 119.70 - 110
Evcall 9.70



EVCALL 9.7
EVFOLD 70

PushEV = [ev(fold)] * x + [ev(call)] * (1-x)
PushEv (total ) = 70x - 9.7(1-x)
PushEV = 70(.33) - 9.70(1-.67)
PUSHEV = 70 * .33 - 9.7 * .67
PUSHEV = 23.1 - 6.5
PUSHEV = 16.6


Did i do this correct?

Time Link to 01:08:20

Boba Fett Picture

Time Link to 00:41:52

I enter this range in PokerStove and As9s has 56.78% equity on the flop. You say we have 43%. I checked out the comments and didn't see any reply regarding that so I probably do a mistake on my side..

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.

Time Link to 00:48:20

Here your talking about villains cbetting range. Maybe it's different at the higher stakes, but in my experience at 50NL and 100NL most villains cbet almost 100% of the time on hands they opend with pf. Their cbet range being their entire opening range preflop. It seems common which is why so many float the flop with air and even the turn waiting for pf raisers to check it seems. Are we being opponent specific in the example to nits? Am I wrong or missing something? Their range could be anything inside of their opening range including sc's and one gappers and they cbet whether they hit or not. Maybe I misconstrued.

Here your talking about villains cbetting range. Maybe it's different at the higher stakes, but in my experience at 50NL and 100NL most villains cbet almost 100% of the time on hands they opend with pf. Their cbet range being their entire opening range preflop. It seems common which is why so many float the flop with air and even the turn waiting for pf raisers to check it seems. Are we being opponent specific in the example to nits? Am I wrong or missing something? Their range could be anything inside of their opening range including sc's and one gappers and they cbet whether they hit or not. Maybe I misconstrued.

are you using a hud? All you have to do is look at the cbet stat to see that people aren't really cbetting 100%. Sure many are 70-80 (and at ssnl it's probably correct to cbet a very high %), so just use what you know about each player to tailor their range.

Also, it's a 3bet pot so the range is going to be tighter, but I still have some air in there. As long as you know the process you can flex the range as you see fit.

Good plan sir ty!

First, I would like to thank you for the wonderful series that you've given us beginners of poker! 3 years after release (maybe even longer) there are still people recommending and watching your videos.

Second, I'm wondering a bit about the calculations made in around the 45 minute mark in the vid. It's when you calculate the minimum of times he needs to fold for the shove to be +EV with the Fold EQ formula.

When you calculate the EV for the fold respectively for the call, you are already making the assumption that he is folding a certain percent of the hands. If we would change the percentage of hands he is calling with, our EV for when villain is actually calling are shove will change.

Therefore, when you estimate that he would only need to fold 3%-ish of his hands, you are calculating that with the EV when villain is actually calling with 32,5% (39/120). Thus, your not regarding the fact that the EV for call will change depending on the percentage of him calling. Your equity and hence your EV for calling is certainly different if he is calling the bet with all of his hands.

For example, let's use the most obscure example when villain is only calling with his 3 combos of TT, or 1/40=2,5%. Putting that into the formula without changing the EV for call would give the following:

EV = 370*0.975+(-12,85)*0.025 = 360,43$

However, our equity if he's calling range is TT+ is certainly not 43%-ish. Pokerstove calculates our equity to about 25,55%. Hence, the EV(call) is: =0.2555*(2005)-875 or -362,7$

This gives the Fold eq EV according to the formula:

EV= 370*0.975+(-362,7)*0.025 = 351,68$

Which is not a big difference, but there is one. There will also be bigger differences when you use other percentages.

Also, against his cbet-range, we're actually a favorite (not 43% as mentioned in the movie. I think it's a mistake, since you say that we have 43% equity against both his c-betrange and his c-bet&call range. Therefore, we wouldn't mind him calling 100% of his hands. And again, with him calling all of his hands, we cannot use the calculated EV that was made on an assumption from what his calling range was.

How to calculate how much he will need to fold for our shove to be -EV. Since we have +EV even if he folds 100% or 0% there must be something in between. Otherwise, we are always expecting +EV regarding his foldpercentage. How to set up this calculation I won't think about more since it's almost midnight here in sweden and I have work tomorrow.

I might look like a big fool writing this wall of text if it turns out that I am mistaken, but aren't the things mentioned above correct?

Your EV when he calls will differ based on how often he's calling only if hands are being taken out/added of the bet/calling range....so to restate it, if you change his bet/calling range, then our equity when called will change.

That doesn't necessarily mean that the EV of him calling will change based on the % of him calling. Maybe his original 3bet-cbet range is wider than I was assuming, therefore there are more hands he's bet/folding and our shove is move profitable but our equity vs his bet/calling range is the same, etc.

Does that make sense?

That make sense, and it never occurred to me. I was all thinking about just changing the cbet/calling-range and entirely forgot that it's also possible to change his 3-betrange.

Thanks for the really fast answer. I guess it's by these questions we improve our thinking about the game aswell. Also, thanks again for the wonderful series. Going to watch the rest ASAP.

Thinking about it even more, the following should be true:

- We've given villain an calling range.

- For our play to be +EV he needs to have ~3% more hands in his c-betrange.

- Now, thinking about his range, we'll see that he is folding even more than 3%, which makes our play good.

Changing the steps a little, first figuring the calling range, then calculating the equity and the Fold eq. Then, after this, trying to figure out his c-betrange. This makes it more clear for me.

Changing the steps a little, first figuring the calling range, then calculating the equity and the Fold eq. Then, after this, trying to figure out his c-betrange. This makes it more clear for me.

Yep exactly, just make sure you go back to the beginning to make sure the cbetting and calling range hands are also in their actual 3bet and cbet range

Aaron, do you still believe that 3-betting AKs against a 15/10 is more +EV than calling in this kind of situation, given the current state of the games? It seems like a) a lot of players go into 4bet or fold mode when facing a 3-bet OOP, and b) by just flatting and then calling/floating most flops, it seems like we can get more value from most of his range, especially Ax, by just flatting preflop than we gain from fold-equity by 3-betting.

(edit: I'm referring to the hand discussed around the 30-minute mark)

Aaron, do you still believe that 3-betting AKs against a 15/10 is more +EV than calling in this kind of situation, given the current state of the games? It seems like a) a lot of players go into 4bet or fold mode when facing a 3-bet OOP, and b) by just flatting and then calling/floating most flops, it seems like we can get more value from most of his range, especially Ax, by just flatting preflop than we gain from fold-equity by 3-betting.

(edit: I'm referring to the hand discussed around the 30-minute mark)

Depends on whether you think your history is enough to get him to 4bet/fold a good amount. Generally speaking, if the guy is so tight that I don't feel like I can profitably 3bet/get it in with some value hand, I shy away from 3betting it to begin with...but if we feel like we can't 3bet/get it in with AK then maybe that indicates we aren't playing aggressively enough against the guy (ie, not inducing him to open up his 4b bluff range).

Certainly flatting some of these hands, especially in full ring games, has more merit...but just be sure to think about what it means about our perceived 3bet range if we feel like we can't 3bet/felt a hand as strong as AK (in addition to thinking about what his opening range is).

Time Link to 00:05:38

if i want to know his openraisefreq from utg i look at my hud ?!....

I don't know if that stat was on HUDs 3 years ago.

if i want to know his openraisefreq from utg i look at my hud ?!....

as whatwonder mentioned, this series was made in late 07/early 08. we have evolved quite a lot since then in terms of stats/hud

Hi Aron.
Thanks for the this great series In timeline: I don't get how you the total pot of 1720? 1:05 isn't 1860?

Hi Aron.
Thanks for the this great series In timeline: I don't get how you the total pot of 1720? 1:05 isn't 1860?

Keep in mind that i can only win/lose based on what is in the effective stacks. Villain has more money... so its our $800 + his $800 + $120 in the middle = $1720

Keep in mind that i can only win/lose based on what is in the effective stacks. Villain has more money... so its our $800 + his $800 + $120 in the middle = $1720

Ok I missed that thanks..

Hi Aron. I'am trying to be good at estimating FE at the table, so can I estimate that, assuming I always lose if he calls my turn shove: If I am risking 80% pot unit to win 80% pot unit(those number accurate, in reality I am risking 1.3 pot unit to win 1 pot unit, but I don't know how I else can estimate, while playing) = Risking 1 pot unit to win 1 pot unit? If that is true --> then Villian needs to fold 50% of the time for me to break even right??


Thanks Sune

Hi Aron. I'am trying to be good at estimating FE at the table, so can I estimate that, assuming I always lose if he calls my turn shove: If I am risking 80% pot unit to win 80% pot unit(those number accurate, in reality I am risking 1.3 pot unit to win 1 pot unit, but I don't know how I else can estimate, while playing) = Risking 1 pot unit to win 1 pot unit? If that is true --> then Villian needs to fold 50% of the time for me to break even right??


Thanks Sune

Yes some quick numbers to memorize... assuming you have no equity at all in the hand... if you bet half pot you need him to fold 1 time in 3 (risk 1 unit, win 2 units). If you bet pot, you need him to fold 1 time for each 1 time he calls for it to break even. If you bet 2x the pot, he has to fold 66% of the time.

If there are still cards to come, then you will need to do the fold equity calcs based on how much equity (outs) you think you have on average.

Yes some quick numbers to memorize... assuming you have no equity at all in the hand... if you bet half pot you need him to fold 1 time in 3 (risk 1 unit, win 2 units). If you bet pot, you need him to fold 1 time for each 1 time he calls for it to break even. If you bet 2x the pot, he has to fold 66% of the time.

If there are still cards to come, then you will need to do the fold equity calcs based on how much equity (outs) you think you have on average.

Ok cool.. Thx..

Good video always thought PFR = Opening Range didnt get that 3bet + players in front does influence it his opening range what`s logic if you think about it just a bit

So if i look on UTG raiser i dont need that formula and PFR UTG % = Opening range?
I mean i look on his UTG PFR specific and not at his pfr overall. So example if his pfr overall is 23% and UTG-PFR is 18% i know that 18% is his range right?
Or are the specific PFRs on all positions alrdy all opening ranges? No right?

I guess it takes a long time, hat iam able to get his range or close to his range without calculating it.

Is there any possibilty to figure out his range faster in the game any shortcuts possible there to be useful on the table?
Is it possible to look for example on UTG +1 PFR% see its lets say 15% if and add 1.5% for each position so make it 16.5%, or if he is Cut-Off he would have 18% or maybe also look at 3bet and oponet/s in front of him and lower or higher it by looking at their pfr?
Or are there any shortcuts possible??

The PFR is getting higher right cause 3bets are not counted in PFR-Stat?

Sry if this sounds retard, I just watched it once im not sure if i understood everything 100%

Keep in mind this video was made before holdem manager or new pokertracker which now has nice positional stats for vpip and pfr and 3bet%. You're right if you look at the UTG pfr% that would be good enough in HEM, you dont need the formula.

I think I heard that this might be a difference between pokertracker and HEM with how they calculate vpip and pfr together. I think there was a discrepancy i ran into once with some of the stats out of the blinds where a student's PT was calculating either vpip or 3b% differently than my HEM was. I cant remember the exact situation though.

Your best bet might be to post in your database's forum and ask exactly how the program you're using calculates these fields. I bet you can skip this extra formula all together these days. These videos could probably use an update to take advantage of some of the nice tools we didn't have 4 years ago :-/

No Problem, thx for your answer and thx for the series still learned a lot!

I am absolutely in love with this video series, but the PFR% formula at the beginning of the video was just something that I don't 100% agree with. It just doesn't seem justifiable to determine a villain's PFR by making his position the primary factor in the equation. Agreed that position is extremely important in determining what villain's open raising range is but I just feel that many other factors apply in trying to determine. I believe the equation doesn't take enough weight on what the players before villain have done, and villain's PFR range will change once a player in front of him open raises and villain will not 3Bet his entire open raising range.

I'm not a math wizard, this grumble is just coming from some kind of twisted logic that I can't get rid of when I was viewing the material on that equation making me a non-believer in the equation's true importance. And one more thing that I dislike about it, it really doesn't seem at all very accurate, or at least accurate enough for me to base any EV decisions on it. I think accounting for your good intuition and feel for villain in this spot will lead you in the right direction to a +EV play. Why I don't believe it to be accurate enough for me is because when you finally do get a range percentage, in this case 11.2%, we changed his possible holdings around to still fit in that 11.2% that is no longer the top 11.2% of hands, so essentially we are left with having to guess the 11.2% of that range the equation gave us, so doesn't that leave us primarily where we started before we used the equation, in having to guess his true range???

I understand that we are still trying to get an estimation and playing a guessing game here regardless but does this equation get us any closer to a more accurate estimation when we could just glance at the HUD and see that villain raises this % of the time from this position. Please correct me if I made a any mistakes in my assumptions and conclusions here. Thanks guys, and keep up the good work WoT.

What you are saying has a lot of truth in it but scroll up a few posts... you can probably get this stat with much less pain and more accuracy by looking at your actual database stats now. These vids were made in late 07 before all the nice tools came out so we had to calculate this by hand. I know it's a bit confusing with this formula and it's not 100% accurate for some of the reasons you gave, but it's more accurate than simply looking at the cumulative PFR% which is all we had back in the stone age :-) You are probably best by skipping this and simply opening up your HEM or PT and finding the associated position stat.

These vids were made in late 07 before all the nice tools came out so we had to calculate this by hand.

Haha ya ur right Wilt I should have taken that into account, sometimes it's tough to always keep in mind that this groundbreaking series was made so long ago back in the "stone age" haha in which case I wasn't around poker wise. I can definitely see the true worth of this formula if you didn't have a spiced up HUD and all the other software goodies that we have access to today.

Haha ya ur right Wilt I should have taken that into account, sometimes it's tough to always keep in mind that this groundbreaking series was made so long ago back in the "stone age" haha in which case I wasn't around poker wise. I can definitely see the true worth of this formula if you didn't have a spiced up HUD and all the other software goodies that we have access to today.

haha yea exactly

Time Link to 00:42:01

So you say goood players will X here with 7s or 8s on this board. Im curious to know what that good players plan is when villian bets flop and turn and a overcard comes over the 10 which will usally happen.

I consider myself to be a pretty good player and I dont 3B 7s or 8s esp for this reason. There are too many flops we are in the dark on and have to pretty much either give up on or get chip spewy. (1 and done, or multiple barrels not knowing where were at)

Time Link to 00:50:44

What about raising small here to let him consider reshipping a worse draw here.
Since his range essentially should still be about the same. Esp. since you expect him to
check 7s and 8s on flop. Its pretty brutal to jam this large for him to fold a hand like 78 of spades,
in other ways he may jam thinking he has fold equity when we raise small.

The real ? here is what do you think about a smaller raise vs the Jam? Im curious to know THKS!

So you say goood players will X here with 7s or 8s on this board. Im curious to know what that good players plan is when villian bets flop and turn and a overcard comes over the 10 which will usally happen.

I consider myself to be a pretty good player and I dont 3B 7s or 8s esp for this reason. There are too many flops we are in the dark on and have to pretty much either give up on or get chip spewy. (1 and done, or multiple barrels not knowing where were at)

cbetting 77 and 88 etc are fine here. The games have changed somewhat over the last 4 years since when this video was made. Checking those hands some is still an ok option too, but I would usually reserve that play for someone I had a pretty good read on his value betting/bluffing tendencies...

What about raising small here to let him consider reshipping a worse draw here.
Since his range essentially should still be about the same. Esp. since you expect him to
check 7s and 8s on flop. Its pretty brutal to jam this large for him to fold a hand like 78 of spades,
in other ways he may jam thinking he has fold equity when we raise small.

The real ? here is what do you think about a smaller raise vs the Jam? Im curious to know THKS!

Small raise is also ok, and is good for balance if we want to raise/fold or raise/induce. I chose shove to make the math easier since the point of this is more learning how to do fold equity calculations and if you small raise here many more factors come into play concerning the overall EV. It's also worth noting that in spots like this good players might not be folding better ace highs here (this applies more to HU than 6m poker) but even in 6m the value range for raising here is v v narrow, so keep that in mind. No 2pairs, a questionable number of sets, and it's very questionable whether we'd be raising Tx here (it would have to be with the intention of inducing rebluffs). So yea, just more food for thought.

Hey Wilt, I love the series and am working on applying the info to my game. This is my first time posting on this so my lingo might be a little off. I have one question about multi street fold equities in deep NL holdem that I don't think you cover in the series. How would I set up the equation if we are so deep that I want to raise with my draw, but because of stack size I think I can't shove and he could 3 bet shove on me that I think I would have roughly break even expectation. Here is an example of pot from today.

I am playing 250bb 5/10 NL game.
I am on the button with 10c7c and middle position opens to 30 and I call on the button and the two blinds call.
Flop Ts 8c 4c. It gets checked around to me and I make it 80. Folds to the PFR who check raises to 215. I think Villain could do this with over pairs, AT KT, and sets, and T8 (maybe 79 but I doubt it against this player) With a backdoor flush and strait with weak top pair I decide to make the call.
Turn comes a 6c giving me a flush draw and an inside strait draw. Villain makes it 300......

OK so here is my question, when he makes it 300 he has about 1800 behind him I think I have a profitable situation to make a move. The 6 completes strait draws and two pair hands, or i could be slow rolling a set. My question is when we did the calculation with the As9s shove hand it was an easy situation because it was a shove. If I make it say 700 here, then I am risking 700 to win about 800, BUT with the top of his range he could ship it, and with the middle of his range he would probably call or fold, and then probably fold to a shove on the river. So if he shoved I would be calling 1400 to win 3300 so slightly negative ev.

My question is how does this change the way I should be setting up the equities. I intuitively see that this could be a very +EV move trying to run a multi street double barrel (especially because I think such a small part of his range could shove and would fold to a river bet), but I don't know exactly how the math applies in a situation in which my raise could be shoved on.

If you understand what I am trying to get at then it would be great to get your insight. Thanks a bunch.

O yea i thought about this after, i just called and then the river blanked and it went check check and showed A T.

Ok from your description it looks like you turned a flush but based on what you're saying I'm guessing you don't have a flush and are wanting to semibluff the turn?

Doing multistreet calculations like this is complex and prone to error (I haven't done many of these myself tbh).

Basically the way you'd set it up is you'd have to break out each scenario to figure them out and then put them all together in the end.

So first, estimate how often he folds the turn to your raise and get that ev. (he folds x% * pot + his bet).

Next, figure out the EV of when he shoves (so decide if you are calling or folding and calculate accordingly). Estimate how often he shoves the turn to your raise.

Of the times he doesn't fold, he will either shove, call turn and you bluff river, call turn and you give up river. So depending on what you'd do to a shove, you can figure out the ev (using the equity you have against his range). Then figure out of the times he calls you on the turn, how many rivers will you bluff vs give up (so you can get a % of time you bluff and % of time you check). Then figure out how profitable that bluff will be (using an estimate of how often you think he folds on the rivers you bluff). Then figure out how much showdown value you have when you don't bluff (ie, when you check, how often do you win and multiply that by the pot size to find your ev of checking).

That will give you the overall picture of the situation for each scenario.

Then basically you'd have to make another ev calculation weighting the scenarios for how likely each is where w, x, y, z are the % weight (likelihood) of each scenario above all adding up to 100%

So it would be like ev = w * (what you win when he folds turn) + x * (ev he calls turn and you bluff river) + y * (ev he calls turn and you give up river) + z * (ev when he shoves turn)

When doing the second scenario where he calls turn and you bluff river and thinking of the fold equity calc, be sure to identify the correct risk/reward. For the value that you are risking, you would use your turn raise size + your river bet size and your reward would be size of pot + amount HE put in the pot on the turn. So my point here is I don't think you want to double count your raise size as money you would win on the river, because you already know ahead of time what % you are bluffing the river, so essentially on the turn you are risking your turn raise size + (% you will bluff the river * river bet size). Make sense? And then on the river the ev of checking would just be the (% you win * pot size)

I'm pretty sure all that is right... but as you can see it gets confusing and it's why I didn't want to tackle it in the videos. I think there is a computer program that can help with this, maybe flopzilla but i'm not sure as I haven't used it.

best of luck
WoT

Hey Wilt, just a quick questio. Do you think it would be useful if you create another one of these math based series now in 2012 since some of the information from this one is.. not as useful anymore, considering all the software etc. Anyway, I think it would be cool if you can and want to create a sort of like season two of this series where you incorporate huds more as well as expand on what you can from the first series. I see no point in going through the basics of pot odds etc. again but I know that I myself would love watching another one of these math series especially if it was a bit more up to date. I'm not saying that what you taught in this series is not useful or accurate today mind you so please don't misinterpret my meaning.

Consider it

Hey Wilt, just a quick questio. Do you think it would be useful if you create another one of these math based series now in 2012 since some of the information from this one is.. not as useful anymore, considering all the software etc. Anyway, I think it would be cool if you can and want to create a sort of like season two of this series where you incorporate huds more as well as expand on what you can from the first series. I see no point in going through the basics of pot odds etc. again but I know that I myself would love watching another one of these math series especially if it was a bit more up to date. I'm not saying that what you taught in this series is not useful or accurate today mind you so please don't misinterpret my meaning.

Consider it

hey thanks for the post. yea i agree it would be good to update it, but this series was such a massive undertaking for me and took me many hours for each video and I'm not sure I have the intestinal fortitude to take that on again in the near future. I do think it would be useful though... i will keep it in mind but don't hold your breath waiting