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

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

Massive video!!! This will be a a HUGE help as I can go back and look at hands with the proper mathematical tools.

No disrespect intended, but the way in which you explain this concept in comparison to last video is much much clearer

THX

Massive video!!! This will be a a HUGE help as I can go back and look at hands with the proper mathematical tools.

No disrespect intended, but the way in which you explain this concept in comparison to last video is much much clearer

THX

Thanks for the feedback, glad you are finding the videos helpful.

Hi Wot,

Want to reply to a thread yesterday, but wasn't sure the math was right. I've added the frequency of combos to a villans 3bet range basis his HUD stats. If you've got a minute pls could you have a look:

Poker Stars $50.00 No Limit Hold'em - 6 players - View hand 1893582
DeucesCracked Poker Videos Hand History Converter

Hero (UTG): $102.10 - VPIP: 21, PFR: 17, 3B: 7, AF: 3.8, Hands: 69997

CO: $50.00 - VPIP: 18, PFR: 17, 3B: 12, AF: 1.9, Hands: 186


Pre Flop: ($0.75) Hero is UTG with K A
Hero raises to $2, 1 fold, CO raises to $6, 3 folds


The author of the thread was assuming a fold was the best course of action, and I didn't agree, but wanted to show that I thought a rasise was the best course of action, then a call, then a fold (as fold is 0EV).

One other thing I'd like to know: is there an EV calc that can includ the times we are forced to call when Villain 5bets? Anyway:



Villains 3bet Range: 88 ( 3 of 6 50%) 99 (5 0f 6 83%) TT+ (30 or 30 100%) AJ ( 6 of 16 37.5%) AQ+ (32 of 32 100%) (KQs 1 of 4 25%) - 77 possible hand combos

calling (or 5betting) QQ+ (18 of 18 100%) AKs (4 of 4 100%) 22 combos

22/77 - 28.8% of 3bet combos are calling
55/77 - 71.2% of 3bet range is folding


How do we fare against his range?

call 3bet :

AhKc: 50.8%
vs
TT+,9c9d,9c9h,9d9h,9d9s,9h9s,8c8d,8c8s,8d8s,AJs+,KdQd,AQo+,AcJs,AdJs,AhJc,AsJc: 49.2%


Villins call range :

AhKc: [b] 33.2%
vs
QQ+, AKs: [b] 66.8%


[b] EV TIME!!! [b/] :

EV (call) = (our equity) * (what we win) - (Villain's equity) * (what we lose) =

.502 * 8.75 - .492 * 6 =
4.39 - 2.952 =
EV = 1.438


EV (3bet/ villain calls) assuming we 4bet to $22

EV = (our equity) * (total pot) – our cost

EV= .332 * 44.75 – 22 = -7.143


EV (3bet/fold)

EV= 6 + 2 + .75 = 8.75


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

EV = (22/77 * -7.143) * ) + (55/77 * 8.75)

EV = ( .2857 * -7.143) + (.7143 * 8.75)

EV = -2.04 + 6.25

EV = 4.21

After all that I think I have shown that the 3bet is more profitable than a flat call….

Please feel free to correct and I’d like to discuss the range I assign a 18/17, but I don’t think I made a massive mistake.

cheers all

Your approach is generally correct but one big thing to think about is that when contemplating ev of a flat call, it's not as simple as just using our equity, especially with a hand like AK which benefits so much from seeing all 5 cards. On a lot of boards we won't be able to realize our equity because we will miss the flop... so to do a good job on trying to figure out the EV of a call, we'd have to try to model thing like how often we can c/r bluff, how often we can c/c flop with jsut A high, how often when we hit do they value bet or barrel off with worse etc. As you can see, this is not easily done. A good way to start would be figuring out your likelihood of flopping a pair or better (roughly 1/3 of the time) and figuring out your equity from that point forward against his range.

Also as to your question about how to look at it if we're forced to call a 5bet, we'd again try to model each action after our 4bet. He folds, He calls (complex), He raises then we'd take our estimation of the frequency for each (can use the same combo method you did) to figure the overall EV for each.

Your approach is generally correct but one big thing to think about is that when contemplating ev of a flat call, it's not as simple as just using our equity, especially with a hand like AK which benefits so much from seeing all 5 cards. On a lot of boards we won't be able to realize our equity because we will miss the flop... so to do a good job on trying to figure out the EV of a call, we'd have to try to model thing like how often we can c/r bluff, how often we can c/c flop with jsut A high, how often when we hit do they value bet or barrel off with worse etc. As you can see, this is not easily done. A good way to start would be figuring out your likelihood of flopping a pair or better (roughly 1/3 of the time) and figuring out your equity from that point forward against his range.

Also as to your question about how to look at it if we're forced to call a 5bet, we'd again try to model each action after our 4bet. He folds, He calls (complex), He raises then we'd take our estimation of the frequency for each (can use the same combo method you did) to figure the overall EV for each.

Cheers for taking the time!

For things like c/r bluff, c/c etc this would be hugely player dependent + I assume we would need a massive sample siz in PT3. So against a random almost undoable without making a series of assumptions; the more we guess here I feel the more unreliable it would become..... BUT it would be fascinating to do this for a stereotypical player at .25NL or maybe more importantly for a reg who you have a large sample size + examples of actual lines taken. This is something I'm doing for one player who I frequently meet. (Future video? 'The workshop', you provide the tools, we do the work and then folks report back about their findings, maybe for a poker study group )

5bet situation seems achievable in my current math rookie state. Many thanks for the pointers, I’ll have a go

I guess that is what stoxEV and Flopzilla help with...... the equity trees and % vs different parts of opps range would be help in check my math.

These videos could probably use an update to take advantage of some of the nice tools we didn't have 4 years ago :-/

This would be absolutely great.

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.

Wilt could you look at this post please? I'm trying to understand FE and I agree with some of this post (that villain is only calling with 2.5% not 3.5% as we have AK spades meaning they will fold 78% of the time and also that 3-betting is much higher EV than calling).

I'm confused about the rest?

Wilt could you look at this post please? I'm trying to understand FE and I agree with some of this post (that villain is only calling with 2.5% not 3.5% as we have AK spades meaning they will fold 78% of the time and also that 3-betting is much higher EV than calling).

Ya I think I forgot to take card removal into consideration when I did this

I'm confused about the rest?

Can you clarify what you're confused about? Is there a specific question?

I managed to work it out, I was just having a bit of a brain freeze as it's been so long since I learned how to do these kinds of calculations.

Absolutely great series. My friend is joining DC and after the Haj School (to learn how to use DC) I'm recommending this as what he should start with. It's great that you still answer questions about this series as well.

Cheers Wilt

Time Link to 00:23:31

figured it out nm