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

## Mathematics of NL Hold'em: Episode Seven

Get the Flash Player to see this player.

### Mathematics of NL Hold'em: Episode Seven by WiltOnTilt

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

#### About Mathematics of NL Hold'em

WiltOnTilt will discuss key concepts related to the mathematics of No-Limit play using Powerpoint. Begin with the basics: probability and pot odds. Then follow Wilt to more advanced arenas: implied odds and reverse implied odds, software tools and mental shortcuts for equity calculations, complex EV calculations, and an exploration of fold equity. And watch this series conclude with a discourse on the ultimate in professional poker math: hand frequencies, valuebetting, and G-bucks.

### Video Details

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

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

or track by Email or RSS

#### Slowjoe

1113 posts
Joined 01/2010

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

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

Same thing though =) thanks

I think the point we need to concentrate on is that the shove is worth less than the call. The point we would learn the most from is to work out at what p(win if called) the shove makes money.

And the calc above looks right to me.

Going back to the second post:

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

I think what I was trying to say was the WoT was looking at EV when called, rather than absolute EV(shove).

So to summarise, I think what you did was conceptually correct, except for the miscalculation of the 14.2% call prob and the mishandling of the odd \$100 to call the first raise from villain.

#### Slowjoe

1113 posts
Joined 01/2010

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

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

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

Also, assuming we're talking about the same hand (shoving 582 into a 762 pot), we're behind 10% initially, and 70% if we're called, so I don't understand where the 1.5% comes from. But just look at your numbers. You have p(win) > 0.5 in all variations. It's a no-brainer that we want to stack off.

Finally, there is a HUGE difference between the example you have given and the one that WoT works on. In your example, Villain shoves, whereas WoT's example has us shoving.

You need to be careful switching side in these situations, because the dead money in the pot makes calling a shove break-even at much less than 50%, whereas the shove is only breakeven at 50% in situations where there is no possibility of forcing a better hand to fold.

#### Slowjoe

1113 posts
Joined 01/2010

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

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

40 posts
Joined 08/2008

Ok, I should have been clearer on a few things. firstly I'm talking about when wilt is considering different bet sizes against villains range and the resulting EV of each to find the best bet size. ( about 13 mins in)

Wilts equation is EV(bet)= Bet*(calling %)+stack*(raising %)-stack(losing %)+ pot

where,
raising % = % of villains range that is behind and shoves to our bet, which we call.
losing % = % of villains range that is ahead and shoves to our bet, which we call.

The problem I had with this is the Pot term which infers that you win the full pot 100% of the time no matter what villains range is which is incorrect.

slowjoe

In the example wilt gave our stacks are equal before we make a bet so in my equation "a stack" actually includes our bet,as I didn't differentiate between our stack and villains, which are only different once we place a bet.

To be clearer perhaps I should have writen it.

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

This is identical to my first equation because in wilts example
(bet) + (our remaining stack) = 800 = villains stack = "a stack" in my example. This is also how wilts original equation was setup.

I should also have used wilts example to keep things clear, but I couldnt be botherd getting his figures from the episode as the fugures don't actually matter.

sorry for not being clearer

40 posts
Joined 08/2008

Edit:

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

I got the risk and reward terms backwards, it should read

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

Reward:
when villain shoves, we call, and we win, our bet + our remaining stack has villians stack covered so we win (pot + villains stack)

Risk:
when villain shoves, we call, and we lose, we lose our bet + our remaining stack

I think when we lose we need to include the bet because we are considering things from before we make the bet so we have not lost it yet.

#### AstonMartin

960 posts
Joined 08/2009

something i dont get, why we always win 100% of the pot, i mean the pot before any bets goes in, if we jam we loose to quads, its becouse is such a meaningless percentage of the time so its not included in the equation ?

its from 15:00 (how much should we bet with AA)

EV(bet)=bet * (calling%) + stack * (raising%) - stack * (losing%) and now + full pot

im bit confused today and it might be stupid question but i cant get why

40 posts
Joined 08/2008

Wilts equation is wrong, I've written a some long posts on this already. It's suppose to be:

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

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

#### Bigfish789

80 posts
Joined 07/2010

In the video around 25:39 it says

EV(shove) = EV(call) + EV(raise)
We're raising 582 on top so the EV(raise) = 582x-582*(1-x) where x is how often he calls with a worse hand.

In that particular example it is EV(raise) = 582*0.3-582*0.7

In english when we raise those additional 582 we get 30% of that value in EV cos he will call with worse, but how can we
subtract 70% of those 582 if he can have better hand only 10% of the time?

Please explain why the formula for EV raise is not like this: EV(raise) = 582*0.3-582*0.1

I just fail to see how can we not consider his only 10% of better hands during the shove. What if it wasn't 10% but 0% and the 30% for calling with worse would still be 30%, how could the shove than be worse EV than call?

thanks,
-Fish

#### Slowjoe

1113 posts
Joined 01/2010

In the video around 25:39 it says

In that particular example it is EV(raise) = 582*0.3-582*0.7

In english when we raise those additional 582 we get 30% of that value in EV cos he will call with worse, but how can we
subtract 70% of those 582 if he can have better hand only 10% of the time?

Please explain why the formula for EV raise is not like this: EV(raise) = 582*0.3-582*0.1

I just fail to see how can we not consider his only 10% of better hands during the shove. What if it wasn't 10% but 0% and the 30% for calling with worse would still be 30%, how could the shove than be worse EV than call?

thanks,
-Fish

Good point. His 30% win/70% lose are based on an assumed call. In fact we can work out that it is 10% call/lose and 30/7 = 4.3% win. It's perfectly possible to argue the toss between Wilt's numbers (which are assuming the call) or to say that there should be a factor for the whole of the EV(raise) term (both 0.3 and 0.7). Ie multiply by 1/7:

582*0.043 - 582*0.1 (and 1/7*0.3 = 0.043).

how could the shove than be worse EV than call?

It's simple.

The money for the shove is in play in two situations

1. When the villain folds a better hand (in this case there are no such hands.
2. When the villain calls. We need to win 50% of the time (when called) for this money to make the shove break-even WHEN THERE IS NO FOLD EQUITY.

In general, fold equity is very often positive, so making a small loss on the shove when called is the breakeven point.

#### Bigfish789

80 posts
Joined 07/2010

oh yes, I was just being stupid. it's crystal clear now. Thanks a lot Slowjoe!

#### kgbmiked

192 posts
Joined 11/2010

Here are my notes on this episode. Hope it helps

Notes on Mathematics of NL Holdâ€™em episode7 by WiltonTilt
By KGBMIKED

This video is about Value Betting, Bluffing, Bluff Sizing, C Betting

Note to self, Watch the UNCONVENTIONAL WISDOM series. (WoT mentions it is awesome).

Changing bet sizes based on different factors is an exploitable strategy but it is also the highest EV strategy provided you are only doing it against people who will not take advantage of our bet sizing.

Most of our profit is going to come from playing exploitabley provided we are not being taken advantage of.

When making a value bet our goal is to maximize our Expectation from the bet.

We are against a player who is a 50/15 with 33% WTSD.

We are on the river with AsAd with a board of 8dJdJs9sAc. We are UTG+2 he is in the cutoff. thereâ€™s \$400 in the pot

1. Might fold a big pair *QQ/KK) to an overbet, but will call pot or less
2. Will call with a medium pair for half pot bet or less, but never calling with an underpair.
3. He is never folding trips or better. If he has a full house/4jacks heâ€™s going to raise all in on the river.

So we then give him a range. We come up with
77+, J8s+, suited semi connected hands with diamonds/pair/OESD

So given the range and thereâ€™s \$400 in the pot, take a guess at what you might typically bet here to maximize against this range given our assumptions, then weâ€™ll do some math to find the best bet size.

So I think I would bet all in here based on his range.

Now to determine the correct bet size, we need to think about how many combos of hands there are that call us.

Letâ€™s first organize the hands in his range into 4 buckets that will likely react the same to a given bet size: medium pairs, Big pairs, Monsters (Trips of Better)
Coming up with the ranges here is kinda difficult because in the video we are not told how the betting went for each street.
Medium Pair combos = TT(6), 9Ts(3), 78s(3), 89s(2), Q8s(3), Qd9d(1),Kd9d(1), A8s(1),T8s(3)
TOTAL = 23

Big Pairs: KK(6), QQ(6)
TOTAL = 12

Monsters: 8Js(2),J9s(2),J10s(2),JQ(8), JK(8),AJ(2), 88(3),99(3),JJ(1),10dQd(1).
Because he may react differently with some of the hands in the Monsters category, we can further divide the Monsters category into 4-sub-catagories of
Boats(12),, Straights(1), Quads(1), and Trips(24) for a total of
TOTAL = 38

The entire calling range is 73 combos

Once we have the number of combos, letâ€™s determine the % of the range each category makes. Divide the number of combos of each category by the total number of combos of 73.

Remember this is his calling range

Medium Pairs: 23/73 = 32%

Big Pairs: 12/73 = 16%

Monsters: 38/73 = 52%

Further dividing Monsters into
Boats:12/73 = 16% Straight: 1.73 = 1.5% Quads: 1/73 = 1.5% Trips: 24/73 = 33%

Bet size EVâ€™s

In general the EV calc will go like this:

EV(bet) = bet * (calling%) + stack * (raising%) â€“ stack * (losing%) + pot

Where the calling %, raising%, losing% are the frequency he has those hands on our cheat sheet of (Medium pairs = 32% Big Pairs = 16% Monsters = 52%
Monsters broken down to Trips = 33%Boat 16% Straight = 1.5% Quads = 1.5%).

Ev(halfpotbet) = bet* (Medium pairs + big pairs + trips + straight) + stack*( boats) â€“ stack * (quads) + pot.
Ev(halfpotbet) = 200 *(.32 +.16 +.345) + (800*.16) â€“ (800*.015) + 400
EV(halfpotbet) = 165 + 128 â€“ 12 + 400
EV(halfpotbet) = +\$681.00

Now lets do the same equation if we bet full pot. Our equation changes a bit because now we are not getting called by medium pairs. So new equation is
EV(fullpotbet) = bet*(bigpairs + trips + straight) + stack*(boats) â€“ Stack*(quads) + pot
EV(fullpotbet) = 400*(.16+.345+.015) + 800*(.16) +400
EV(fullpotbet) = 208 +128+400
Ev(fullpotbet) = \$736

So a full pot bet on the river is more profitable then the \$681 we would have made if we just bet pot.

So now lets see what our EV is if we jam. The equation changes because he will not call with big pairs anymore if we jam.
EV(Jam) = bet*(trips + straight + boats) â€“ (stack * quads) + pot
Ev(Jam) = 800(.33+.015+.16) â€“ (800*.015) + 400
EV(Jam) = 404-12+ 400
EV(Jam) = \$792.00

So we see that the \$792 EV of a jam is higher then the \$681 of a half pot bet and the \$736 of a pot bet.

Villain on the button raises to 35, sb folds and our hero defends his big blind with Ts6s.
We are the BB and PFR comes from the button.
Flop(80) comes Td8h7c
Hero leads out for 50 and our villain calls
Turn(180) Qh
Hero bets 133 and villain this considers this for a little bit and calls
River(466) Tc
Hero thinks for a second and bets 100, now villain min raises to 200
Do we call or shuv here?
Reads: We have the best hand 90% of the time
We expect to have the best hand 30% of the time when our shuv gets called.

So now we need to figure if we are trying to value bet or bluff? Since villain is probably not folding anything he min 3 bets here we have 0 fold equity so the play is definitely with the intention of value betting, not bluffing.

So now we need to find our EV of a call
EV(Call) = .90(466+100+200) - .10(100)
Ev(Call) = .90*766 â€“ 10
EV(Call) = \$679.40

Now we need to see if our EV of a shuv will get us more EV

Our hero estimates the villain calls with a worse hand around 30% of the time. Is this often enough for us to shove?

Since we donâ€™t expect him to call with any worse hand then us, then our EV canâ€™t go up, it can only go down because he will only call with a better hand then us.

Ev(shove) = EV(call) +EV (raise)

Weâ€™re rasing 582 on top so the EV(raise) = 582x-582*(1-x) where x is how often he calls with a worse hand

Therefore:
EV(shove) = EV(call) +582x â€“ 582 *(1-x)

We estimated that villain calls with a worse hand 30% of the time so we then plug this in for x and get

EV(shove) = 679.40 + 582(.30) â€“ 582 * (1-.3)
EV(shove) = \$446.60

So Ev(shove) = \$446.60 which is less then our EV(call) of \$679.40.

So even though we think we have the best hand 90% of the time how can a shuv be worse? Because the thing that matters is not how often he has the best hand but how often he calls us with a worse hand. So this begs the question, how often must he call with a worse hand for a shove to be better then a call?

So now we need to solve for x where EV(shove) = EV(call)

EV(shove) = EV(call) +582x â€“ 582*(1-x)

Then we set it to 0 so we can get x

0 = 582x â€“ 582(1-x)
0 = 582x â€“ 582 + 582x
X = 50%

So he needs to be calling here with a worse hand 50% of the time in order for EV of a shove to be more then EV of a call. So in conclusion, in most situations on the river, where our fold equity is 0, a bet or a raise is only profitably if you expect to win at least 50% of the time.

In a tournament situation on the river with a dry side pot, 3 way pot with one player all in. We want to value bet, how often must we be called by worse?
EV(bet) = 1x-1*(1-x)
Ev(bet) = 1x -1+x
Ev(bet) = 2x â€“ 1
X = .50 So we need to be called with a worse hand more than 50% of the time for us to value bet the river and it be +EV.

So here is another example where we want to know what the best bet on the river is

We are playing against a player who is hyper aggressive and tough and can read hands and is a good strong player. Remember against a donkey who is never folding anything our huge overbet was the most +EV. Now we are not playing against a donkey, we are playing against an aggressive reg. We are on the river after leading all 3 streets into him and we backdoored the nut flush. We have Ah4h and the board is 5h8cJsKh9h. Pot is 500 and we have another 1000 behind and so does he.
We estimate that 70% of his hands are folding on the river because they were draws or weak pairs
30% of hands which are willing to call a reasonably sized bets (say pot or less)
Top 5% of hands will call an overbet (150% of pot)
Top 5% will raise a reasonable bet, but no hands will raise an overbet.

So how do we best attack him?

If we make a standard pot value bet of 500 we think heâ€™ll continue with all 30% of his decent/strong hands and top 5% will raise.

Ev(500 bet) = 500 *.25 + 1000 * .05
= 125 + 50
=\$175

If we overbet, heâ€™ll call with his top 5% of hands

EV(750 bet) = 750* .05
= \$37.50

So overbetting does not work good against this type of good aggressive player.

So now lets see if we bet \$200

EV(200 bet) = 200*.25 +1000*.05
= 50 + 50
= \$100 so if he raises the top 5% of hands and just calls the next lower 25% of his range then this is not as good as betting pot.

BUT, he may see this last 200 bet as a blocking bet because we have a marginal hand. When he seeâ€™s this weak river bet he could read this as a blocking bet and turn one of his hands into a bluffing hand. He could have 910 that he doesnâ€™t want to turn into a hero call, things like that. So because he has 70% of hands that wont call and we look weak it is not unreasonable that he will try and bluff us.

So we now modify the EV calc to account for this
EV(200) = 100+1000x 100 = the ev of a 200 bet we figured out before
Where x is the % of time he decides to bluff raise us

So now we need to find x so we set up an inequality to see how often he would have to bluff us to make our EV of betting 200 the same as our EV of betting 500.

EV(500)<EV(200)?

175<1000x
x>7.5%
So he has to bluff shuv on us(x) 7.5% of the time for this play to get us the same EV as betting 500. We would expect a good aggressive regular who can read hands and sense weakness to make this play much more then the 7.5% so the bet of 200 most likely gets us the most EV.

So against the donkey we overbet because they call with much worse hands. Against an aggro regular we know he has many hands that arenâ€™t calling on the river anyway and we bet that gives the villain an opportunity to make a huge mistake after we have made our hand. We are taking advantage that there are many hands we could have that we would fold if he shuved here.

OK so here are some things to think about:

Do you know how often a pot bet bluff needs to work in order to be profitable?

Well, lets set up an EV calc to find out assuming the pot is 100

EV(pot bluff) = 100x â€“ 100(1-x)
X = how often they are folding
Then set it to 0
0=100x-100+100x
X = 50% of the time. So our bluff needs to work 50% of the time if we are betting pot in the river for us to be breakeven on this play.

What about a half pot bet?

EV(halfpotbluff) = 100x - 50(1-x)
0 = 100x - 50(1-x)
0 = 100x -50 +50x
50 = 150x
X = 33.33% of the time he needs to fold when we bet half pot in order to break even.

Here is a hard example:
Final board reads: (\$100) 9d6d4h2h2c. and we have Td7d we missed and we decide to bluff. How often does he have to fold for this to be EV of 0
We estimate that he can call a pot bet 20% of the time
1/3 pot bet or less he folds an extra 10% of the time and the other 70% of the time he has a busted draw/overcards.

Is this a good spot to bluff?

Since he will mostly have weak hands and busted draws it looks like a pretty good spot to bluff, but how big should we bluff

So final board is (\$100) 9s6s4h2h2c
He calls a reasonable bet (pot or less) 20% of the time
He calls extra small bet (1/3 pot or less) = 10%
He folds (busted draw,etc) = 70% of the time

So if we bet pot, that is if we bet 100 to gain 100 our setup is
EV(pot bluff) = 100*.80 â€“ 100 *.20
Ev ( Pot bluff) = \$60

So 60\$ is good, but what if we bet 40\$ instead of \$100

EV(bet40bluff) = .8(100) â€“ .2(40)
EV(bet40bluff) = 72\$

Since he has so many missed straights and flushes that he has to fold we can risk less and win more by betting 40% of pot.

What if we bet extra small say 25\$

EV(25bluff) 100*.70 â€“ 25(.30)
EV(25bluff) = \$62.75

So this is still more EV then betting pot, but it is not as high EV because he is going to call with an extra 10% of his hands.

So say we want to figure out the exact optimal bet size could we do this? Yes, even if we have to just start plugging in bets and guess and check.

So lets do it, we know it is around \$40 so lets try \$45

EV(45bluff) = 100(.80) â€“ 45(.30)
EV(45bluff) = \$66.5 so this is not it. Lets go the other way and remember that his threshold of adding 10% to his calling range is at 1/3 pot. Which is \$33.33

So lets say we bet \$33.33

EV(33.33bluff) = 100(.80) â€“ 33.33(.20)

Ev(33.33bluff) = \$73.33

So we found our optimal bet is \$33.33 and it give us \$73.33 in EV

So now lets switch over to the topic of C Betting

We should be thinking about how the board texture effects whether or not we C bet and how much we C bet vs different players and different board textures

The 3 bluffing axis that are related are
1. bet size
2. hand range related to board texture
3. player type
and we should always be thinking about these 3 bluffing axis when considering how much to bet and whether or not we should bluff at all.

So lets take a classic dry board texture of Ac7h2d and we are thinking about C betting. We should realize right away that this is one of the best board textures to bluff or to c bet because if they donâ€™t have an Ace it is going to be hard for them to continue and there are virtually no draws that they can be considering calling. The thing we need to realize about this board texture and how it relates to hand ranges is that against unaware opponents we can c bet a significantly smaller amount with our air hands and give ourselves a better price on our bluff like we did in the previous example. Giving ourselves a better price on a bluff raises our EV. Then, when we have AK we can bet much closer to pot to get maximum value out of our hand. We of course canâ€™t do this against any of the regulars but if we are up against a 45/10 we can. We will be getting action from another player on this flop mostly when he has an Ace also so we should be c betting max we can because these players arenâ€™t folding anyway.

What about a board of 6d7s8s and we have AK. Many times we should not be C betting this board because even if we bet pot, there are a lot of hands that will be calling here and then it puts us on the turn where we still may be good, but we donâ€™t know where we are at so we are forced to check/fold.

611 posts
Joined 02/2011

Just wanted to add a couple of comments to the thread (later is better than never!). Started to listen to this series 2 weeks ago. Just finished episode 7. WiltOnTilt you did a very good job on bringing very good content during the whole series, very well explained. Each principle and each piece of theory is alway clearly explained with good examples. I am now making more EV calculations during post sessions reviews. Doing theses kind of homeworks helps me to have a deeper understanding of the game and also by the way, add a lot of confidence to my game.

The least I can say here is thank you very much!

#### GrimbleGrumble

39 posts
Joined 04/2008

I have learnt so much from this series. Not having done any maths since school it has at times been a struggle but definitely worth the effort.

I have a question about which calculation we should be using/modifying to figure out the EV of a thin river value bet vs checking behind, when we will have to bet/fold to a shove 100% of the time.

Is it enough to take the formula

EV (bet) = bet * (calling%) + stack * (raising%) – stack * (us losing%) + pot

and take out the + stack * (raising%) since we are never calling a raise, and replace - stack * (us losing%) with - bet * (us losing%) since we are now just losing our bet, not our stack?

This would leave us with

EV (bet) = bet * (calling%) – bet * (us losing%) + pot

Would this be an accurate way of calculating this, or am I being a silly sausage?

Should we be actually using this part of the video

EV (raise) = EV (call) + EV (raise)

and changing it to

EV (Vbet) = EV (check) + EV (bet)

This does seem to make more sense to me, but there are a few things about using this that are hurting my brain.

At the risk of hurting it more I will try and detail my problems:

In the hand I am trying to calculate the EV of, we are value betting \$12 into a \$19 pot. I figured out that there are 25 combos we beat that check call, 16 combos that beat us and check jam and 9 combos that we beat but check fold.

So we win and get paid 50% of the time, lose and get shoved on 32% of the time and pick up the pot 18% of the time.

When we check back we win 68% of the time and lose 32% of the time.

The EV of checking is nice and easy to calculate:

EV (check) = .68 * 19 - .32 * 0

EV (check) = \$12.92

So the EV of our bet will be

EV (Vbet) = \$12.92 + EV (bet)

And we calculate the EV of a bet using this formula:

x= how often villain calls with worse, 1-x is how often we get jammed on and lose

EV (bet) = (bet size) * x - (bet size) * (1-x)

And this is when my brain really starts to hurt, because I am not sure which numbers to plug in to the formula.

I already said that we win and get paid 50% of the time, lose and get shoved on 32% of the time and pick up the pot 18% of the time, and that when we check back we win 68% of the time and lose 32% of the time.

In the video it is clearly stated that we are not concerned about how often our opponent folds for this kind of scenario, since when he does fold, our EV can be no higher than if we just checked.

Which numbers go into the formula then?

68% and 32%, or 50% and 32%?

Or do we completely remove all counting of folding combos and call it (25/25+16) 61% and 39%???

Removing all consideration of folding combos seems wrong since this changes our understanding of how often we expect to get called and win/ get shoved on entirely.

So what about the other options?

It seems counter intuitive to put in 68% and 32%, since we are clearly not being called 68% of the time. A part of that 68% consists of hands that are checkfolded.

Putting in 50% and 32% seems a bit off since then our numbers don't add up to 100%. Does this matter?

We can't put in 50% and 50% surely??

Arrggg my brain is really hurting.

I know this is a really old series/episode but if anyone can aid my confusion that would be great. Not for me, you understand but for Fluffy, my pet cat. She gets really upset when my brain hurts and cries. I can hear her now. Poor lil thing.

#### WiltOnTilt

2404 posts
Joined 10/2007

I'm pretty sure if you are in position and you are considering a value bet vs a check behind, and we are assuming that if we are never folding the best hand if raised, then from an individual hand EV perspective, the litmus test for whether or not we should bet comes from simply how often he calls with worse when he puts \$ in the pot, and if he calls our bet more than 50% of the time with a worse hand when he puts \$ in the pot, then we should bet.

The pot giving us an overlay wouldn't ever make it better than checking unless there is some other contingency such as we bet to prevent ourselves from being bluffed or if we bet it could open up some combos for him to bluff raise that he otherwise wouldn't. So if we remove those considerations (and maybe something else I'm not thinking of right now), I think we can just focus on how often he calls us with a worse hand when he has a hand he wants to put \$ in.

I think the reason your brain is hurting is because you might be confusing "how often he calls" compared to his overall range vs "how often he calls with worse when he decides to put \$ in the pot."

Assuming the above, we can just ignore the times we bet and he folds a worse hand... so the x would be how often he calls with worse and 1-x would be how often he calls with better and/or raises us and we fold.

x + (1-x) = 100% of the time he decides to put \$ in the pot

EV (bet) = (bet size) * x - (bet size) * (1-x)

I'm pretty sure that's right

#### GrimbleGrumble

39 posts
Joined 04/2008

Thankyou so much for such a lucid response. You really hit the nail on the head regarding the source of my confusion.

Brain no longer hurting, Fluffy is happy!!

HomePoker ForumsMicro Stakes Online NL → Mathematics of NL Hold'em : Episode Seven