Calculating the EV of shoving

OK, this is what I got so far;

Hero holds AKs. Effective stacks 100bb. ($10)

Villain's 3bet range is: 77+,A2s+,KJs+,QTs+,ATo+,KJo+,QTo+ (42 combo's of PP's, 36 of Axs, 6 of KJs+, 8 of QTs+, 33 of ATo+, 18 of KJo+, 24 of QTo+...= 167 combo's)

He calls 4bet shove w/ QQ+, AKs, AKo. (21 combo's)

Equity against villain's calling range is 42%

Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)

Villain has to call $9 if I shove.

Now to start the calculation,

F = Villain folds 146 combo's. 146/167 = 0.87. F = 0.87
P = 1.30

F*P = 1.13

(1-F) = 0.13

F*P + (1-F) = 1.26

That is as far as I got, not sure if I have counted combo's correctly either.

*[E*(P + S) - (1 - E)*S]

That ^^ hurts.

I don't know how to read it, is it 2 separate sums either side of the '-'?

Great to see you're working through this.

You got it right as far as F*P=1.13

After that, you've gone slightly wrong, and to get it right you have to understand the brackets (that's why I said in the other thread it's very difficult to explain it entirely without the brackets).

An example is if I say to you what is 4 x 5 + 3

You could say 4x5=20 + 3 = 23
Or you could say 4 x (5+3) which is 4 x 8 which = 32

So the brackets are important, because they tell you to do the sum inside the bracket _before_ the rest.

So when you do F*P + (1-F) you're doing that wrong - (1-F) on it's own isn't much use, it's just that it's (1-F) of the time that he calls (whenever he doesn't fold), so (1-F) gets multiplied by the EV when he calls.

F*P + (1-F) [E*(P+S) - (1-E)*S]

The square brackets are used just to make it more readable, you could just as correctly write:

F*P + (1-F) (E*(P+S) - (1-E)*S)

To answer your question of "is it 2 separate sums), yeah, you need to evaluate (P+S) first (1.30+9.00), then you multiply that by E. Then you evaluate (1-E) and multiple that by S. Then you take (1-E)*S away from (E*(P+S)). Then you take the result of that, and you multiply it by (1-F).

So,

F*P + (1-F)[E*(P+S) - (1-E)*S]

0.87*1.30 + (1-0.87)[0.42*(1.30+9.00) - (1-0.42)*9.00]

1.13 + 0.13*[0.42*10.30 - 0.58*9.00]
1.13 + 0.13*[4.326 - 5.22]
1.13 + 0.13*-0.894
1.13 - 0.11622 = 1.01378

or rounding that off, you expect to make about $1.01 each time you shove in that scenario.

Look back at the worked example I did above, and you'll see that I work my way out, evaluating things that are in brackets first, then continuing to work my way "out" from the bracketed parts.

F*P + (1-F)*[E*(P+S) - (1-E)*S]

This is one thing:
F*P
This is the portion of your EV that you gain by Villain folding.

and this is one thing:
(1-F)*[E*(P+S) - (1-E)*S]
This is the portion of your EV that you gain (or lose) by Villain calling.

I used the square brackets to help you see the order, but as Boris pointed out, they're treated the same as parentheses.

The part in the brackets would be your EV if Villain ALWAYS calls, but since Villain only calls (1-F)% of the time, we multiply the amount by the frequency of occurrence.

Inside the brackets is the same thing. The part E*(P+S) is your EV when you win the pot, and (1-E)*S is your EV when you lose the pot. In both cases, we multiply the amount of the result by the frequency of that occurrence.

If you do all of the calculations in the parentheses first, then do the brackets, then add the F*P last, you'll have it.


I'm going to re-write what Boris did and explain each step, just in case it helps.

(F*P) + (1-F)[E*(P+S) - (1-E)*S]
This is our equation. Note that I added parentheses to the F*P part, just for clarity and consistency.
On the next line, we just replace the letters with the numbers for our example.

(0.87*1.30) + (1-0.87)[0.42*(1.30+9.00) - (1-0.42)*9.00]
On the next line, we do all the math that is inside parentheses and nothing else.

1.13 + 0.13*[0.42*10.30 - 0.58*9.00]
Now we want to do the brackets, but we need to remember to always multiply/divide before we add/subtract things unless parentheses tell us otherwise.
On the next line, we do the multiplication inside the brackets.

1.13 + 0.13*[4.326 - 5.22]
Now we're ready to do the work inside the brackets. See how the subtraction happens before multiplying by 0.13, because the brackets (fancy parentheses) tell us to?
On the next line we do the subtraction inside the brackets.

1.13 + 0.13*-0.894
So now we're ready. It may be confusing to see *-, but it's just because we're multiplying 0.13 by -0.894. The negative sign is there.
On the next line we do that multiplication, and we solve the equation which we've reduced to a single subtraction.

1.13 - 0.11622 = 1.01378

Being all slick in Excel:

Select the cell A1
write "Fold Equity" (w/o quotes) or whatever you want to remind you what B1 is.
Select the cell B1
Enter the value 0.87 and press Enter
re-select cell B1
in the top left corner, where it tells you the cell name (B1), click there and type "F" (w/o quotes) and press Enter

repeat this process for cells B2, B3, B4, but with the appropriate values and letters, labeling them in column A so you know what they are.
1.3 -> P
0.42 -> E
9 -> S


Then just copy the following line and paste it anywhere in your spreadsheet. You need the equals sign at the beginning.

=F*P+(1-F)*(E*(P+S)-(1-E)*S)

Now you can change any of the numbers in your column B and the solution automatically updates.


EDIT: It helps readability of the sheet if you change the format of the equity cells (B1,B3) to %-ages and the other cells to currency.

OK, second attempt. I apologize for how I worked it out if anybody struggles to follow, I literally copy and pasted exactly how I worked it out.

Hero has QQ

Villain 3bet range - 77+,A2s+,KJs+,QTs+,J9s+,T8s+,98s,A2o+,KJo+,QTo+,JT o

Combos = 43 combo's of PP's, 46 Axs, 7 KJs+, 6 QTs+,

8 J9s+, 8 T8s+, 4 98s, 138 A2o+, 18 KJo+, 12 QTo+,

12 JTo...302 combo's.

Villain call 4bet shove w/ TT+, AQs+/AKo. (44 combo's)

Equity against villain call 4bet shove range - 53%

Size of pot - Hero raise 0.30, BU 3bet to 1.20, SB 0.05, BB 0.10.

Pot = $1.65

Villain has to call $8.80

EV Calc

(F*P) = Villain folds 258 combo's. 258/302 = 0.85

F = 0.85

P = $1.65

F*P = 1.40

E*(P+S) = 1.65 + 8.80 = 10.45

0.53*10.45 = 5.54

(1-E)*S = 0.47*8.80 = 4.14

1.40 + (1-F)*5.54 - 4.14

1.40 + 0.15*5.54 - 4.14

1.55*1.40 = 2.17

We stand to win $2.17 each time we shove?

It looks good up to here:

Originally Posted by Cobra_1878

1.40 + (1-F)*5.54 - 4.14

1.40 + 0.15*5.54 - 4.14

1.55*1.40 = 2.17

We stand to win $2.17 each time we shove?

Which should be:
1.40 + (1-F)*(5.54 - 4.14)

1.40 + 0.15*(5.54 - 4.14)

1.40 + 0.15*(1.40)

1.40 + 0.21 = 1.61

EDIT: You got some right answers with some terrible notation here:
(F*P) = Villain folds 258 combo's. 258/302 = 0.85
should be:
F = Villain folds 258 combo's. 258/302 = 0.85


E*(P+S) = 1.65 + 8.80 = 10.45
should be:
E*(P+S) = E*(1.65 + 8.80) = E*(10.45)

0.53*10.45 = 5.54

Originally Posted by MadMojoMonkey

It looks good up to here:



Which should be:
1.40 + (1-F)*(5.54 - 4.14)

1.40 + 0.15*(5.54 - 4.14)

1.40 + 0.15*(1.40)

1.40 + 0.21 = 1.61

EDIT: You got some right answers with some terrible notation here:
(F*P) = Villain folds 258 combo's. 258/302 = 0.85
should be:
F = Villain folds 258 combo's. 258/302 = 0.85


E*(P+S) = 1.65 + 8.80 = 10.45
should be:
E*(P+S) = E*(1.65 + 8.80) = E*(10.45)

0.53*10.45 = 5.54

OK, I think I got it now. Will have another attempt at it tomorrow.

Gotta love ftr

Lacks declaration of the variables used.

Originally Posted by jackvance

Lacks declaration of the variables used.

This thread is a continuation of a discussion that started here:
http://www.flopturnriver.com/pokerfo...46#post2171746

Here is the pertinent bit:

F is the number of combos that Villain folds divided by the total number of combos Villain currently holds.
E is the equity (found using equilab or something similar) of Hero's hand vs. Villain's calling range.
P is the amount of the pot (including any bet Hero may be facing)
S is the amount that is currently in Villain's stack (or Hero's stack, if Villain has more chips).

Hero has TT

Villain 3bet range 22+,A2s+,KTs+,QTs+,J8s+,T9s,98s,

87s,76s,65s,A2o+,KTo+,QTo+,JTo ( 73 combo's of PP's,

46 of Axs, 10 of KTs+, 6 of QTs+, 10 of J8s+, 4 of T9s

4 of 98s, 4 of 87s, 4 of 76s, 4 of 65s, 138 A2o+,

30 of KTo+, 18 of QTo+, 12 of JTo...= 363.

Villain call 4bet shove range TT+, AJs+, AQo+, KQs...= 65 combo's.

Equity - 42%

Pot - $1.30

Villain has to call $9

EV Calc

(F*P) = 0.82*1.30 = 1.07

E*(P+S) - (1-E)*S = 0.42*10.30 - 5.22

4.326 - 5.220 = -0.89

(1-F) = 0.18

0.18*-0.89 = -0.16

Thanks Savy.

If you put it in brackets on the calculator so it's 0.18 * (-0.89) that should work, but 0.18 * -0.89 is just 0.18 * 0.89 but minus.

2 * -3 = -6
2 * 3 = 6

Originally Posted by Cobra_1878

(F*P) = 0.82*1.30 = 1.07

E*(P+S) - (1-E)*S = 0.42*10.30 - 5.22

4.326 - 5.220 = -0.89

(1-F) = 0.18

0.18*-0.89 = -0.16

One more step.

Add the 1.07 to the -0.16.

EV = $0.91

Originally Posted by MadMojoMonkey

One more step.

Add the 1.07 to the -0.16.

EV = $0.91

ARRRGGGHHHH, why do I miss something out every fucking time. Important thing is I feel confident I know how to do it now, thanks for all your help everyone, especially MMM, it's much appreciated.

Congratulations, man. You're one step closer to pro.

I still think you should do at least one more. If not ITT, then maybe in another hand you post or something, where you point out why you did or didn't shove in a spot.

PokerStars - $0.10 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

MP: $18.00 (VPIP: 30.51, PFR: 22.03, 3Bet Preflop: 7.14, Hands: 59)
CO: $10.11 (VPIP: 27.27, PFR: 21.82, 3Bet Preflop: 0.00, Hands: 56)
BTN: $15.75 (VPIP: 26.92, PFR: 7.69, 3Bet Preflop: 0.00, Hands: 26)
SB: $13.14 (VPIP: 26.92, PFR: 23.08, 3Bet Preflop: 16.67, Hands: 26)
Hero (BB): $10.16
UTG: $9.70 (VPIP: 20.00, PFR: 17.50, 3Bet Preflop: 3.70, Hands: 82)

SB posts SB $0.05, Hero posts BB $0.10

Pre Flop: (pot: $0.15) Hero has 6 Q

fold, fold, fold, fold, SB raises to $0.25, Hero calls $0.15

Flop: ($0.50, 2 players) 7 K 7
SB bets $0.30, Hero raises to $1.10, SB raises to $2.40, Hero ???



Villain 3bet range - TT+,77,AKs,AsJs,AsTs,As9s,As8s,A7s,As6s,As5s

As4s,As3s,As2s,K7s,Q7s,JsTs,J7s,T7s,97s,87s,75s+,A Ko,A7o,

T7o,97o,87o,75o+...= 28 of PP's, 3 of AKs, 4 of AJss-

A8ss, 2 of A7s, 4 of A5ss-A2ss, 2 of K7s, 2 of Q7s,

1 of JsTs,2 of J7s, 2 of T7s, 2 of 97s, 2 of 87s, 4 of 75s+,

9 of AKo, 6 of A7o, 6 of T7o, 6 of 97o, 6 of 87o,

10 of 75o+...= 101 combo's.



Call 4bet shove w/ KK+, 77, AKs, AJss-A8ss, A7s, A5ss-

A2ss, K7s, Q7s, JsTs, J7s, T7s, 97s, 87s, 75s+, AKo,

A7o, T7o, 97o, 87o, 75o+...= 86



Equity = 25%

Pot = $4

Villain would need to call 7.51

Ev Calc



(F*P) = 0.15*4.00 = 0.6

(P+S) = 4.00 + 7.51 = 11.51

E*(P+S) = 0.25*11.51 = 2.88

(1-E)*S = 0.75*7.51 = 5.63

2.88 - 5.63 = -2.75

(1-F) = 0.85

0.85*-2.75 = -2.34

0.6 + -2.34 = -$2.26???

^

Looks good.

Looks like the math is all good there, Cobra.

WooHoo!! Thanks a lot MMM, really appreciate the help.

Going slightly off topic here but...

Had this hand the other day

PokerStars - $0.10 NL (6 max) - Holdem - 4 players
Hand converted by PokerTracker 4

Hero (BTN): $11.28
SB: $8.37 (VPIP: 25.00, PFR: 22.22, 3Bet Preflop: 20.69, Hands: 76)
BB: $8.95 (VPIP: 17.24, PFR: 10.34, 3Bet Preflop: 9.09, Hands: 29)
CO: $19.93 (VPIP: 21.43, PFR: 14.29, 3Bet Preflop: 0.00, Hands: 29)

SB posts SB $0.05, BB posts BB $0.10

Pre Flop: (pot: $0.15) Hero has K A

fold, Hero raises to $0.25, SB raises to $0.85, fold, Hero raises to $2.05, SB calls $1.20

Flop: ($4.20, 2 players) 8 J 5
SB checks, Hero bets $2.40, SB raises to $6.32 and is all-in, Hero ???

OK, so if I give villain a range of QQ-JJ,AdKd,AdQd,AdJd,AdTd...I have 22.3% against that range. I did the calling an all-in calculation, not really sure how to term it, and it gave me 23%. 3.92/16.84 = 0.23

My question is about the range I assigned though, is it too narrow/too wide???

After villain shoves there is $12.92 in the pot and it is $3.92 to call. So calling risk 3.92 to win 12.92. Your pot odds are 3.92/12.92 = 30%. That means you need 30% equity against his range to call and break even in the long run.

You have 6 outs against a pair lower than kings which is roughly 24% equity with two streets to go which isn't nearly enough.

About the range. That is way too tight for someone 3betting close to 20% overall. Probably his real 3bet is a little lower like 10-15% which would mean about 15% from the blinds.

After that people's 3betting ranges can be polarized or linear. A 15% linear range is the top 15% of hands. A 15% polarized range would be the super premiums and a lot of suited connectors, suited aces, and pocket pairs. Most people's 3bet ranges are polarized.

So for this guy that range is way too tight. I think a more realistic range would be like A5s, A8s, AJs, 88 - QQ, and maybe a few combos of suited connectors that give him a pair or baby fd to account for the times he shoves a weak hand because he puts you on AK and thinks you missed the flop.

Something like:

88+,AJs,A8s,A5s,KJs,QJs,JTs,AdKd,AdQd,AdTd,Ad9d,Ad 7d,Ad6d,7d6d,6d5d,Ad4d,5d4d,Ad3d,Ad2d,AJo

which gives you even less equity:

http://www.pokerstrategy.com
Board: 8d5dJh
Equity Win Tie
MP2 20.95% 20.27% 0.68% { AcKc }
MP3 79.05% 78.37% 0.68% { 88+, AJs, A8s, A5s, KJs, QJs, JTs, AdKd, AdQd, AdTd, Ad9d, Ad7d, Ad6d, 7d6d, 6d5d, Ad4d, 5d4d, Ad3d, Ad2d, AJo }

In any case this is a fold. I would not 4bet AK preflop at the micros. Just flat and see a flop. If you hit an A or K then you have the nuts. If you don't then c/f. Or just 4bet/shove.

The thing about constructing ranges is that you'll never get it exactly right. You just want a mix of hands he might realistically have so the equity you get from equilab is approximately correct.

Originally Posted by MadMojoMonkey

F is the number of combos that Villain folds divided by the total number of combos Villain currently holds.
E is the equity (found using equilab or something similar) of Hero's hand vs. Villain's calling range.
P is the amount of the pot (including any bet Hero may be facing)
S is the amount that is currently in Villain's stack (or Hero's stack, if Villain has more chips).

Hi. This is my first post and I am flashing back to reading an essay in front of class in the eighth grade. Please be more gentle than they were.

I have a question about the difference between an EV calc of a bet vs a raise. In other words, what happens to the money that we have to put into the pot just to call the action we are facing? In the calculation done based on the OP, there is .75 that is never included.

Looking at the post above, P should include any bet Hero may be facing. But, that seems to mess up the F*P fold equity by including an amount that is not really part of what we win when the villain folds.

It would seem like it has to be included somewhere in our pot equity calc. For instance, if we are assuming that we never folding so it is not an additional risk, shouldn't it be included in the E*(P + S)? On the other hand, since folding is technically always an option, should it be part of (1 - E)*S, because that is what we are risking...and that is really what that portion of the calculation is about.

I hope I have made some sense. I am really curious about this because as the size of the bet we are facing increases, the larger impact it would seem to make on the final EV calc.

Thanks so much for any help...and more importantly, thanks so much for all the great posts I have been reading the last few weeks!

Originally Posted by abelardx

After villain shoves there is $12.92 in the pot and it is $3.92 to call. So calling risk 3.92 to win 12.92. Your pot odds are 3.92/12.92 = 30%. That means you need 30% equity against his range to call and break even in the long run.

You have 6 outs against a pair lower than kings which is roughly 24% equity with two streets to go which isn't nearly enough.

About the range. That is way too tight for someone 3betting close to 20% overall. Probably his real 3bet is a little lower like 10-15% which would mean about 15% from the blinds.

After that people's 3betting ranges can be polarized or linear. A 15% linear range is the top 15% of hands. A 15% polarized range would be the super premiums and a lot of suited connectors, suited aces, and pocket pairs. Most people's 3bet ranges are polarized.

So for this guy that range is way too tight. I think a more realistic range would be like A5s, A8s, AJs, 88 - QQ, and maybe a few combos of suited connectors that give him a pair or baby fd to account for the times he shoves a weak hand because he puts you on AK and thinks you missed the flop.

Something like:

88+,AJs,A8s,A5s,KJs,QJs,JTs,AdKd,AdQd,AdTd,Ad9d,Ad 7d,Ad6d,7d6d,6d5d,Ad4d,5d4d,Ad3d,Ad2d,AJo

which gives you even less equity:

http://www.pokerstrategy.com
Board: 8d5dJh
Equity Win Tie
MP2 20.95% 20.27% 0.68% { AcKc }
MP3 79.05% 78.37% 0.68% { 88+, AJs, A8s, A5s, KJs, QJs, JTs, AdKd, AdQd, AdTd, Ad9d, Ad7d, Ad6d, 7d6d, 6d5d, Ad4d, 5d4d, Ad3d, Ad2d, AJo }

In any case this is a fold. I would not 4bet AK preflop at the micros. Just flat and see a flop. If you hit an A or K then you have the nuts. If you don't then c/f. Or just 4bet/shove.

The thing about constructing ranges is that you'll never get it exactly right. You just want a mix of hands he might realistically have so the equity you get from equilab is approximately correct.

Thanks, I get that sum wrong all the time.

I think his range has to be significantly narrowed after he calls a 4bet though? His 3bet range is obviously a lot wider than his calling a 4bet range.

Also, I 4bet bluff on the BU against the blinds so I have to balance that out by 4betting w/ my value hands as well.

Originally Posted by boutron

Hi. This is my first post and I am flashing back to reading an essay in front of class in the eighth grade. Please be more gentle than they were.

No prob.

Originally Posted by boutron

I have a question about the difference between an EV calc of a bet vs a raise. In other words, what happens to the money that we have to put into the pot just to call the action we are facing?

A bet is just a special name for the first raise. Conversely, a raise is just a special name for a bet that isn't first. The math is identical.
Please be aware that the math in this thread is about the EV of a shove, not a call.

Don't confuse this specific equation as good for evaluating calls. The difference is that in this equation, the action is closed. There can be no future bets, and the equities at this moment are the only equities that matter.

Originally Posted by boutron

In the calculation done based on the OP, there is .75 that is never included.

Please quote the bit you're referencing.

Originally Posted by boutron

Looking at the post above, P should include any bet Hero may be facing. But, that seems to mess up the F*P fold equity by including an amount that is not really part of what we win when the villain folds.

P represents the amount Hero wins when Villain folds. This is the amount of the pot, any bets Villain has made, and any bets Hero made earlier on this round of betting.
E.g. there's 10 in the pot before the first bet, Hero bets 5, Villain raises to 20. The value of P that Hero should use in doing the EV of a shove calculation is 10 + 5 + 20 = 35. P is the total money in the pot at that moment.

Originally Posted by boutron

It would seem like it has to be included somewhere in our pot equity calc. For instance, if we are assuming that we never folding so it is not an additional risk, shouldn't it be included in the E*(P + S)? On the other hand, since folding is technically always an option, should it be part of (1 - E)*S, because that is what we are risking...and that is really what that portion of the calculation is about.

WE ASSUME WE ARE SHOVING!!!

Other than that, it sounds like you're talking about a specific post in this thread, but you didn't quote it, so I don't know which of the many posts in the thread to which you refer.

Please quote the post you are referencing and I'll try to give an answer.

Originally Posted by boutron

I hope I have made some sense. I am really curious about this because as the size of the bet we are facing increases, the larger impact it would seem to make on the final EV calc.

The equation is the same, whatever numbers you plug into it. If you have no fold equity, then F=0. If you have a pure bluff, with no equity when you get called, then E=0. The math still shows you whether it's a +EV shove. The math does not tell you if it's the most +EV line to take, only the EV of your proposed line (shoving).

Originally Posted by boutron

Thanks so much for any help...and more importantly, thanks so much for all the great posts I have been reading the last few weeks!

Welcome to the forum.

From the OP:
Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)
Villain has to call $9 if I shove.

From the first replay, which you then explained thoroughly in the next reply:
F*P + (1-F)[E*(P+S) - (1-E)*S]

0.87*1.30 + (1-0.87)[0.42*(1.30+9.00) - (1-0.42)*9.00]

1.13 + 0.13*[0.42*10.30 - 0.58*9.00]
1.13 + 0.13*[4.326 - 5.22]
1.13 + 0.13*-0.894
1.13 - 0.11622 = 1.01378

Thanks so much for the response. I don't think I explained my question very well. When I refer to the difference between bet and raise, I am referring to the fact that a raise includes the amount that I have to call from the action that I am facing. In the example above, that is .75. The Hero is putting 9.75 in the pot when he shoves, of which only $9 is the raise. Only the $9 shows up anywhere in the math.

So, what happens, in the equation, to that .75. I am glad you answered, MMM, because in your variable explanation, you have:
P is the amount of the pot (including any bet Hero may be facing)

So, my question is what is happening to the bet the Hero is facing in the calculation? It's hard to imagine it is completely insignificant, especially if it is very large.

OT, just a quick background, as I hope to dive fully into these forums, I spent many hours in the cardrooms of Gardena in the late 80's, starting at the Normandie Club. After grad school, I supported myself for nearly a year playing 10/20 at the Bicycle Club. Then, the real world intervened and I pretty much forgot about the game. Recently, a family situation has me moving to an area with live poker and I thought I might brush up. OMG! What a shock! This is not your father's poker game.

Anyway, I am putting my energy into learning NL online, as that is the main action where I will be going. Between the highly empirical approach to the game, plus the difference in limit vs no-limit, it has been quite a brain shock. Luckily, this and other sites have made it SO much easier. In MY day, you had to special order Sklansky or SuperSystem from the Gambler's Book Club in Vegas.

Thanks again!

Hehe... I keep trying to find out why I'm right and you're wrong, but to no avail. Good catch.
Boris? You got me started and I never really scrutinized this bit. Am I blind?

Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)
Villain has to call $9 if I shove.

Hero is BU, I guess.

F*P + (1-F)[E*(P+S) - (1-E)*S]

This part:
E*(P+S) - (1-E)*S
is the conditional EV of when Villain calls.
The P+S is the amount Hero profits when he wins the hand.
The S should be the amount Hero loses when the loses the hand.
As such, you are correct in noting that bit went uncounted.

Yes. it seems we've been a bit liberal with the value of S.

I'm going to go ahead and say this is correct:

0.87*1.30 + (1-0.87)[0.42*(1.30+9.00) - (1-0.42)*(9.00+0.75)]

and hang my head in shame.
Sorry Cobra... there's 1 more set of parentheses.

Whew. I've been going over a bunch of my hands, calculating the EV for various plays. I was thinking I might have to go redo them all!

The math still shows you whether it's a +EV shove. The math does not tell you if it's the most +EV line to take, only the EV of your proposed line (shoving).

I'm glad you included that in your earlier post. I think that is the one piece of info that I am really going to take from this topic. Just because a play has a +EV doesn't mean that it is the best play.

Thanks again for your response. Now, if you can just help me break the habit of calling river bets w TPTK this forum will be perfect!

Stop calling river bets w/ TPTK... unless you are bluff-catching a Bluffy McBlufferson. Not too many micro-stakes players make river bluffs, or if they do, they do it all the time.

Originally Posted by MadMojoMonkey

Hehe... I keep trying to find out why I'm right and you're wrong, but to no avail. Good catch.
Boris? You got me started and I never really scrutinized this bit. Am I blind?


Hero is BU, I guess.


This part:
E*(P+S) - (1-E)*S
is the conditional EV of when Villain calls.
The P+S is the amount Hero profits when he wins the hand.
The S should be the amount Hero loses when the loses the hand.
As such, you are correct in noting that bit went uncounted.

Yes. it seems we've been a bit liberal with the value of S.

I'm going to go ahead and say this is correct:

and hang my head in shame.
Sorry Cobra... there's 1 more set of parentheses.

Wait, what?

I'm confused now.

This formula we've been working off of for the past bit, it's not 100% correct.
I didn't notice that we've failed to notice that Hero's shove amount is not the same as Villain's call amount, since Hero is facing a bet.
So in the example

Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)
Villain has to call $9 if I shove.

You have to shove $9.75 to put Villain all-in.

So this
F*P + (1-F)[E*(P+S) - (1-E)*S]

should be this

F*P + (1-F)[E*(P+S) - (1-E)*(S+B)]

B is the size of the bet that Hero faces.


The total amount Hero loses if he shoves, Villain calls, and Hero loses the hand is the $9.75.
Hero has to "call and raise" when he shoves, so the total amount Hero could lose is ESS + whatever bet Hero is facing.
or (S+B)

Each term has the form: (probability of occurrence)*(value of occurrence)
So (1-E) is the probability that Hero loses when the shove is called
and (S+B) is the amount of the loss.

Originally Posted by MadMojoMonkey

This formula we've been working off of for the past bit, it's not 100% correct.
I didn't notice that we've failed to notice that Hero's shove amount is not the same as Villain's call amount, since Hero is facing a bet.
So in the example

You have to shove $9.75 to put Villain all-in.

So this
F*P + (1-F)[E*(P+S) - (1-E)*S]

should be this

F*P + (1-F)[E*(P+S) - (1-E)*(S+B)]

B is the size of the bet that Hero faces.


The total amount Hero loses if he shoves, Villain calls, and Hero loses the hand is the $9.75.
Hero has to "call and raise" when he shoves, so the total amount Hero could lose is ESS + whatever bet Hero is facing.
or (S+B)

Each term has the form: (probability of occurrence)*(value of occurrence)
So (1-E) is the probability that Hero loses when the shove is called
and (S+B) is the amount of the loss.

OK, thanks MMM. I think I got that.

Is this one right?

PokerStars - $0.10 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

MP: $8.41 (VPIP: 20.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 5)
Hero (CO): $10.24
BTN: $9.64 (VPIP: 26.32, PFR: 5.26, 3Bet Preflop: 0.00, Hands: 19)
SB: $19.49 (VPIP: 20.31, PFR: 14.06, 3Bet Preflop: 4.17, Hands: 64)
BB: $10.00 (VPIP: 21.74, PFR: 10.87, 3Bet Preflop: 0.00, Hands: 95)
UTG: $10.00 (VPIP: 21.43, PFR: 21.43, 3Bet Preflop: 25.00, Hands: 14)

SB posts SB $0.05, BB posts BB $0.10

Pre Flop: (pot: $0.15) Hero has 7 A

UTG calls $0.10, fold, Hero raises to $0.40, fold, SB calls $0.35, fold, UTG calls $0.30

Flop: ($1.30, 3 players) 3 7 T
SB checks, UTG checks, Hero bets $0.95, fold, UTG raises to $2.50, Hero ???



Villain c/r range - TT+,77,33,ATs,KhQh,Jh9h,

Jh8h,T7s,98s,8h6h,6h5h,5h4h,ATo,98o...= 28 of PP's,

3 of ATs, 1 of KQhh, 1 of J9hh, 1 of J8hh, 2 of T7s,

4 of 98s, 1 of 86hh, 1 of 65hh, 1 of 54hh, 6 of ATo,

12 of 98o = 61 combos.

Call 3bet shove with TT+,77,33,Jh9h,Jh8h,9h8h = 31 combos.

Equity = 47%

$4.75

$7.10

EV Calc - (F*P) + (1-F)*[E*P+S) - (1-E)*(S+B)]

(F*P) = 0.49*4.75 = 2.33

E*(P+S) = 0.47*11.85 = 5.57

(1-E)*(S+B) = 0.53*8.65 = 4.58

5.57 - 4.58 = 0.99

(1-F) = 0.51

0.51*0.99 = 0.50

0.49 + 0.50 = 0.99

It looks like you used $2.50 for the value of B, but you need to subtract the dead money in front of you.
B is the amount you would be calling if you weren't shoving.

B = $2.50 - $0.95 = $1.55

Originally Posted by MadMojoMonkey

It looks like you used $2.50 for the value of B, but you need to subtract the dead money in front of you.
B is the amount you would be calling if you weren't shoving.

B = $2.50 - $0.95 = $1.55

Yeah I did use the $2.50, didn't think it seemed right when I done it. Thanks.

Edited original calculation, should be correct now.

Looks good. I didn't crunch all the multiplication steps, but you got all the right values in the right spots.