EV calcs thread

[rpm]

ok. as far as i can see it, barring metagame considerations and maybe some other stuff, if one can perform accurate EV calculations, then you can correctly analyse any situation in poker, and the only variable which you can fuck up becomes your ability to accurately assign your opponents a range and determine how they play it. my limited understanding is that EV calcs calculate the EV of all the possible outcomes of a given action and add them together, to find the overall EV. i really do not know how to do this beyond an extremely basic level (maybe one or two possible different outcomes and their probabilities) so for my own benefit as well as (hopefully) anyone else's who participates, i propose using this thread to post examples of situations in holdem, whether real or fictional (ie vs a caricature), involving EV calculations for others to solve and hopefully we will all benefit from a better understanding of the game as a result. i would provide an example to start us off but i don't know how to create card images without copying a HH into the converter (can someone help me with that?)

[rpm]

i'll try to start the ball rolling. before i do, i believe i played this hand badly, i am posting it to attempt to analyse the EV. in hindsight i think his checkraising range is more like QQ+, AsKs which has me crushed and isnt folding. at the time i (was slightly tilted and) got the impression he could have been trying to see if his TT-JJ was any good rather than playing another street OOP with them (by check/calling). villain is 25/16. for the sake of trying to learn i'll say he calls my 3bet with 88+,AQs,AK. i'll also say that he checkraises me on the flop with TT+, and AK, and calls my shove with QQ+,AsKs only.

No-Limit Hold'em, $0.50 BB (9 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com
SB ($85.95)
BB ($82.55)
UTG ($43.75)
UTG+1 ($61.35)
MP1 ($51.35)
MP2 ($104.45)
MP3 ($53.55)
Hero (CO) ($62.40)
Button ($47.65)
Preflop: Hero is CO with Q, 10
3 folds, MP2 bets $2, 1 fold, Hero raises $6.50, 3 folds, MP2 calls $4.50
Flop: ($13.75) 4, 3, 7 (2 players)
MP2 checks, Hero bets $9.50, MP2 raises $22.50, Hero raises $46.40 (All-In), MP2 calls $33.40
Turn: ($125.55) 2 (2 players, 1 all-in)
River: ($125.55) 4 (2 players, 1 all-in)
Total pot: $125.55

ok so when i 3bet the flop, i am risking 46 dollars to win 13.75 + 9.5 + 22.5= 45.75. three things can happen: he folds, he calls and i win, he calls and he wins. each has a probability i have determined through analysis of his ranges, and equity against them.

of the range he checkraises there are
TT (3), JJ (6), QQ (3), KK (6), AA (6), AK (16) = 40 combinations

of those 40 he calls with
QQ (3), KK (6), AA (6), AsKs (1) = 16 combinations

so he is calling my shove 40% of the time and i have

Board: 4d 3s 7s
Dead:
equity win tie pots won pots tied
Hand 0: 33.693% 33.24% 00.45% 5265 72.00 { QsTs }
Hand 1: 66.307% 65.85% 00.45% 10431 72.00 { QQ+, AsKs }

33.6% equity when he calls.
now i start to struggle.

i'll try to do the maths in dollars rather than BB's.

he folds 40% of the time and i profit 45.75
0.40 * 45.75 = 18.3

he calls 60% of the time, and when he does, i win 125.55 33% of the time and lose 46 67% of the time.

0.60 * (125 * 0.33)
0.60 * (-46 * 0.67)

i don't know how to do the equation when there are brackets and negative figures. if anyone could help me with that it would be much appreciated. as would comments on the whole operation, i'm sure i messed up some numbers or processes somewhere. i'll attempt to finish this one after a few hours sleep.

[Donachello]

I'm not 100% here but I believe your end equation would something like this.
(.4*45.75) +/- .6(.33*125 - 46*.67) = EV/hand. In this case the total comes out to be 18.3 +/- .6(41.25 - 30.82)---> 18.3 + .6(10.43) which even there shows that this is a +EV shove given the ranges. Unless I have the equations wrong.

Also if you're doing this in the heat of the moment and don't have time for calculations You can see that 125.55 is not quite but close to 3x 46 which means you'd only need to win a little over than 1/3 of the time for just that part to be +EV and when you factor in your fold equity to your actual equity it pushes you over the edge into +EV.

Spoon or whoever is welcome to correct any mistakes I made.

[EasyPoker]

I'm not 100% here but I believe your end equation would something like this.
(.4*45.75) +/- .6(.33*125 - 46*.67) = EV/hand. In this case the total comes out to be 18.3 +/- .6(41.25 - 30.82)---> 18.3 + .6(10.43) which even there shows that this is a +EV shove given the ranges.

I don't know either, but this just seems to be obfuscatory and nigh on impossible to learn from.

[kiwiMark]

Note that the time he calls and you win you stand to gain $79.15, not $125.55, as you don't include your bet in what you're winning.

(Imagine you have $100 at the time of the decision, when you bet $46.40 your stack is now $53.60, so the time you win and take the whole $125.55 pot your stack becomes $179.15, for a net gain of $79.15.

Hopefully that makes sense, if not just say and I'll try and explain better)

As for your equations, you are correct, your EV is equal to:

0.4 * 45.75 = $18.3 for when he folds, and then:

0.6 * (0.34 * 79.15) = $16.15 - As for doing this calculation, you can ignore the brackets when it's all multiplication, so I'd just punch in "0.6 * 0.34 * 79.15" into my calculator. If you're wanting to do it in your head with approximations of the numbers, as I say you can just ignore the brackets and multiply any of those numbers by any of the other two, and then multiply the result of that by the third, yet unused, number, and the answer will be the same, no matter in what order you do it.

0.6 * (0.66 * -46.40) = $-18.37 - Here, just follow the same as above, if it were me I'd completely ignore that it's negative while doing the maths, and then just remember to tack on a negative once I've figured out the answer (as I know this is the situation in which I lose money, so it makes sense and is easy to remember that it needs to be negative).

Then of course, you've got:

EV = 18.3 + 16.15 - 18.37 = $16.22

Again, I hope that's followable and the kind of thing you were looking for, if not feel free to say and I'll have another shot =)

this just seems to be obfuscatory and nigh on impossible to learn from.

It can seem that way, but you get used to it sooner or later. While often not practical at the table, this kind of analysis during your session reviews to see if you made the correct play is what will allow you to develop an "intuition" for if a play is going to be profitable or not, in real time, on the poker table. I cannot stress enough how much it's helped me. (Thanks, spoon! )

[rpm]

"I don't know either, but this just seems to be obfuscatory and nigh on impossible to learn from."

to be able to effectively to do these kind of sums during a hand, is for me, unattainable. but i'm hoping with enough practice in my analysis i can begin to start to form an understanding of whether certain moves will be +EV or not, just from being able to detect a weak range and getting a feel for my equity against nut ranges. (ie in the hand above villains nut range when he called was so full of overpairs that i still had decent equity when called, except against the one combo of AsKs)

but if you don't feel like you will benefit, you don't have to participate

[rpm]

ok kiwimark just said almost exactly that ^^. nh kiwi. i agree

[rpm]

oh yeah and for my first ever triple post, thanks kiwi that pretty much nailed it. the onboard calculator on my computer doesn't even seem to have a possibility for negative numbers so that's where i was being thrown off. i'll post another hand once i find one that might be interesting, and try to write an essay, in the meantime, anyone else feel free if you struggle with this kind of stuff to post HH's.

[EasyPoker]

Ok cheers for that KM and RPM

[rpm]

Note that the time he calls and you win you stand to gain $79.15, not $125.55, as you don't include your bet in what you're winning.

(Imagine you have $100 at the time of the decision, when you bet $46.40 your stack is now $53.60, so the time you win and take the whole $125.55 pot your stack becomes $179.15, for a net gain of $79.15.

Hopefully that makes sense, if not just say and I'll try and explain better)

so when i do the EV of villain calling and me winning, its

% villain calls * my % equity when he calls * pot after villain checkraises + how much i shove (or probably more aptly put, how much villain has to call when i shove ie how much i profit on top of what's in the current pot)

is that correct?

[kiwiMark]

Yup, you got it

[EasyPoker]

How do we work out the "% villain calls" tho?

[kiwiMark]

Give him a range before you act. Count how many hand combos in that range. That's your total hand combos. Now decide what hands he calls with, and count how many hand combos that is.

That / total hand combos (* 100) = % villain calls

[rpm]

preflop time. today i was studying the maths behind 3betting a wider-than-value range preflop in order to learn to better exploit the TAGGfish of which there seem to be plenty these days

villain raises to 4bb in the HJ with 24% of hands.
we decided to 3bet what ever hand we have (this is in a vacuum) to 12bb on the BU.
of the 24% villain is opening, he only continues to a 3bet with 9%

what is the EV of the 3bet in a vacuum, disregarding postflop equity?
think i've got these preflop ones relatively under control. i'll wait to let others attempt if they want before i post my (attempted) answer

[EthanH1]

ok i have been following these EV treads for a while and thought id have a go and post.

so 3bet EV.

villain raises to 4bb in the HJ with 24% of hands.
we decided to 3bet what ever hand we have (this is in a vacuum) to 12bb on the BU.
of the 24% villain is opening, he only continues to a 3bet with 9%

villain at 24% has 234 combos
and continues with only 9% 80 combos

80/234 = 0.34 times he call our 3bet.
= 0.66 times he folds.

so .66*5.5(amount in pot to win his bet plus blinds) = 3.63 +EV

let me know if i have gone wrong there some where??

[kiwiMark]

villain at 24% has 234 combos
and continues with only 9% 80 combos

80/234 = 0.34 times he call our 3bet.
= 0.66 times he folds.

so .66*5.5(amount in pot to win his bet plus blinds) = 3.63 +EV

let me know if i have gone wrong there some where??

Looking good, just a couple of things:

1. In this case you can simplify your first step a bit to 9%/24% (which will give you 0.34, just the same as figuring out how many hand combos it is, and then dividing those, like you did).

2. The amount we win when he folds is correct, but what happens the times he doesn't fold?

[Stacks]

Ev[bet] = (%call) * (Ev[call]) + (%fold) * (Ev[fold])

Ev[call] = (Equity) * (total pot) - (amount to call)

Maybe I'm the one making a mistake here, as I haven't done one of these in about 3 months (poker break), but from the range you gave him {TT+, AK} from checkraising there is 40 combos (taking your word for it, and not going to discuss the accuracy of said range). You suspect he continues with a range of {QQ+, AsKs}, which is 16 combos. This would mean he calls with 16/40 or 40% of his c/raising range, while folding the other 60% of the time. However, I believe everyone's calculations here have him calling 60% of the time and folding 40%.

"he folds 40% of the time and i profit 45.75
0.40 * 45.75 = 18.3"


If so, that might explain why my math is different. Not sure if Kiwi made the same 'mistake', but my answer is differing from his as well.

Either way, here is my take.

EV[shove] = (%call) * (Ev[call]) + (%fold) * (Ev[fold])

% call = 40% = 0.40
% fold = 60% = 0.60

The Ev of a fold here would simply be the current pot, or:

Ev[fold] = 13.75 + 9.50 + 22.50 = $45.75

The Ev of a call here would be:

Ev[call] = (equity)(total pot) - (amount risked)
Ev[call] = (0.33)(125.55) - (46.40)
Ev[call] = 41.43 - 46.40
Ev[call] = -$4.97

Thus the final equation would read:

Ev[shove] = (0.40)(-4.97) + (0.60)(45.74)
Ev[shove] = (-1.99) + (27.44)
Ev[shove] = $25.45

[kiwiMark]

Whoops, yeah, I had the calls/folds percentages swapped around (as did rpm). Other than that, the maths is all still fine. Stax does it a slightly different way than I do (I like mine better, but I guess his is less steps), but the result is the same.

[Stacks]

Referring to the 3bet EV.

If villain opens for 4xbb, and we 3bet to 12xbb, we would need him to fold 12/17.5 (That's the amount we risk divided by total pot) or ~69% of the time to be immediately breakeven on the fold equity alone.

So if you are estimating just how often he needs to fold, then you can do it that way, and compare that to the range estimate of hands he is opening to hands he is continuing with.

If you are wanting to see how much you are making per 3bet, we can do that with a few assumptions. Let's assume you are always bluffing here, and he either folds or shoves to your 3bet. When he shoves, since you are bluffing you always fold.

Ev[3bet] = (%hefolds)*(Ev[folds]) + (%heshoves)*(Ev[shoves])

Your Ev the times he shoves will be -12bb, as you will always fold, thus always losing.

The Ev of him folding will be +5.5bb, as you will win his 4bb + blinds (1.5bb).

So the EV of a 3bet is:

Ev[3bet] = (0.62)(+5.5) + (0.38)(-12)
Ev[3bet] = 3.41 + (-4.56)
Ev[3bet] = -$1.15

[kiwiMark]

fwiw Stax I think the 3bet EV was posed more as a question/exercise for nublets, rather than something he needed help on.

Also your folding/calling percentages are out a bit (should be 38 and 62), and you can't seem to decide if you want *'s between your brackets or not.

<Stax> step up your math game jeez.
<Stax> and your presentation skills
<Stax> significant leaks that need to be addressed.

[Stacks]

Yeah, my folding/calling percentages were based on Ethan's 234 and 80 combos, which leads to 34% calling and 66% folding. However, that is incorrect and the correct combos should be 318 (24%) opening range, and 122 (9%) continuing range. Which would lead to 38% calling, and 62% folding.

I'll edit my math above to correct that.

And FUUUU about my asteriks!

Edit: Just noticed what Kiwi was talking about with regards to the 3bet EV calc. Didn't realize it was a situation rpm posed to get others to give it a try, or I wouldn't have responded till more attempted it.

[rpm]

well spotted on the flushdraw jam calculation, stacks. i'm guessing kiwi just saw my attempt and had enough misguided faith in me to cause him to stuff his own one up. anyone think of any other common scenarios which an understanding of EV would help with? i personally struggle with value betting properly so i might try to find a river v.bet scenario where we can try to determine villain's calling range and the resultant EV of our bet. gotta go to a tute at the moment.

[kiwiMark]

Value betting is fairly easy. If you have >50% equity versus villain's calling range, you can bet for value.

[rpm]

pwned

[kiwiMark]

Wasn't supposed to come off as belittling, more as a "whoop whoop, this one's simple!"

[Stacks]

Kiwi in irc:
<Kiwi> I totally pwned him... I was so belittling, and I loved every minute of it.. I'll go say that it wasn't belittling and instead it was just an easy one, but it totally the opposite. I'm such abelittling asshat.







*Disclaimer - Above is false*

[rpm]

haha its cool. it's just that you told me the answer in half a sentence. i was about to start posting hand HH's and whatever else trying to determine the EV of my vbets. the end result would have obviously been "wow! who would have thought? if you beat half his calling range or more it's EV". on a more serious note. i should start trying to use this knowledge at the tables, my value bets are usually "whats the most i can bet and still have villain call with a decent amount of hands i beat".

[EasyPoker]

Value betting is fairly easy. If you have >50% equity versus villain's range, you can bet for value.

Thanks for this.

[rpm]

been doing some work on preflop theory. could some mathematically-inclined gambler tell me if my calculations here are correct? also, let me know if anyone wants some hypothetical preflop EV problems to solve together in here, otherwise i'll leave you all alone and only post questions when i seriously cant figure out how to do something.

Both hero and villain start with 100bb effective
Hero open A8s in the CO for 8bb after 4 limpers
BU 3bets to 24bb with a range of
A2s-A9s, QQ+,AK
of this range villain folds A2s-A9s to a shove, and calls with QQ+,AK
it folds to Hero who shoves 100bb.

villain’s 3bet range breaks down as follows:
calls a 4bet:
QQ (6) + KK (6) + AA (3) + AK (12) = 27

folds to a 4bet
A2s-A9s = 8x3 = 24

when villain calls, hero's equity is

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 28.879% 27.73% 01.15% 51285216 2121072.00 { A8s }
Hand 1: 71.121% 69.97% 01.15% 129401472 2121072.00 { QQ+, AKs, AKo }

possible outcomes
villain folds 47% of the time, Hero wins 37.5bb
villain calls 53% of the time, Hero wins 37.5bb + 76 = 113.5 29% of the time
villain calls 53% of the time, Hero loses 92bb 71% of the time

0.47 * 37.5 = 12.625
0.53 * (113.5 * 0.29) = 17.5
0.53 * ( 92 * 0.71) = -34.61
EV = 12.625 + 17.5 – 34.61
EV = - 4.485

thanks

[rpm]

if the above methodology is correct, then if we change hero's hand from A8s to AKs, the shove becomes about 20bb more profitable because villains calling range thins out (less AA's KK's and AK's) and our equity versus that calling range improves too. interesting.

[jaytoi]

Value betting is fairly easy. If you have >50% equity versus villain's CALLING range, you can bet for value.

right?

[kiwiMark]

0.47 * 37.5 = 12.625
0.53 * (113.5 * 0.29) = 17.5
0.53 * ( 92 * 0.71) = -34.61
EV = 12.625 + 17.5 – 34.61
EV = - 4.485

Everything looks good up until this point, where it looks like for the first calculation you accidentally wrote down 12.625 instead of 17.625. Which means the final EV should be slightly positive.

if the above methodology is correct, then if we change hero's hand from A8s to AKs, the shove becomes about 20bb more profitable because villains calling range thins out (less AA's KK's and AK's) and our equity versus that calling range improves too. interesting.

I haven't done the math so can't comment on the 20bb, but yes, it will definitely become more profitable. The power of blockers! One nitpicky thing, there won't be any less AA's when we hold AKs as opposed to A8s.

Originally Posted by kiwiMark
Value betting is fairly easy. If you have >50% equity versus villain's CALLING range, you can bet for value.

right?

Yessir.

[rpm]

Everything looks good up until this point, where it looks like for the first calculation you accidentally wrote down 12.625 instead of 17.625. Which means the final EV should be slightly positive.

cool. thanks.

and yeah you're right about there being no difference in the possible combos of AA if we hold A8 or AK