Calculating EV
Posted by Tom Coldwell
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Nice. Clear, though not tones of new info. Liked the last bit - I'd never thought to figure that out.
Great vid Tom. You do a really nice job articulating concepts and breaking them down in a slow and rational manner. Even seasoned poker pros can benefit from reviewing these concepts every now and again.
Regarding investment limits, do you see any reasons to pass on a 1,000bb Investment limit spot in certain situations even though it may be slightly +EV. A common example in my case would be I'm playing in a super soft live game where getting 1,000bbs in on the flop is slightly +EV. Are you in the camp that if you're rolled for a game you take any +EV spot?
Thanks for the comments guys, glad you found this helpful :)
Regarding whether I believe in taking all +EV spots, it kind of depends what you mean. If you're playing a super-deep live game, I wouldn't be looking to push a tiny edge early in a hand unless I thought that was the best chance I had of playing my hand profitably. My general belief against really bad players is that, when we're really deep, we'll perform best by pushing hardest later in the hands when edges become larger and our skill advantage more pronounced.
However, my (admittedly limited) experience of the kinds of villains you'll see in these games is that they really won't put you in many spots where this will matter 'cas all they do is call unless they are SUPER strong. In those cases, you just push every edge as you have enough chips that you won't get all in by the river too easily anyways so you just max each spot throughout the hand.
Tom im jus watching ur EV calculation in first 7 mins of vid and u re doing EV for 2 ppl stacking off 100 bb oone with equity 35 percent as follows
0.35*200-100
i think it should be
0.35*200-100*0.65 ( u don't lose a 100 percent of times ! )
That changes number significantly in close spots EV calculation
Next example u re doing same equation I'm kinda not sure thats correct, you don't take into account percentage of times we lose investment but u calculate as we lose it 100 USD 100 percent of time
Was afraid same miscalculation basic wil follow up further so i didn't check rest of vid, please look into this and reedit vid or confirm ur calculation is correct? :S
I can confirm however that my calculations are 100% accurate. What you've done here is assume the -100 codes for losing our investment. In reality, it codes for making our investment (ie putting chips into the pot). The 200*0.35 is our average return (35% of the pot) whilst the -100 recalibrates it relative to what we've put in. Basically it's average amount out minus average amount in (which is a constant).
Another way to look at this is to assume a situation where we put our money in preflop 100% (AA75 against KKKK say). In that scenario, my calc would be 200*1 - 100 = 100 for our average return of 100bbs. Yours on the other hands would be 200*1 - 100*0 = 200 for an average return of 200bbs despite our opponent only putting 100bbs into the pot. Clearly this is impossible and therefore cannot be correct.
Hope that helps.
ye I'm thinking of what ya saying, but u calculate EV from point where money is already in the pot, so u putting 100 to win 200, ur EV is 200 bb still, in AA against kkkk, u expect to win 200 bb ~ expected value, what u invested doesn't matter, what u calculated looks like returned investment calculation, kinda confused NOW
my formula looks like this
W : % we win
G : how much we win
L : How much we lose
EV=W x G - (1-W) x L
Sorry I'm jus supersuper CONFUSED now '(
i found 2 EV definitions
Expected value is the amount of money a certain play expects to win or lose in which case my formula applies
second
Expected Value (EV) is the average return on each dollar invested into a pot.
in which case ur formula applies
stil confused '(
The only way to use your formula (which is unnecessarily complex FWIW) is to input your opponent's stack as what you call "G" instead of the entire pot. Otherwise you're inputting some money more than once.
I cannot emphasise enough that your formula isn't giving the correct answer in any situation (as you're using it). You can modify the numbers you're inputting to make it work, but it isn't as simple as my method (especially in more complex situations). As such, I strongly advise you make yourself comfortable with the processes I cover in this video.
lol @ me and math - no wonder i always say - get it in :) cause apparently almost every situation by my formula is ev plus :S:S:S idk i think i got it lol in forum months ago i nvr rechecked it, yours jus confused me cause it didn't fit at all my numbers
just took plain old paper and pencil and did the kiddy like math for an hour, urs seems right mine is OFF wrong lol :S , sorry to bother :) i wouldn't but formula is also here from forum and simply didn question it i jus used it :S
i opened ur vid to recheck required equity formula cause my numbers didn't fit wit someone else's in todays tread, didn't get to that point yet, BUT THANKS very much for VID, apparently I do need it, wil study it thoroughly next week :)
Hi,
im the one who thinks this is scary, so im going way out of my comfort zone by posting this, i never had any of this sort of math during school, but i really like to learn this and thats why this video is of great value to me, so thanks a lot for taking the time to come up with this!
Can you guys check if i did everything right?
Couple of hands:
Hand 1
QcJsTc4s v.s. AsTsKd9c on Kc4c7hAd flop
Equity 40%
Pot is
20,50+130,50+130,50=281,50$
(281,50*0.4000)=112.60-130.50= -17.90bb
Hand 2
8s9sQsQc V.S.AdTcKcJs V.S. Ah6hKs3s on Ts6sJs flop
Equity is 38% 3way
Pot on flop
is 11+80+80+80=251$
(251*0.3800)=95.38-80= +15.38bb
Hand 3
KhKsQsJd V.S. Ac2cJh3h V.S. AsQhJcTd on 4h9cQc flop
Equity is 30.26%
Pot on flop
is 30+80+80+80=270$
(270*0.3026)=81,70-80= +1,70bb
Hand 4
AdKsQhTs V.S. AcAh2h4c V.S. 5s6d4h5d (pre-flop AI)
Equity is 28.38 3way
100+100+100=300
(300*0.2838)=85,14-100= -14,86bb
Hand 5 (included HH because am not sure if i did the math right!)
Seat 1: BTN ($89.03 in chips)
Seat 2: SB ($70.49 in chips)
Seat 3: Hero BB($102.82 in chips)
Seat 4: UTG($100 in chips)
Seat 5: UTG+1 ($217.04 in chips)
Seat 6: CO ($50 in chips)
SB: posts small blind $0.50
Hero BB: posts big blind $1
*** HOLE CARDS ***
Dealt to Hero [Ac 4h 9c Ad]
UTG: raises $2.50 to $3.50
UTG+1: calls $3.50
CO: calls $3.50
BTN: calls $3.50
SB: folds
Hero: raises $18 to $21.50
UTG: folds
UTG+1: calls $18
CO: calls $18
BTN: folds
*** FLOP *** [Tc 5c Ks]
Hero: bets $69.20
UTG+1: raises $69.20 to $138.40
CO: calls $28.50 and is all-in
Hero: calls $12.12 and is all-in
Ac9cAd4h
V.S. Kc7c5d4s V.S. AsTsKh8h=50bb stack on KsTc5c flop
Equity 3way
is 37,24% , HU 47,30% V.S. Kc7c5d4s (shortstack hand counted as dead)
Pot on flop is .50+1+3.50+3.50+3.50+3.50+21.50+18+18+28.50+28.50+28.50=158.50$
(158.50*0.3724)+(105.64*0.4730) -81.32= 59.02 + 49.96 – 81.31
108.98 – 81.31 = 27.67
EV= 27.67bb
Thanks a lot in advance!
1) Looks like you're putting 130.5bbs into a pot which was originally at 20.5bbs. Assuming you do indeed have 40% equity, this one is accurate.
2) Again, the calculation has been done correctly with the inputs you've used. However, suggesting you have 38% equity with the Q flush on that board is incorrect given you have one out (7s) and a backdoor full house draw. I'm kinda assuming you accidentally typed it as a flush board as opposed to one merely containing two spades.
3) Same again. You've used your inputs correctly and gotten the result you should have.
4) Ding! (I take it two players were in the blinds given the absence of any dead money).
5) Almost perfect. Only thing you did wrong was include a extra bb in the main pot (you were in the BB so you counted your 21.50 raise and an extra 1bb which had already been included in your 21.50). Apart from that (which really makes very little difference to the result), it's correct.
So all in all, 4.999/5 which rounds rather nicely to 5/5 :) Good job!
*I didn't check any of your equity numbers because you were asking about the calculation mechanics as opposed to the hands themselves. If any of those aren't accurate, they will naturally impact the results but given it looks like you plugged everything into PPT you've nothing to worry about.
Hey, thanks for the video, everything was almost clear for me.
What is unclear is the last part, in the investment limit example. When you start with 65.51 has to be minus -65.51. (time 20:50). After that, the last two lines are getting confusing by me. Could you explain maybe more how and why you do those last two parts?
Are there some easier ways to calculate those EV%? During a game would it be hard to calculate if I only have 30secs to do them.
Hopefully that makes sense (lemme know if not). Either way, this isn't a calculation you need worry about all that much, it's more a theoretical thing for people who like that sort of thing and it's certainly not something I expect to be using in-game.
As for how to speed up these calcs, the best advice I can offer is to practice so they become second nature, the have a calculator available if at all possible, and to round/approximate numbers where possible (this might harm accuracy, but we're usually only concerned with a rough ball-park figure anyways).
Thank you, I understand it now! :D
When finding our equity limit (investment/pot=required equity) don't we have to add on the bet where facing? (investment/investment+pot=required equity) ?
For example, if the pot is $100 and our opponent bets $100, we divide our required investment ($100 to match villain's bet) by the pot ($300 - $100 in the middle + $100 bet + $100 call) which gives us 33.33% or 1/3.
Hope that clears things up!
I think its basically the same thing though right? I mean $100 pot - villain bets $100 - now we have to invest $100 to win a $200 pot. So we can go investment/(investment+pot) and get the same number. $100/($100+$200). Not really a big deal that is just how I was taught it - risk/(risk+reward).
However, putting it in terms of risk/reward as you have done is completely fine and will give you the correct result. If you find it easier to conceptualize thinking about it that way, go for it!
Hi Tom (I hope you're still reading these comments)
I had a query relating to equity. Take hand 2 for example with 59% equity with wrap and FD. How do you calculate in game what your equity is (/more importantly, what the most +EV play is)?
Obv out of game with the hands face up it's easy to see but with hidden holecards how do you know?
Thanks
EDIT: Is the investment limit useful/relavent to HU pots? Is it possible for you to give me a good example for a HU situation?
As for how to calculate equity, first thing we do is assign villain a range of possible hands based upon the previous action and our knowledge of him. Beyond that, we can plug this info into something like ProPokerTools, although in game this is impractical. The best thing you can do is simply play a lot and do a lot of post-game work until you begin to get a good feel for how hands do against various hands/ranges. Not much else you can do as there's no quick solution I'm afraid :(
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