Thanks for this. This is exactly what I was looking for in response to my original question. Not sure how useful it will be to me now I have realised the error of my ways, but thanks anyway.

Could someone explain me something that I am not getting..... I tried to find the answer so far but all I could find was that it was "a common mistake".


What I do not understand is why do we not account for the complete pot when calculating "he calls you win allin"

I personaly did that part like this:

2240 * 25% * 18.5%

I get to the 2240 because the starting pot is 400, we put in 920 and villain will call with 920 leading to a final pot of 2240.

Apperantly I am missing something here... but is that not the way to calculate equity of an outcome ?

Thanks in advance !

cliffs: Sausage terms in op were looking at changes in stack size the term you gave was looking at final stack size.

2240*25%*18.5% is a less convoluted way of looking at things. If you use this method then sausages original equation should look like this:

75%*(400+920) + 2240*25%*18.5% =1093.6

so the change in stack size would be 1093.6-920= 173.6 which was his answer

they are 2 different ways of looking at it , sausages equations do not account for the full pot size because his terms are calculating changes in stack size:
1) when you win an allin you win 400 in the pot + opponents 920 left and you win it 18.5% of 25% of the time hence (1320*18.5%*25%)
2) when you lose you lose your stack(920) and you lose it 25%of 81.5% of the time hence -(920*25%*81.5%)

either method will give you the same break even points

Thanks wobbly, I now understand why we arrived at different end results. He indeed looks at the change in stack size, I look at, what I call, total equity.

I allready discussed this with sausage before he posted here and we arrived at different numbers wich I did not understand because my calculation appeared correct..... we were just looking at different things.

So when we calculate the EV of a "move" (in this case the shove etc) wich is the correct way to look at it ? Because so far nobody has said to me that my way is not correct (since many people use sausage's way of calculating, I just assume mine is though)

Still a little confused but getting a little more clear every day

Thanks so far !

Both methods are "right", they just find slightly different things, sausages finds the net gain/loss, the other finds the expected stack value.

So in the example in op if you add what sausage terms effective stack to his answer it should be the same as the one gained from the way you do it , if it doesn't then something is wrong somewhere.
ie
if sausage gets 200 you should get 200+920 = 1120
if you get 1200 then sausage should get 1200-920= 280

Thanks again Wobbly for your explanation.

Now for the last very stupid question.... wich of the two is EV ? I will explain why I don't get it..... because I had a discussion about this before with Sausage and it turned out we both calculated EV in different ways.

Sausage's calculation was:

(400*75%)+(1320*25%*18.5%) - (920*25%*81.5%)=
300 + 61.05 - 187.45 = 173.6


My calculation was:

400*75%)+(2240*25%*18.5%) - (920*25%*81.5%)=
300 + 103.6 - 187.45 = 216.15


As we can see, two different outcomes....

So after doing some searches on the internet, I have found several postings that suggest that Sausage's way is the correct way of calculating EV. Also CREV, for wich we created a model, shows the exact numbers that Sausage also calculated, so no doubt about it. we can assume that is the correct way to calculate it.

But then there is something I don't understand..... wich is bothering my mind ever since

Why are we, when we win, not using the total number of chips we win from the total pot. Why are we only using the 400 and then the 920 that villain is putting in ? I would say that when we win, we win 18.5% of the total pot.

I always thought that EV was calculated on the final total potsize...

That part I just don't get.... but as said before, it seems to be a common mistake wich I found regularly during my searches, however, I have not found the explanation why it is a mistake.

Thanks in advance if you or anyone can clear this up !

Your equation is mixing up terms that quantify stack size change outcomes with terms that quantify total stack outcomes.

term by term:

(400*75%)
This is the stack size change when your opponent folds, what you want is your final stack size when your opponent folds(weighted for freq of fold) which is:
((400+920) *75%)

((2240*18.5%)*25%)
This is fine, this is the average stack size when called(weighted for freq of call). This accounts for all the allin situations.

- (920*25%*81.5%)
This is the stack size change when you are called and lose, but is completely irrelevant here because it is already included in the previous term, which takes into account every single allin situation.


Putting this altogether the equation you want for stack sizes is:

((400+920)*75%) +((2240*18.5%)*25%)



EV just means expected value you can calculate the expected value of all sorts of things.

statistically speaking:
sausages way is the ev of the change in stack size
your way is the ev of your total stack
to get from one to the other just add or subtract your effective stack (ie 920)

In most poker discussions I've read people seem to use EV for change in stack size, as in the ev of that play is +68 chips.

Thank you very much !

I see the big error I make now. I am not including the final stack size everywhere that I should.

Simply said (for most probably a lot more complicated, but not being a math guy, I am just putting it in my own words here):

in the first part, (400 * 75%) I am forgetting that I should also add my starting stack. That part of the formula should be: ((400 + 920) * 75%) = 990

My second part was allready "correct": ((2240*18.5%)*25%) = 103.6

Last part, well, thats when we loose, so that will be simple to calculate as 0

Adding all those up I will end with 1093.60

Wich is the AVERAGE STACK that I will end up with.

To get back to EV, I would need to subtract the starting stack from the ending stack.

That would be 1093.60 - 920 = +173.60 EV

Wobbly, BIG thank you very much for taking the time and effort to make it all clear to me !!

Yeah, I think you got it for most practical purposes , one nitty point,
This isn't quite right there simply isn't a last part.
The number 18.5% isn't the amount of times that you win the pot, its the equity you have in the pot.
Which is what % of the pot you win on average.
Usually these chips are gained thouugh winning the pot but sometimes they are gained through a chop

take the case of 44 v QQ
your equity is 18.67% if you have 44
this is made up of the times you win lose or chop
win % = 18.45
chop % = 0.44
lose % = 81.10

if you wanted to not use equity but instead use amount of times you win, lose or draw, then there would be a "last part"
using the example from op,instead of:

( 2240*18.67% * 25%)

you would have:

((0.1845 * 2240) + ( 0.22* 0.5 * 2240) + (0.8110*0) ) *25%

But thats a pretty nitty point, I think you understand whats going on.

you're welcome.

Now I do yes, and no harm in being nitty, it is something that should be able to be 100% correct and for that, we sometimes need to be nitty to push out the last half percent

gg