Wow! Thank you very much for your quick and complex response!
I am sorry to steal your time and I deeply appreciate you taking care of me!!
Unfortunately, I think something doesn't work, maybe I was wrong with the calculations, I don't know :S
You formula and the classic formula,
have different results after calculating the same "spot" (call vs shove from the opponent). That is, for this imaginary hand, the values of "P_Steal" and "EQ_Steal" in your formula do not matter.
Classic formula (also published at the beginning of this thread).
(EQ_Fold - EQ_Lose) / (EQ_Win - EQ_Lose) = EQ_ICM
Ronny formula: (in the end, I subtracted "EQ_Fold", to know if the result is profitable, I know this is not the problem):
(EQ_Steal*P_Steal) + (EQ_Win*((1-P_Steal)*P_Win)) - (EQ_Lose*((1-P_Steal)*(1-P_Win))) - EQ_Fold = EQ_Shove (If I'm not mistaken, it's actually "EQ_Shove" equals "EQ_ICM" because I subtracted "EQ_Fold")
So as I say, i think that by calculating the same situation (spot) where the values "P_Steal" or "EQ_Steal" don't matter in your formula, both formulas should give the same result, but it's not. What am I wrong about?
++++++++++++++++++++++++++++++++++++++++++++++++++ +++
Attached photo,
https://prnt.sc/qcrewh
From my calculators in excel (I know that those formulas are correct to each other, except yours formula, matches the other formulas and with the EV in ICM make CALL that says HOLDEMRESOURCES).
Summary of Variables:
-EQ_Fold = 35.19
-EQ_Lose = 17.38
-EQ_Win = 43.5
-P_Win = 55.35% (Equity in favour).
-EQ_Steal and Fold Equity = 0 (since we're paying, but you can add any value to "EQ_Steal" which will always be 0, as long as Fold Equity is also 0, and in any case it doesn't change the result too much).
The results of the calculations:
-FB = 2.14
-CDC = 53.34%
-Nº1 Formula) EQ_ICM = 55.35% Minimum Equity to Call.
-Nº2 Formula) EQ_ICM = 55.35% Minimum Equity to Call.
-Nº3 Formula) EV/BB ICM = 0 (Break even, since I put 55.35% Equity).
Formula Ronny (your formula) = -15,52 ¡¡IMPORTANT!! Your formula should yield a result of 0 (since we have 55.35% of "P_Win", which is the minimum need according to the formulas "No.1, No2, and No3"). I guess it's my mistake.
Legend:
-EQ_Win = $ The chips are worth when you win
-EQ_Lose = $ Worth chips when you lose
-EQ_Fold = $ The chips are worth when you're
-EQ_Steal = $ Worth chips when you steal
-EQ_Shove = $ Is the chips valid when Shove
-EQ_ICM = $ Final Profit (compared to the rest of moves)
-P_Win (Equity in favor) = Our %Equity in favor (divided by 100 for Excel)
-P_Lose (Equity against) = Our %Equity against (divided by 100 for Excel)
-P_Steal and %Fold Equity (divide by 100 for Excel)
PS: After simulating several hands with the "Ronny formula", you would think that the Fold Equity and the "P_Win" (Equity favor) are not too important, what really affects the result are the values of "EQ_X", which makes a lot of sense to me, but it doesn't seem to work well on the example set out, where the result is "-15,52" instead of the right one that would be "0". I don't know where I'm wrong!
I'M SORRY I WROTE SO MUCH! I CANNOT SLEEP TRYING TO MANUALLY CALCULATE THE PUSH IN ICM