This is a discussion on Expected Value (EV) issue within the online poker forums, in the Learning Poker section; I am attempting to create a basic shove chart but I'm getting way different results then normal shove charts and I don't know why. I
I am attempting to create a basic shove chart but I'm getting way different results then normal shove charts and I don't know why. I don't know if the formula I am using is missing something... With a 10% ante and 9 people at the table my formula is saying that the small blind should be shoving every hand as long as they have 17BB or less. Clearly this is insane. Could anyone please tell me what I'm doing wrong? Here is the formula and values I'm using and an example with 72o.
Fp = 1 - Cp Wa = 1.5 + (Ap * Pdc) Ev = Fp * Wa + Cp * (Eq * (Wa + Bb) - (1 - Eq) * Bb)
Cp = Call percent - The percentage of hands the big blind will call your shove Fp = Fold Percent - The percentage of hands the big blind will fold Ap = Ante Percent - Then percent of the big blind the ante is (usually 0%, 10% or 12.5%) Pdc = Players dealt cards - The total number of player that were dealt cards (and therefor that anted) Wa = Win amount - The amount in the pot when you shove (Small blind (.5) + Big blind (1) + antes) Eq = Equity - The chance you win a showdown against the big blinds expected hands Bb = Big blinds - The number of big blinds you have left to shove Ev = Expected value - The number of big blinds you can expect to win on average per shove
My hand: 72o
My stack: 15 big blinds after ante and posting of small blind
Big blind call range: 22+, A2s+, K8s+, Q9s+, J9s+, T9s, 98s, 87s, A8o+, K9o+, QTo+, JTo (this seems really loose to me for a 15 bb shove but the tighter the range the higher the EV due to the fold percentage)
Cp = 25.19% (The above listed hands make up 25.19% of all possible hands)
Fp = 1 - Cp Fp = 1 - 25.19% Fp = 74.81%
Ap = 10%
Pdc = 9
Wa = 1.5 + (Ap * Pdc) Wa = 1.5 + (10% * 9) Wa = 1.5 + .9 Wa = 2.4
Eq = 28.18% (Run in Equilab)
Bb = 15 (Specified above)
Ev = Fp * Wa + Cp * (Eq * (Wa + Bb) - (1 - Eq) * Bb) Ev = 74.81% * 2.4 + 25.19% * (28.18% * (2.4 + 15) - (1 - 28.18%) * 15) Ev = 1.79544 + 25.19% * (28.18% * 17.4 - (71.82%) * 15) Ev = 1.79544 + 25.19% * (4.90332 - 10.773) Ev = 1.79544 + 25.19% * -5.86968 Ev = 1.79544 - 1.478572392 Ev =.316867608
So shoving 72o from the small blind with 15bb has a positive EV? This can't be right. What am I doing wrong?
I didn't check the math because I'm not a math person by any means lol
However, I suspect this math is correct, or at least somewhat close to it. I suspect the "weird" thing is having an ante for this calculation and the fact that the SB is already "invested" into the pot (hence giving better odds to call).
According to the CardsChat 30 Day Course, the guideline presented was to shove any "magic range hand" or better (course "magic range" was any pocket pair and any suited Ace, but naturally we also would like to shove with hands like AKo) if at 10 or less bb and 15 bb or less with an ante in play.
Obviously, this is a guideline simplification. For instance, it doesn't take into account how large the ante is etc.
Upon a superficial glance, but not looking at the math itself, I don't think this is too far off with SB at 17 bbs or less, but 72o sounds way too loose to me.
Perhaps this similar scenario I posted would be worth your quick glance. Maybe your 17 bb shove is too loose because you assumed Villain ranges too loose? After all, our opponents do not shove anything 100% of the time