Help me with this math...

[n1nj4.br]

Hey guys.

I've been trying to do a "formula" concerning push situations in cash games. Bassically I want to know how much equity should I have against a villian call range if he folds X% of time to my push.

I.E:
effective stacks 100(bb)
sb 0.5
bb 1


Hero (UTG) raise to 3.5
foldsto villian (BTN) who makes it 12
blinds fold, back to hero.

Now I want to know how much equity should I have if villian is folding 66% against a push.

So I did a little math:
(money in the pot * fold%) + (pot size after called * equity) = (money invested pushing)

so it would be:
17(F%) + 201.5(EQ) = 96.5

assuming villian folds 66% of time:

16.34 + 201.5(EQ) = 96.5
201(EQ) = 80.16
(EQ) = 39,88%


Ok, i thought my math was good, but once I did one simple thing, i realized that there is something wrong. If villian folds 100% of time, than i need 0 equity to make this play +EV. But, if i put it in the formula, thats not what i gonna see.

So, help me to find the right formula.

ty in advance.

[tarheeljks]

too lazy to check your math right now. just read this:
calculating fold equity

[br.bm]

I think you didn't put your own loss into the equation.
Also, I like to start calculating the 0EV point.

Pot = potsize before push
F% = Foldequity
VS = villians stack on the flop
VEq = villians Equity
OS = our stack on the flop
OEq = our Equity


EV = 0 = (Pot * F%) + (VS * OEq) - (OS * VEq)

100% = OEq + VEq
--> VEq = 100% - OEq

EV = 0 = (Pot * F%) + (VS * OEq) - (OS * [100%-OEq])
EV = 0 = Pot*F% + VS*OEq + OS*OEq - OS
EV = 0 = Pot*F% + (VS+OS) OEq - OS
now isolate OEq
OEq = (OS-Pot*F%) / (VS+OS)

OEq = (96,5 - 17*0,66 ) / (88+96,5)
OEq = 0,46222 = 46,22%

Our equity against his range has to be at least 46,22%.


Villian folds 100%
--> VEq = 0%, VS = 0 (because we never win it)
EV = (Pot * F%) + (VS * OEq) - (OS * VEq)
EV = (Pot * 100%) + (0 * OEq) - (OS * 0%)
EV = Pot

[n1nj4.br]

Br.bm, i think there is still something missed. I.E, if villian folds 90% of time, how can i find the answer?

I think somehow the F% should affect VS.

[br.bm]

no, it only affects how often you win the pot uncontested

anyway, I named VS and OS wrong. It should be:
VS = villians stack before the push
OS = our stack before the push

If you want F%=90% use the final line:
OEq = (OS-Pot*F%) / (VS+OS)

[br.bm]

Uh, sorry I was wrong

I didn't figure in that you win the "pre push" pot when you win the hand if he calls.
Also, we have to make two major cases:
F%: he folds
100%-F%: he calls

so the main equation should be:

EV = F% * [pot] + (100%-F%) * [Oeq * 100 - Veq * 100]

[Lagtastic]

my brain hurts...

it must be a total fluke that i am a winning player and never make things this complicated

[br.bm]

the first 100 is villians complete stack
and the second 100 is wrong and should be OS (before the push)
EV = 0 = F% * [pot] + (100%-F%) * [Oeq * VS - Veq * OS]
We want to isolate Oeq
use this equation to eliminate Veq:
100% = Veq + Oeq
Veq = 100% - Oeq
0 = F%*Pot + (100%-F%)* [Oeq*VS - (100%-Oeq)*OS]
100% = 1

0 = F*Pot + (1-F)*[Oeq*VS - (1-Oeq)*OS ]
0 = F*Pot + (1-F)*[Oeq*VS - OS + Oeq*OS]
multiply 1-F with the last bracket:
0 = F*Pot + Oeq*VS - OS + Oeq*OS -Oeq*VS*F + F*OS + Oeq*OS*F
build a bracket to isolate Oeq:
0 = F*Pot - OS + F*OS + Oeq(VS+OS-VS*F+OS*F)

Oeq = [OS-F(OS-Pot)] / (VS+OS-VS*F+OS*F)
F=0,6
Pot = 15,5
OS = 100-3,5 = 96,5
VS = 100
Oeq = [96,5 - 0,6(96,5-15,5)] / (100+96,5 - 100*0,6+ 96,5*0,6)
Oeq = 24,6%


I'm not sure if this is right ... maybe I use pen and paper tomorrow and do it again.
24% pot equity seems pretty low ... but hey villian folds 60% of the time.
So if we do it 100 times:
we make 12*60 when he folds = 720
How often do we have to win his 100 to make it 0 EV?
If Oeq is 50% we don't loose or win anything on the other 40 hands. so we are very +EV
If he wins 75% and we 25% then he wins
75% * 40 * 100 = 3000
and looses
25% * 40 * 100 = 1000
-------------------------
-2000 for us

looks like 24% is wrong

[br.bm]

maybe this is right -.-
EVc = EV when Villian calls
EVf = EV when Villian folds

EV = EVf + EVc

EVf = F% * Pot
EVf = 0,6 * 15,5 = 9,3

EVc = OEq * 100 - VEq * 100

100% = OEq + VEq
VEq = 1 - OEq

EVc = OEq * 100 - (1-OEq) * 100
[...]
--> EVc = 200*OEq-100

EV = EVf + EVc = 0
0 = F*Pot +200*OEq-100
[...]
OEq = 0,453 = 45%

[Pokerfarian]

EV (Folding) = 0
EV (Shoving & not getting called) = +17BBs
EV (Shoving & getting called) = 201.5W - 96.5
You get called 1:2 folds so it's a good shove iff 34 > 96.5 - 201.5W ; iff W>0.31

This generalise to good shove iff W(Potifcalled) +(CurrentPot)(F/(1-F)) > $
W = win %, F = fold %, $ = $ you're putting in