POKER MATH: Calculating Fold Equity
We are on a holy mission in the name of the poker gawds to discover the lost and secret art of quantifying fold equity. Seeking math wizards and numerological mages who have reached enlightenment in these arts.
I am using the formula
EV = P(f) + (1-f)[EV(P+R+R) - S]
this has the same result as
EV = P(f) + (1-f)[EV(P+R) + (1-EV)(-S)]
and we are trying to find the value for f (fold equity) where EV = 0 or break even.
The following once in a lifetime scenario plays down at a poker table in some obscure and secret underground location.
BB posts 400,
SB posts 200,
Action folds down to BU
BU raises 800,
SB raises 800 all-in,
BU calls 800 (maybe or maybe not),
At some point the SB collected the following variables and proceeded to do a most simple mathematical calculation.
Pot if fold (P) = 1400 (3.5BB)
Stack if lost (S) = 1400 (3.5BB)
Raise (R) = 800 (2BB)
EV = 56.09 (66 vs K8o)
= P(f) + (1-f)[EV(P+R+R) - S]
= 1400f + (1-f)[0.5609(1400+800+800) - 1400]
= 1400f + (1-f)[0.5609(3600) - 1400]
= 1400f + (1-f)[2019.24-1400]
= 1400f + (1-f)619.24
= 1400f + 619.24 - 619.24f
f = -619.24 / (1400 - 619.24)
f = -619.24 / 780.76
f = -79%
Eureka we have found the answer, fold equity is -79%. BOOM!
Keeping his best poker face to not reveal any tells
of his complete and utter confusion the SB quickly runs the calculation again, from a less than ideal spot this time.
EV = 25%
= P(f) + (1-f)[EV(P+R+R) -S]
= 1400f + (1-f)[0.25(1400+800+800) -1400]
= 1400f + (1-f)[0.25(3600) -1400]
= 1400f + (1-f)[900-1400]
= 1400f + (1-f)-500
= 1400f - 500 + 500f
f = 500 / (1400 + 500)
f = 500 / 1900
f = 26%
Snap! Dude on BU you should fold 1:4 times for us to break even, who's your daddy. But the BU called and he watches his chips get shipped away...
Now, the question of the universe and everything can anyone PLEASE tell me what on earth -79% is supposed to mean?