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hi folks,

please could someone literate in math talk me through how to solve the fold equity formula.

x=breakeven folding frequency
p=current size of pot
l=maximum loss
w=maximum gain
v=villain's equity
h=hero's equity
0 = XP + (1 - X)(-LV + WH)

so for example, the pot's 100 and we shove the turn for 90 with 35% equity (villain covers). comments about doing it myself or my level of intelligence welcome but unappreciated, believe me i've tried (something i should have done at school).

thanks.

First expand:

0 = XP + 1*(-LV + WH) - X*(-LV + WH)
0 = XP -LV +WH +XLV - XWH

Now move terms without X to other side (and switch signs):

LV-WH = XP + XLV - XWH

now factor X out:

LV-WH = X(P+LV-WH)

now divide both sides by (P+LV-WH) to get X alone:

X = (LV-WH)/(P+LV-WH)

and you're done

ok first of all thank you for helping. so using my example i did this:

L=90
P=100
V=.65
H=.35
W=190

0 = 100X - 58.5 + 66.5 + 58.5X - 66.5X
58.5-66.5 = 100X + 58.5X - 66.5X
-8= 92X
X= -.0870

it seems as though i've messed this up somewhere to get this answer

Your algebra is correct.

In this case you get a negative probability which is nonsensical but it just implies that shoving is always +ev in this situation when you have 35% equity!

It is easy to see that by considering the two extremes.

a) Imagine he never folds so X=0 then your EV is:

EV = XP + (1 - X)(-LV + WH)
= 0*100+(1-0)*(-90*0.65 + 190*0.35)
= 8

b) Imagine he always folds so X=1 then your EV is:

EV = XP + (1 - X)(-LV + WH)
= 1*100+(1-1)*(-90*0.65 + 190*0.35)
= 100

So it is always +ev to shove here. It is of course more +ev if he always folds!

ok got it. thanks a lot i really appreciate it!

Happy to help

trickster (and anyone else) if you're interested in a more tl;dr discussion of that formula, I just wrote up a fairly lengthy blog post on it

Thanks for this thread guys. It helped me double-check my math homework this afternoon.

Believe or not, I found your blog post with an Internet search.....which brought me right back to this thread on the DC Forum.

Cool. The internet is a small world! Glad to know it helped out.

mellowgold has pretty much nailed it. If you want some more examples/elaboration on this I'd recommend having a look at the Running the streets series where we go into a bunch of these calculations/spots.