My question is; Is there an equation to calculate the correct line in terms of EV?

Ill use a hand ive been talkin about in the HU section

After talkin over this hand I explained that I check shuved and went on to calculate the EV of this move:

What Id like to know is there a way of like finding out the EV of just calling the bet like I can imagine it would have to be like

EV =
(0.799 x $2.20 + estimated$river) + (0.201 x -$2.20)

If we call and he calls river shuv when we hit 15.98 - 0.442 = +$15.538
If he check folds the river 1.7578 -0.4422 = +$1.3156

and EV of folding is Zero right?

Maybe I should also check the EV of check raising, like he may just call the raise to keep my bluffs in so we dont lose our whole stack when we miss on the river but he would have to call such a small shuv if we hit? Or I dont know if thats just ******ed,

Is there an equation to like compare lines like I have or do I just have to work it all out like I have just now

Only if you know the entire game tree from that point forth.

Brokenstars basically answered the question but there are some things you can do

1. Even if the turn bet is not all in you can do the EV analysis as you did, which gives you a first cut look at the situation. It would be equivalent to having a check-check on the river. Then adjust as necessary.

2. You can make several assumptions about what may likely happen on the river such as you posted, do the EV for each and weight by the estimated occurrence frequency for an overall EV. Note, a fold by you on the river is not 0 for the decision point is the turn action and a river fold has EV = - your last turn investment. You should use a realized equity if possible.


3. You can do an implied odds analysis whereby if you hit and win with the hit you may be able to stack your opponent. This is most applicable when the current situation does not give you the pot odds you need for making a call. BTW, you have 15 outs with a flush and straight draw giving you equity of about 30%. How did you get 80% ?

What you’re asking is what a solver is for.

It’s impractical for a human to compute on paper. Unless you’re a wizard in excel? But even then I think it’s too impractical.

if you knew the game tree it wouldnt be too hard.... making assumptions about ranges/actions can probably get you to a close answer and shouldn't take more than a couple dozen minutes.