cEV formula question
Hi there guys, it´s been a while since i posted here. I was away from the tables from over a year but now i am back and would like to review a few stuff that i am not sure anymore.
For instance, simple cEV calculations.
Let´s see this example.
We´re playing 6-max table (cash game). Everybody has 100bb and the action is folded around to the SB who open raises to 3bb, BB 3Bets to 9bb and SB fires back 4Betting to 27bb in total and BB ends up 5Betting all-in.
Giving i put villain on a 70% opening raising range and a 10% calling range.

Assuming the formula i am using is correct...

cEV = ((the % of the time we win * the amount we expect to win) – (the % of the time we lose * the amount we expect to lose) + (The % of the time villain folds * The amount we expect to win when villain folds))

For the fold equity i have...

FE = 1 - (Calling range / Opening range)
FE = 1- (.10 / .70)
FE = 1 - 0.1429
FE = 0.8571 or 85.71%

So...

cEV = ((0.40 * 200bb) - (0.60 * 100bb)) + (0.8571 * 36bb))
cEV = ((80bb - 60bb) + 36.86bb))
cEV = 20bb + 36.86bb
cEV = 56.86bb

Thoughts?

The general EV equation for hero shoving is:

EV = (1-fe)*EVcall + fe*(Pot before shove)

If we assume the decision point is the BB shove with 40% equity then for a call, hero wins SB’s stack plus the 9 he put in earlier or he loses the shove amount of 91.

EVcall = 0.40*109 - 0.60*91 = -11

You left out the (1-fe) factor

EV = 0.1419* (-11) + 0.8571 * 36 = 29.3