[bata2]

Lets see how EV changes:
279$ EV before the hand is dealt
265$ EV after folding
301$ EV after push and steal
365$ EV after push and win
158$ EV after push and lose


Now lets define some broad calling ranges. The villain in the hand is somewhere between tight and regular.
Tight 10%:
30.4% T8o
69.6% 77+, A9s+, ATo+, KQ
Regular 25%:
34.8% T8o
65.2% 22+, A2s+, A5o+, KT+, QT+, JT+
Wide 40%:
37.7% T8o
62.3% 22+, A2+, K2s+, K5o+, Q7s+, Q9o+, J8s+, JTo+, T8s+, 97s+ 86s+, 76s, 65s


And, lets perform an EV calculation :

Tight range:
EV =.90*301 + .10(.304*301 + .696*158)= 270.9 + 201 = 291$
Regular range:
EV =.75*301 + .25(.348*301 + .652*158)= 225 + 52 = 279$
Wide range:
EV =.60*301 + .40(.377*301 + .623*158)= 180.6 + 95.4 = 275$


So the push is:
+26$ (9.8% increase) if he calls 10%.
+14$ (5.3% increase) if he calls 25%.
+10$ (3.8% increase) if he calls 40%.


Given possible EV gains from a push, lets see how the BB equity changes:

378$ EV before the hand is dealt
392$ EV after I fold
360$ EV after I push and steal
299$ EV after I push and win
449$ EV after I push and lose

Tight range:
EV =.90*360 + .10(.304*299 + .696*449)= 324 + .10(90.9+312.5) = 324 + 40.3 = 364.3$
Regular range:
EV =.75*360 + .25(.348*299+ .652*449)= 270 + .25(104.1+292.7)= 270 + 99.2 = 369.2$
Wide range:
EV =.60*360 + .40(.377*299 + .623*449)= 216 + .40(112.7+279.7) = 149.4 + 156.9 = 306.4$

So BBs equity before the hand is dealt is 378$. It will rise to 392$ if I fold, and fall to 360$ if he folds to my push.

So lets see the EV(BB) of possible actions:
+14$ if i fold.
+4.2$ if he calls 10%.
+9.2$ if he calls 25%.
-53.6$ if he calls 40%.

Lets compare :
Fold: EV(me)=-14$ EV(bb)=+14$
Calls 10%: EV(me)=+26$ EV(bb)=+4.2$
Calls 25%: EV(me)=+14$ EV(bb)=+9.2$
Calls 40%: EV(me)=+10$ EV(bb)=-53.6$

Now the only thing we need are success percentages:
I will bust:
6.92% if he calls 10%. Success: 93.08%
16.3% if he calls 25%. Success: 83.70%
24.9% if he calls 40%. Success: 75.10%


So, given the above information, this push is a Must, or ?