Lets suppose hero OR in BTN, Villain calls BB.
Ranges:
Hero:22+,A2s+,K2s+,Q7s+,J8s+,T7s+,96s+,86s+,75s+,6 4s+,54s,A2o+,KTo+,Q9o+,J9o+,T8o+,97o+,87o,76o
Villain:TT-33,A9s-A2s,KJs-K3s,Q9s-Q8s,J9s-J8s,T7s+,96s+,85s+,75s+,64s+,53s+,A9o,A5o-A4o,KJo-KTo,QTo+,JTo
Board:8dAh2s
Pot:10
Equity hero:72.01%
General advise (pio, snowie, my experience...) here is checking back, but studying the hand in detail i get that the most EV movement is betting (lets suppose we are betting 50% pot)
We have:
EV check = Equity * pot-->EV=7.201
EV when we bet-->we can divide it in 3 parts, EV_bet_fold,EV_bet_win, EV_bet_lose

Lets suppose villain is going to fold 62.79% calling TT-99,8h8s,8h8c,8s8c,53s+,Ad9d,As9s,Ac9c,As8s,Ac8c,Kh 8h,Ks8s,Kc8c,Qh8h,Qs8s,Qc8c,Jh8h,Js8s,Jc8c,Th8h,Ts 8s,Tc8c,9h8h,9s8s,9c8c,Ad7d,As7s,Ac7c,8h7h,8s7s,8c 7c,Ad6d,As6s,Ac6c,8h6h,8s6s,8c6c,Ad5d,As5s,Ac5c,8h 5h,8s5s,8c5c,Ad4d,As4s,Ac4c,Ad3d,As3s,Ac3c,Ad2d,Ac 2c,Ad9h,Ad9s,Ad9c,As9d,As9h,As9c,Ac9d,Ac9h,Ac9s,Ad 5h,Ad5s,Ad5c,As5d,As5h,As5c,Ac5d,Ac5h,Ac5s,Ad4h,Ad 4s,Ad4c,As4d,As4h,As4c,Ac4d,Ac4h,Ac4s
Hero equity vs this range is 41.58%
EV_bet_fold = %fold * pot-->6.279
EV_bet_win = %call * equity_vs_call * final_pot-->0.372* 0.4158 * 20 = 3.09
EV_bet_lose = %call * (1-equity_vs_call) * bet-->0.372 * 0.5842 * 5 = 1.08

Then, EV_total = EV_fold+EV_bet_win -EV_bet_lose = 8.289, which is greater than the EV_check.
I can imagine that i am doing something wrong, but i dont know what, any ideas, please?

when he doesn't fold you have to substract the bet from your EV because it is an additional investment. did you take that into account in your calcs?

also in those spots the EV should be very similar because you gain alot of EV betting by folding out his equity share. this is mostly true when there are alot of overcards to the middle pair.

No, and you are right

Yes, but in this case there are no overcards to hero midpair, i am taking KsKc as hero card. Sorry i forgot to mention it.
In fact hero range does not have any sense here, just hero hand. I cannot edit the original post

After substracting hero bet from EV_bet_win, results are:
EV_bet_win = %call * equity_vs_call * (pot+bet)-->0.372* 0.4158 * 15 = 2.32
Then, EV_total = EV_fold+EV_bet_win -EV_bet_lose = 7.519, which still is greater that EV check

This is so confusing. I am not sure how you can find EV's without the entire game tree.