[NL2-NL10] nl4sh KK IP vs drawy board and x/r on flop

• Bronze
Joined: 26.01.2010
Boss, \$0.02/\$0.04 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

CO: \$0.81 (20.3 bb)
BTN: \$3.95 (98.8 bb)
SB: \$4.28 (107 bb)
BB: \$18.24 (456 bb)
Hero (UTG): \$3.93 (98.3 bb)
MP: \$2.58 (64.5 bb)

Preflop: Hero is UTG with K K
Hero raises to \$0.16, MP calls \$0.16, 2 folds, SB calls \$0.14, BB folds

Flop: (\$0.52) 2 8 7 (3 players)
SB checks, Hero bets \$0.40, MP folds, SB raises to \$1.32, Hero raises to \$3.77 and is all-in, SB calls \$2.45

Turn: (\$8.06) 2 (2 players, 1 is all-in)
River: (\$8.06) 7 (2 players, 1 is all-in)

Results:
\$8.06 pot (\$0.80 rake)
Final Board: 2 8 7 2 7
SB showed 8 8 and won \$7.26 (\$3.33 net)
Hero showed K K and lost (-\$3.93 net)
MP mucked and lost (-\$0.16 net)

Opponent is kinda LAG.Stats : vpip 24 / pfr 22 / af 3 / 140 hands only.In this small sample as i notice later he has high fold to steal stat (100 so far).
One of the worst flops.
As i made some calculations with equilab i made some thoughts :

1)Opponent range for his move (x/r).
22,77,88,78,any XdXd,and maybe AdX KdX.Against this range i am behind sth like 65-35%.On flop i need 0.8 to call so its ~ 0.8/2.2= 36% needed equity.

So if i call i am kinda correct with my thought (am I?) and make a new decision on turn maybe.

2)i decided to push to protect my hand against so many draws.Opponent so far WTS 31 / W\$SD 56.Did i made a correct choise there ?

Thanks !