OK, there's three of these.

Hand 1

BB is a short-stacked fish, basically dead money.
Only 4 hands on BTN, but he's 75/50 with a 3-bet of 100% (2 of 2), so probably pretty aggressive.
This is a good spot to jam, right? Especially with the short-stack overlay? Or do we not know enough about BTN?

Full Tilt No-Limit Hold'em, $0.05 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

saw flop

UTG ($3.65)
MP ($10.62)
Hero (CO) ($8.41)
Button ($4.51)
SB ($10.06)
BB ($1.62)

Preflop: Hero is CO with J, J
2 folds, Hero bets $0.15, Button raises to $0.52, 1 fold, BB calls $0.47, Hero ?


Hand 2

SB is 50/8 over 12 hands, so probably loose-passive.
I don't think villain has a premium because he just called the BTN steal and he couldn't know I would 3-bet.
So I put him on a range of 99-JJ, AQ, AJs, or something like that. I'm 50% against that range.
Go all-in?

Full Tilt No-Limit Hold'em, $0.05 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

saw flop

SB ($6.42)
Hero (BB) ($5.73)
UTG ($6.16)
MP ($6.47)
CO ($2.05)
Button ($4.47)

Preflop: Hero is BB with Q, A
3 folds, Button bets $0.15, SB calls $0.13, Hero raises to $0.60, 1 fold, SB raises to $5.40, Hero ?


Hand 3

Villain is 50/50 over only 4 hands. Snap?

Full Tilt No-Limit Hold'em, $0.05 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

saw flop

Button ($5.13)
SB ($6.94)
Hero (BB) ($6.70)
UTG ($1.74)
MP ($4.69)
CO ($2.90)

Preflop: Hero is BB with A, K
4 folds, SB bets $0.15, Hero raises to $0.45, SB raises to $6.94 (All-In), Hero ?