PokerStars, Hold'em No Limit - $0.01/$0.02 - 6 players
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UTG: $2.12 (106 bb)
MP: $2.02 (101 bb)
CO (Hero): $2.50 (125 bb)
BU: $2.31 (116 bb)
SB: $0.79 (40 bb)
BB: $2.00 (100 bb)

Pre-Flop: ($0.03) Hero is CO with Q♣ Q♠
2 players fold, Hero raises to $0.06, 2 players fold, BB 3-bets to $0.20, Hero calls $0.14

Flop: ($0.41) 6♦ J♥ 7♣ (2 players)
BB bets $0.13, Hero raises to $0.57, BB folds

what vpip had you oponent?

Many hands get posted where we are in this situation with QQ and we get 3 bet. I like flatting as you did especially when we are in position as raising will not get better to fold and it may get 88-1010 to fold. I like calling here and keeping worse in the hand. As far as the play post flop I dont like raising there on the flop for the same reason. You are not likely to get AA, KK, or JJ to fold so you will be called by hands that are beating you and get hands like 1010 and 99 to fold to you which we would not want since we could get more value from them. I like just calling there and hoping there is not an A or K on the turn and continue calling. Raising generally in any street in these spots will make worse hands fold and never get better hands to fold. The only silver lining could be if you got AK to fold there which is not a bad thing for equity protection.

A side note is the flop is still not great even though there are no overs as it now brings in JJ as hand that is beating us now. Best flops would be 2,5,8 type of flops where there are no connecting cards and also cards that dont let large pairs that are below now beat us like JJ or 1010.

I would play same way. NH!