Depends on villain a bit but what would your plans be if you 4 bet to say 27-30BBs (or more) and then get 5 bet jammed? At that point unless the villain is a maniac I would put them heavily on AA or KK. That might be of big value to us since we could wind up saving chips in the long run but we have to not mind putting in 20% of our stack and then folding away any equity we have. I dont like folding QQ without at least getting some more information so I am not a fan of that route. When you 4 bet you might also get them to fold out their 99-JJ hands which is exactly what we dont want. I would call here and keep their worse hands in. It wont be the easiest to play post flop since we will be out of position (unless this is one of the blinds that does this to us) but we have a strong enough hand to not be scared to play post flop and see how the hand develops.
it all depends on the importance of the tournament and the status of the player at the table, in general, you need to make 4 bets and if the opponent decides to go all-in, then we can safely accept it, since only KK and AA beat us
When I have a deep stack, I usually call 3Bet with QQ than 4Bet. But if you read the opponent is a weak player and will 5Bet or Call 4Bet with a worse hand like JJ, TT, QJs,... it's possible to 4Bet to get value here.
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Especially if the Villain is also in early or mid position, I would often just call a 3-bet with QQ when 150BB deep. I feel, that if we 4-bet, we start to narrow the opponents range in a rather unfavourable way for our hand. One might then say, it this mean, we are 4-betting only aces or kings, and if this is not unbalanced. And it kind of is. But especially if its UTG open and UTG+1 3-bet, this action is already so strong, that a perfectly acceptable GTO strategy would be to just call with our entire range including AA or KK. In that way the opponent cant just bluff us to high heaven postflop, and we can possibly get away from hands like QQ and JJ on low boards, because we have AA, KK and sets to call him down with.