.50/1 Global Full-Ring

Reg opens to $3 MP w 100bb
Recreational player 3b to $10.5 in HJ w 200bb
Folds to Hero in SB w QQ, Hero has 200bb

Basically, from a recreational player, I expect his range to be pretty snug from these positions, not getting too out of line. Because of this, I am very much inclined to want to 4b a hand like AA as I would expect him not to fold often to a cold 4b, continuing very often.

I don't know much about this recreational, but just drawing general conclusions that he is going to be under 3betting here, and primarily be using stuff like JJ+, maybe some TT, AK, and maybe some AQs at a low frequency.

In a scenario like this, do we just 4b our AA/KK, and then do some cold calling with stuff like QQ/JJ/AK? It's super faceup to play like this, but I also don't think this comes up often enough for us to want to be flatting a hand as strong as AA very often(if ever). We can choose to not have a flatting range and maybe 4b a hand like QQ+, AK, and then fold AK/QQ to a 5b(depending on size), expecting a very overly tight 5betting range.

Any thoughts?

EDIT: just messing around with equities in flopzilla, and it seems like we can almost pitch a hand as strong as AKo preflop against this tight of a 3betting range..... This is something I would totally do in a Live game, but have never really considered it in many online scenarios. But this actually seems like a reasonable spot to do it if we think the 3bettor is on a tight range. Our equity with a hand like AKo is not that great, and the inital PFR is also uncapped. AKo could be used as a 4b bluff, but also seems totally fine to just fold preflop. I think JJ falls into this same category, but with worst blockers, so can also probably be folded. QQ is in a very strange spot, but can probably be justified with a call and proceeded postflop with caution. Maybe can cold call KK at a low frequency to keep JJ-QQ in 3b range and then can play post flop situations. AA can be close to a pure 4b. AKs probably can be played either way as well. Maybe AKs specifically, having borderline equity, but greater than AKo, can be used as the "bluff" region, blocking AA/KK, and potentially being able to fold out things like JJ preflop, or sometimes other hands that he shows up with at a low frequency. I think it's going for a stretch to expect JJ to fold preflop often however, but this actually seems to be a reasonable bluff candidate if we are going to choose any.