$50/100 500bbs deep, tricky spot with KK84ds v Gus

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$50/100 500bbs deep, tricky spot with KK84ds v Gus

BN: toweliestar: $9810
SB: Jeans89: $6093.50
BB: broksi: $57420
UTG: N Channing: $24392
HJ: MrSweets28: $51957
CO: M.O.P.: $24060
Preflop ($150.00) (6 Players)
MrSweets28 was dealt K K 4 8
N Channing folds, MrSweets28 raises $340.00 to $440.00, M.O.P. folds, toweliestar raises $1150.00 to $1590.00, Jeans89 folds, broksi raises $3790.00 to $5380.00, MrSweets28 calls $4940.00, toweliestar calls $3790.00,
This is one of the two major decision points in the hand. Gus (broksi) is cold 4betting here with roughly 15% of hands, if I had to guess. He'll 4b all AAxx, almost all KKxx, all AKJxss, most Axxx ds, most ds connectors, KQJTss, KT96ds. At under 125bb, I think this is an easy jam, but as you can see, we aren't under 125bb. Given the stack size situation, involving toweliestar, I ended up deciding to call, planning to get it in if towelie jammed, regardless of what Gus does (he will rejam almost full range). Thoughts?
Flop ($14160.00) 5 7 7 (3 Players)
broksi bets $2200.00, MrSweets28 calls $2200.00, toweliestar folds,
Standard, I think.
Turn ($18560.00) 5 7 7 3 (2 Players)
broksi bets $20705.00,
Hrmm. Gus pots here more than anyone probably (it's basically his only bet size in this spot, so don't read into the sizing). He'll have AA, KK/QQ/JJ+fd, gutter+fd, double fd, wrap, along with trips+ (though I do expect his 4b range to not be extremely low card heavy). I asked myself whether I have any FE, and I honestly didn't know the answer. I have seen him pot-fold in situations where you wouldn't expect anyone to be folding (due to the fact that it's his only bet size in many spots), but I'd never seen a spot that resembles this.
I feel good about my pre flop and flop decisions, but I haven't sat down and run the math given perceived ranges, so I wouldn't be shocked if I was wrong. The thing I liked about calling and getting it in if Gus re-jammed is that towelie knows I have a strong range here, and I don't think he'd jam often without AAxx, or at the very least, an Ace in his hand, making Gus' range end up weaker v mine.

On the turn, again I haven't run the math, even since the hand, but I also am very confused about his range. If you aren't too familiar with Gus' play, at least feel free to comment assuming it's an unknown hyper-agg Scandi :)

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