^ don't think the nutted-ness is as relevant here. I mean if he does have those in his range, should be such a small percentage of the time. KK is probably inclined to not check raise flop or 4 bet flop much. 4bet probably more repping 22, KTo, KTs, T2s, K2s, as his main value range on flop. If he's saying he can be nutted here sure it helps but those holdings are probably more relevant as stroggoz is probably cbetting 100% flop with that small sizing.
i still don't know what to make of the 4bet // turn // river.