K-Q(s) in the CO, 4bb raise, button (agressive player) calls, no other players.

flop is AQx, rbw. Bet to make button fold, tease bet to feel it out, or check it?

Hmm well generally 50% pot is probe but you should just be aggresive and bet out trying to steal against 1 opponent-remember hitting the flop is hard granted though with raiseing and in general a higher card flop is more likly to be hit

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4x the BB is pretty big, and often indicates a middle pocket pair, like 77. The X in your example could be the card to watch out for. Knowing the button is aggressive could also put him on Arag, which is something to be cautious of - but since he's aggressive, he'll let you know if he hit it. I like a bet of 3/4's the pot here. It says "Hey I do have something," which discourages anything but hands that are better than yours from raising. However, they might call you down - be wary of big river bets.

well if you check, an agressive player is going to automatically bet regardless of what his hand is. this does not mean check raise all in, it means bet 1/2 of the pot and hope he folds. if he calls, hit a king, Q, or fold.