How to extract $$$ with a set.

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New to this forum. If the bro who made the laydown here wants to PM me about Lasik, please do.

This is a $10-$20 blind NL game, ave stack is about $3000, some have up to $10K.

Raised pot to $60 called 4 ways and I am in MP. The BB folds. I have 44 and the flop comes A-T-4. Beauty. The SB bets into me $120, I count to 20 and then call. Others fold.

Turn is inconsequential. He bets out $300.

What is your play here? I raised to $800, he went into the tank and then folded.

How does the board play this? My read on him is either AT or AK. Given the hesitation, more likely he had two pair.