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Thinking now i should have made it about 2k and see what he does, wouldnt have looked so desperate

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NOOOOOOOOOOOOOOO!!!!!!!!!

Don't even consider reraising 40% of your stack with AK. What happens when you miss the flop (as you will 2/3 of the time) and he bets into you?

Given stack v. blind sizes in this hand, if you're going to raise it needs to be a push.

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I think there are some merits in re-raising with say, 1500-1800 in this specific situation. Miini-raises can range from slow-played monsters to probing bets by mid-PPs trying to get a feel where they stand. By re-raising you are representing a big hand. If villain re-raises, muck, lick your wounds hoping to get a decent hand with your short stack. In the buy-ns that I play, I have yet to encounter a re-re-raise below JJ, Ditto if he calls and bets out on the flop. However, there is the likelihood (I'm not a math guy and don't know how to calculate this) that villain checks if the flop contains overcards to his PP or misses with his AK, AQ or maybe AJ which I can then take advantage of by pushing. I also find that in lower buy-ins it is quite often to see insta-call of pushes with small/mid-PPs. These are the players who are either afraid or indecisive to play post-flop and most likely check if flop is missed.

Correct me please, if my thought process is convoluted.