[slogger]

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While it's true that I likely have the best hand preflop, I'm out of position here. 2/3 times you'll miss the flop with AK, and I'm out of position. Even if I'm best on the flop (without improving), it can be very difficult to play this hand with 3 other people in the pot.

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This is why you should 3-bet. First, you likely have the best hand, so you're betting for value. Second, you're representing a big pair, with which you can bet almost any flop and get opponents who missed (and even some who hit the flop) to fold when they're drawing live (or ahead). Third, if it's capped by UTG, you have more information to work with as the hand proceeds.
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On the other hand, if I keep the pot small, it's easier for me to get away from it if the flop misses me. Thus, I may lose bets preflop, but I might gain them later by making fewer (or less serious mistakes).

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First of all, if the primary thought you have when holding AK in the BB is allowing yourself to get away cheaply, then you might as well fold and take up knitting. Second, here, you hit the flop in best way possible (TPTK, no other paint that makes two-pair likely for UTG, and no flush draw). This is not a time to be saving bets. There are already 7 BB in this pot, and you are giving up a vary fair chance (at the least) to collect them and more, so that you can save 3 or 4.
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It is clearly not optimal, but not terrible either. In this case, it ended up saving me a bet since I would have folded on the flop in either situation.

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[img]/images/graemlins/confused.gif[/img]How do you know you would have folded the flop in either situation? Certainly you can't predict that the flop action would have looked the same had you 3-bet preflop. Even if it was, folding would be very bad here.

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Many experts would agree with me here. For instance, Matthew Hilger recomends just calling in this situation in his Internet Texas Hold 'em book.

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No disrespect to Mr. Hilger, but take care in who you classify as an expert. And even when you've identified one, be sure to interpret his or her advice carefully, lest you misapply it to your own detriment.

If you haven't read SSH yet, I think now would be a good time.