OK...so I just played in my first real (not online) NL Holdem tournament at Mohegan Sun. There were 39 players and I placed 16th. Anyway...the hand I got knocked out on I had A 6 suited middle position. I decided to play it because they were suited...which may have been my first mistake. At this point my chip stack was about 9,000 (starting stack was 6,000) and the blinds were up to 500 1000. Pre flop was not raised and I was sitting middle position, with the big blind, someone else to my right, me, and then the button in the hand (the button started the hand with about 12,000 chips). The flop comes something along the lines of 10 7 4 rainbow. The first 2 check as do I, with the button then betting the min bet 1000. The big blind and the other fold...leaving it to me. I'm thinking he is pretty much just making a position bet as we all checked and raised it to 3500...which he calls. The turn is a 5. At this point I went all in with my final 4,500 chips or so. The button immediately called and turns over AK offsuit...leaving me needing a 6 on the river...which I did not get. The button did not have even an inside straight draw or any possibility of a flush. I left thinking that even though I lost the hand...I would probably have made the same play had I known what he had...because I know for sure I would fold AK with no draw possibilities at all in that situation. So basically my question is...did I make a decent play and just run into someone who is one of those people who won't fold AK no matter what and made a lucky call or is there something I did wrong here? Because at this point I feel I would make the same play again and 90% of people in his position fold.

You don't say the blinds, but if the minimum bet is 1k you have 9BBs, so fold or shove preflop.

Also, learn to use paragraphs.

One of the things you did not consider was the size of the pot and the bet sizing. With 4 people in the hand there would be 4500 in the pot. (assuming the small blind folded) So when the flop comes and everyone checks to the button, he has the opportunity to bet and see who folds. At this point the pot has 5500. Your raise to 3500 means that he only has to put in 2500 more for a chance to win 9000.

So what I am getting at is the concept of pot odds. The ratio of the bet size in relation to the size of the pot. So in your situation your opponent probably made a good call on your raise because you did not bet enough. So when you go all in (pot size is 9000+4500 = 13500) he only has to call 4500 to win that pot.

Now I know my analysis is not complete but this should give you some information to dig into.

with less than 10 bbs id have folded and waited for a better spot to shove calling or even reraising here is not a good idea in my opinion less thab 10bbs is a shove or fold if you ask me