I had this hand in a small live tournament this weekend. It was about a $50 average buy-in after the rebuy and add on and “dealer appreciation” bonus chips and there were about 22 players to start. The blinds were in 15-min levels, so it went up pretty quick and the stacks were short by the time this hand happened.  I was in the big blind with about 75k and was probably third in chips, being outchipped by a couple blinds by two.  There were 8 players remaining with about 3 players with less than 3 blinds. Top 5 finishers paid.  I don't remember the whole structure, but first was $675 and the 4th and 5th were about $100 and $75 respectively.  I didn't really care about the money for less than first place, so wasn't really interested in strategizing to just make it to the final 5.

Blinds were 4000/8000 with a 800 ante.

I was in big blind and dealt As8s.  It was folded around to the cutoff who called. Everyone else folded.  I checked.  Villain was to my left at our previous table and I had seen him flat calling several of flops with pocket pairs, including jacks and tens, but he seemed to be happy to fold modest pairs and draws to a bet. I think I thought that if I raised here he would call, but that he might fold easily later.

Flop is 2h 6s 9s. I checked here.  I did it sort of reflexively, though I am pretty sure villain folds any non-pair here, or if he calls it's often for the same flush I'm chasing. So, in retrospect, I think I should have bet here about 15k. He checks back.

Turn is Kh. I check again. He bets the minimum 8k. I had not seen him try to lead with nothing before, so I suspected he had something. I think he'd have raised AK or KK, so I think he likely has a K with a modest kicker or maybe T9s or 98s.  I thought about folding but I decided to shove.  I think I ultimately misjudged the facts at the time, but here's my thought process which I'd like critiqued.

1. He almost never has a monster hand here. 99 and 66 are definitely possible monsters, but 22 and KK are unlikely. I also think he would have raised with QQ and JJ, but maybe not with lesser pocket pairs.

2. He's previously folded middle pairs to aggression and shown them, so I suspect he would at least strongly consider folding JJ-TT, 88-77.

3. I have flush and ace outs. (After later thinking about this and pokerstoving it, I see that my equity against my estimates of his range was quite lower than I'd guessed it was, so there's that learning opportunity too. At the time I thought I might have about 40% equity, but it's closer to 28, and most of villain's equity comes from the K which is totally what he's representing. I probably should have taken the hint.)

4. I thought his min bet indicated a little weakness and that he might really not want to risk nearly all his stack on calling with a marginal hand. 

So, I shoved.  He tanked a long time before talking himself into a call.  He showed KdTd. Now that I think about it, he can probably see that I have worse than a pair of kings, since I'd surely have bet out on the turn for value against a relatively passive villain. Because of this, I think he could have realized that I maybe have a few monster hands but the vast majority is worse than his holding.

River was 2c, so I didn't hit. Villain had me slightly covered so I was out.

So what are the key places to improve here?  I think they are:

1. I should have raised pre-flop with a suited A8 against a single late position caller. I probably would have folded to a reraise.

2. I should have bet the flop since it was not a bad flop for me and was unlikely to hit his calling range.

3. I could have check-called the turn, since I had 3 ace outs to what would likely be best and all the spade outs to the nuts.

4. I could have check-folded the brick river and still had an above average stack.

So, really how bad was my shove here? What factors would have to change to make it a good play? If I'd gotten a small pair on the flop in addition to the spade draw I see my equity goes up to about 42%, so would that make it better? Or would that just reinforce the check-call line a little more?

thanks!