First of all, banish the min raise from your poker repertoire. Min-raising gives marginal hands the odds to call and out-flop you.
Second, you're 4 hands into a tournament and you're stealing blinds? I'm all for being aggressive, but early in tournaments guys are more apt to call these button and cut-off raises. I think it's fine to raise K9s here for value, but you need to proceed with caution once the blind calls.
Ok, so you make a 4x bet on the flop. I'm not sure what your blinds are here (10/20?), but I'm thinking the pot's at 90 or so with the pre-flop raise, call and the blinds. I'm fine with the pot-size bet here of 80-90. He calls; I'm thinking he's on a draw or got some piece of the flop at this point.
The turn is where I think you blew yourself up. He checks to you when the blank falls. Pot's 270-300 at this point and you massively over-bet it. Why? If you think he's on a draw, a 2/3 to pot-size bet gets the job done--ruins his drawing odds if he's on a draw and gets value for your hand, without committing your entire stack to the hand. As it is, you fire out 500-600, and he thinks and CALLS (wtf?).
At this point, I'd be done with the hand. (Note: I'd have been done with the hand if he'd have called a more reasonable bet, too) He's not on a draw; he flopped some sort of monster that he's been slow-playing. Guys that are on draws typically call quickly and even the most brain-dead player would realize that your massive over-bet ruined any drawing odds. Again, if he's on the draw, a 2/3 to pot-size bet gets value for your hand, wrecks his odds and doesn't over-commit you to the hand.
When he checks to you on the river, you need to check behind and lick your wounds when he shows the straight. His sick river check certainly looks like he didn't hit anything, but you've been showing aggression throughout; he might think you'll do what you did (i.e. shove) and pick you off. From your perspective, though, you should be thinking "What kind of hand that MISSED can call this bet?" The answer, of course, is "none". I think the only hand that calls your turn bet and your river bet is one that has you smashed.
Short version:
Make a bigger (3x BB) raise pre-flop.
Make a reasonable (2/3 to pot-size) turn bet.
Check behind on the river. A busted draw can't call your river bet.
Just my $.02,
Edmond
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