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Tough Spot in 125k Guarantee Tournament

Ok so i have a tough spot in a tournament I just played in. Tournament was at Columbus Hollywood Casino, buy in $350 with 125k guarantee. I took top 15 in a $50 satellite earlier in the week to win a seat.

Level 4: blinds are 100,200 with a 25 ante
I am at 40k off of a 30k starting stack. Haven't lost a hand at showdown yet, have a good image.
Preflop:
folds to me in cutoff, i have Kc10c and raise to 600. Get called by small blind and big blind.

Flop:
10s9c7s... check to me and i cbet 800 into a pot of around 2k. The small blind calls and bb folds.

Turn:
Jd... he checks to me and I check back. At this point I'm thinking he has a lot of two pairs that might check raise and I dont want to get blown off my hand with a pair, a gutter and an over. I think it might be worth betting to charge some flush draws but wanted to keep the pot small.

River:
Qd... he leads out and bets 2.3k into a pot of 3.6k I decide to raise to 5k. Looking back I dont like this raise. I don't know what hand would lead river and call a raise that I'm beating. Maybe I get a crying call from a set or two pair but I think his river bet is sort of polarizing to a straight or missed spades or something. He probably would just be check calling 2 pair or a set. And I really doubt he has a set bc of preflop play and flop play. JJ and QQ would raise pre and any other set would raise on the flop most likely. So after my raise he jams for 20k...

I tank for awhile. One factor was if I could have AK. If i could have AK then he wouldn't be raising river with just a king (assuming hes a thinking player). The only way I have AK here is if it's AK spades or sometimes AK with the Ace of spades. I wouldn't cbet this flop with just AK as it hits a calling range hard. I keep thinking and since he didn't 3bet out of the small blind and called a flop bet on that board, I really don't see how he has AK either unless it's AK spades or AK with the ace of spades...

So with me having K10 there are only 12 combos of AK left. AK probably should almost always be a 3bet out of the sb but lets say hes playing tricky and only 3bets 2/3 of them. (i think that number is honestly low) So now there are only 4 combos of AK left. With me cbeting the flop, he really should only be continuing with AK with the ace of spades... which is only 1/4 of the combos so he should only have 1 combo left then. But lets say he looser and calls with AK and the king of spades (he cant have AK of clubs which also could be a call bc of backdoor flush bc i have the king of clubs) then he has 2 combos of AK.

On the river he has 2 combos of hands that are beating me but he has sooo many combos of hands that I'm chopping with. He has KQ, KJ, K10, K9s and maybe K9off, K8s, K7s and maybe Kx with spades if hes playing loose from the small blind.

So if he never has any bluffing frequency then its a fold bc im only calling to chop but if ever bluffs (front door spades missed) and if ever overvalues a set of two pair then its a call.

I end up making the call, I expect to chop the majority of the time while winning sometimes and losing sometimes. He ends up having AK of hearts.... When I originally bet I was planning on bet folding. But when I thought about the hand it really didn't make sense for him to have AK.

My main questions for this hand are: should I bet that turn? should I just be just calling on the river when he lead into me? (I think yes, because the only hands that call/raise I am chopping with/lose to.) and should I call off on the river? River 3bets are so rarely bluffs that I'm either chopping or losing in the end. Also is my logic working through the combos correct?
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