[Deorum]

Let me take a stab at your thoughts:

Flop: This is not really a scary board for any hands, and
although no1 is going to fold a pocket pair, and possibly
not any two cards, you decided to play your pocket kings as
if you had overcards. This allows people to give you more
action on later streets by putting doubt into their minds
as to the strength of your hand. It might induce
excessive action from somebody who hits a jack or something
on the turn. It also allows for a nice checkraise if the
button decides to bet. Your kings are only vulnerable to
one overcard and there are no other draws. Since people
are going to call with an ace high hand anyway, you cannot
protect against an ace falling on the turn by betting, you
can only valuebet against these hands at the time. If the
ace does hit, you likely can get away from your hand
cheaply depending on the action, but your opponents have
an equally likely chance of pairing their kicker and giving
you some action on that. The small bets lost from hands that
would have called drawing slim to dead is perhaps made up
from all of this.

Turn: That was pretty much a blank, no reason to scare
everybody off now with a raise while they are drawing slim
to dead to hands that will pay you off if they hit
something. Also, you get to threebet and trap BB if button
decides to raise here. This play is also consistent with
the overcards deception.

River: Okay, clearly we bet here and hope somebody calls.
It should be an easy call with any pair, as your opponents
should still be suspicious that you have overcards. Button
must have figured that it was more likely that BB would
overcall than it was that you would pay him off if he
raised. Either that or he was afraid you had 99.

So how far off was I?