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In your villain description, you said that they play a fairly tight range. But given the position (Button) and preflop action (limp and then calling when closing the action), I think we need to assign a pretty wide range. This range will include a lot of 9x. In position, button could bet pair of 9’s for protection and call your raise.
For value, you would raise two pairs like K9 and 98. But you’re unlikely to check raise with just a single pair of 9’s. So the 9s on the turn seems better for button range than yours.
With the straight draws missing on the river, I don’t see a K (or 9) folding. Even though 76 is at the bottom of your range, I don’t think a bluff gets through enough to be profitable.
