Reads: ~50 year old passive nit. He is pretty loose preflop in limping. He is pretty cautious postflop even with good hands. He once tank/called a turn check raise all in with K10 on a A65A board. Seemed like an insta call to me.

I recently played a hand with him where I raised with AKo UTG, he flatted with 1010 in the BB, we went heads up, and flop,turn, and river checked through. The board was all low cards except for a Queen, and he took it down. Most players would bet at least at one point with pocket tens and only one overcard on the board.

Folds to him in the CO. He seems like he meant to limp with two $1 chips but put in two $5 chips, making it $10. I'm about 90% certain he genuinely meant to limp.

Button folds and I make it $30 in the SB with Q8. BB folds and he flats pretty quickly. Flop comes K84. He now has $75 left and I cover.

Hero?

Don't raise q8 preflop from the sb. Sounds like you can check it down with your showdown value against opponent you described

CB $30

He either has a K or middle pair and if he doesn't, he will fold. Even if he he has middle pair, he might fold if he's that weak.

If he call/raises, you're beat.

As soon as he flats your raise, you know he has something good. Check it down.

It would be great if I could get some type of mathematical proof as to why "check it down" > shove or vice versa. I'll start with a few assumptions based on my read:

1. He will always try to check down JJ or worse.

2. He will fold JJ or worse to a shove a non-zero % of the time.

3. He will never try a bluff with say AQ or AJ if I try to check it down.

I'm torn between checking it down or Cbetting a tad more than 1/2 pot. I think we can be happy checking it down and picking up a nice small little pot with a crappy hand at the same time knowing that we are probably only getting called or raised by better if we bet. Well when I think about it I think a Cbet doesn't accomplish much because he will fold most of his air or really weak hands we beat anyways which have little chance of improving by the river. So throwing out a Cbet let's us know what we knew already which is that there is little value to be had by any more money going into the pot.

Bet small and see how he reacts...

A Cbet keeps our other $45 out of the pot if later cards make the hand messy. If he's holding 2 overs, we take it now. If he's holding a mid pair, he might be able to convince himself we hold the K since he's so passive and we raised PF.

Hero raised because he thought the player was weak, why not stick with the plan and exploit passive play without shoving it all in if we're behind?

Results: We checked it down all three streets. Flop was actually K84, turn was J and river was Q. I won the showdown and villain didn't show.