Live 1-2

Had a VERY specific spot arise in a game a couple days ago

player in a 1-2 game raises to $13, hero is on button/CO w 99 and 3-bets to $40(specific player has a sizing tell; he raises JJ+ $25 preflop, and then raises a wide range for less lol)

Then unexpectedly, the most old man coffee of old man coffee cold calls the $40 3b, and the PFR folds. The old man coffee in the BB has $100 remaining, and I think is going to be incredibly faceup with all actions, and I think his range is literally something like TT-QQ, KK/AA at like 50% each. And then maybe AK just gets flatted, as alot of live low stakes players will not just jam AK.

It got me thinking, hypothetically, if we had a way of knowing someone always had 16 hands that beat us, and 16 hands that we beat(but that have equity, in the case of AK), is there merit in betting the flop to capitalize on the times he misses(say on a 556 board), assuming he always folded unless he had a pair?

In this instance I don't think there is merit in betting on a low board, mainly because I think someone like this guy might have 18-24 overpair combos, meaning more than half of his range is just ahead of us, and I don't think equity denial is as important when the ranges are so narrow(I might be wrong on this)... From a risk/reward, say a $30 bet into a $90 pot makes him fold AK, technically it's a profitable bet, as our risk/reward is in check, but we also aren't really accomplishing getting called by worst.

In the case his range was perfectly symmetrical, we would lose $-30x16 = $-480 when he is ahead, and when we are ahead, we would win $90x16 = $1440, and if we check down, he realizes 25% of $90, which is 22.5, which we can multiply by 16x-22.5 = -360, while we realize 75%, or $67.5x16 = $1080

So, I guess it is a comparison for the answer...

By betting
-$480+1440 = $960

by checking
-$360+1080 = $720

Hmm. So, actually, in that case, if my calculations are correct, it seems like betting for the collection of dead money would still be the more profitable option.

I suppose a third option, that would be even more profitable, if we didn't think he was capable of turning hands into bluffs, would be to bet really small and try to get called by A high. Like if we bet $20, I could see this guy calling with AK. Then could even bet $20 on turn and continue to get cry called by A high, with confidence that he will not turn hands into bluffs.

Feel free to tell me I'm wrong, but this seems to make sense. Cool stuff

EDIT

I was curious to know at what point could we continue to just bet small, and even with a 22 value/16 A high ratio, betting still outperforms checking. We can take this a step further, and say if he had all TT-AA, betting and checking would perform similarly. But, I think a major take away, is that this guy might have more unpaired hands than AK. He might cold call AQs, and possibly stuff I wouldnt expect like KQs, AJs, or AQo. What this tells me, is that betting small on the flop is alot higher utility than I previously realized.

22 over pairs
16 ak

-$30x22= -660
90x16= 1440
780