Check-Raising OOP after Range Check: Range Construction?

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Check-Raising OOP after Range Check: Range Construction?

I've been digging deeper into blind vs. blind play recently and I have some confusion specifically about how to construct our check-raising range after we range check as the SB.


So the main boards that we can simplify to checking range as the SB PFR are low suited connected boards. There are several examples but let's take this one (GTO+ checks 75.1% here, I simplify this to checking range in game):

In general, our check-raising range is constructed around holdings that (i) can go for value and (ii) have the incentive to deny equity/protect against future board runouts. Below we see the XR range against a 30% pot size stab of the BB. We clearly see how value holdings that need to protect against overcards are raised the most (apart from the obvious nutted hands), 99-88, A7, K7 etc. Observation 1: Across hands, the driver for check-raising aggression among value hands does not seem to be equity (as then AA would raise the most out of the overpairs), but equity denial.

If we follow through with this logic, then which combinations of e.g. 99 or A7o should be check-raised the most? Well those that have the strongest incentive to protect against future board runouts for them, so the combos without a club. Those with a club can comfortably call as they'll pick up flush draws if the third club hits. Those without a club would want to get money in more quickly as their incentive for equity denial is the strongest. However, if we look at the individual combos, it seems to be exactly the opposite (see below). Observation 2: Across the combos of an individual hand, the driver for check-raising aggression among value hands seems to be equity(!), not equity denial.

This seems like a contradiction to me. When choosing hands to check-raise, we choose the driver of equity denial over equity. When choosing individual combos within a hand, we choose equity over equity denial. Feels very weird to mix these two logics in range construction. Am I not seeing something? Is there a third factor that explains this divergence?

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