AK vs BB 3-bet: call pre, mostly call flop, mix turn, and river call is defensible given price and blockers.
Flop Kd9c2s: we flop top pair top kicker with SPR ~2.5. BB leads 8 into 32.5, giving us about 4.1:1 and needing ~20% equity. Solver prefers calling with AK here, using the raise mostly as a polarized value/protection line; our raise is slightly too small for that plan.
Note: Raising the flop is okay but the size is too small for a polarized value/protection line; solver prefers calling AK here and using larger raises more selectively.
Turn 7h: pot is 80.5bb, we have ~58bb behind, so stacks are effectively committed. Solver mixes between betting ~50% pot and checking; checking is fine to avoid getting check-jammed by a very strong range and to let BB continue with worse hands.
River 4d: BB shoves 57bb into 137.5bb, we’re getting about 2.4:1 and need ~29% equity. AK’s blocker effect and the fact that some of BB’s range is capped at one-pair hands make calling reasonable, though jamming or folding are also viable depending on read.