[HP]

I am too lazy to verify this myself, but one way to verify this is too:

Use pokerstove. Double check that KK is at least a 0 EV call for BB. You can make jacks and lower dead cards i believe. Then, double check that AKs and QQ are at most a 0 EV call

After that, double check that AKo is at least a 0 EV push (where folding is considered 0 EV) for SB given that BB calls with AA/KK. Then, double check that pushing AQs and QQ are at most 0 EV

If all of the above are true, you've got yourself a Nash Equilibrium, and both players are playing in an un-exploitable fashion. I'd define that 'perfect poker'

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If not, in general, how does this sound?

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Not good. I suspect you may be wrong. I suspect the un-exploitable strategy for the BB should be something like "call AA/KK 100% of the time, call with AKs 32.83% of the time, fold everything else"

I think it's way too much of a coincidence there are no 'boderline' hands (hands where they fold some non-zero percentage of the time, but don't fold some non-zero percentage also) in either of the player's ranges.