Re: Theoretical T55 scenario
I can't imagine you'd play them much differently.
JJ and AT are almost equivalent in value except for one detail. AT has more outs to improve. AT also is more likely to win a split pot. Otherwise they are effectively the same.
Since a difference of 2 definitely clean outs (JJ) to 2 clean outs and 3 tainted outs (AT) is very very small and rarely will make a difference in any equity calculations, I think I'd play them very similarly.
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