The Solver Logic

The in-position flop check-back removes most overpairs and top-pair-strong-kicker hands but retains Ax hands — AK, AQ and AJ (e.g. A♣Q♥) were often checked back for pot control or showdown value. An ace turn therefore promotes much of the in-position remaining range to top pair, giving them an equity advantage and making the out-of-position player an underdog in equity terms. Probing small makes no sense when behind in equity — it builds a pot the out-of-position player is unlikely to win. The only profitable out-of-position actions are to check (concede the betting initiative when behind) or overbet with a polar range (two pair or better for value, air for fold equity), exploiting the nut advantage in the nutted hands they do hold.