I suggest having a section on the screen for current game to indicate next best moves. Ideally, it would have a strength number, but that could be hidden/omitted and simply ranked from strongest to weakest moves.

This suggestion is similar to the other one, titled "ALTERNATE CALCULATIONS." Joking aside, the other one appears to be an option to recalculate on demand. This one, on the other hand, is to inform you of additional options, actively.