Hard boards demand the third rule. Somewhere mid-solve the duplicates go quiet, and the only way forward is a connectivity argument: this cell cannot be shaded because the white cells would be split in two, or must be shaded because the alternative walls off a region.
Every hard board is still verified to have a single solution reachable by forward logic — bifurcation-only puzzles are discarded at generation. Warm up on the daily puzzle first; it rotates gentler boards.