CO's EWR->HKG is always polar flight, unless there's some special event like increased solar flare or something like that.

UA's ORD->HKG depends. I flew it winter of 2002. We flew over N. Central Alaska, but not over N. Pole.

Neither HKG->ORD nor HKG->EWR fly over N. Pole. They ride the jetstream in N. Pacific instead.

There were more flights earlier from Europe to Anchroage and Europe to Japan, but now the Japan flights can fly over Russia.