Yu-Gi-Oh! R started being published in Monthly V Jump in Japan on April 21, 2000, about 1 month after the end of Duel Monsters in Weekly Shonen Jump. Like anime movies and OAVs, this series does not fit in with the original. If it were animeated, Iím sure it would be an OAV.
Okay, now for the story. Tenma Yakou, Pegasusí brother, wants revenge on Yugi for beating his brother at Duelist Kingdom (kinda like Otogi did). While Kaiba is in America, he takes over Kaiba Corp. Kaiba Corp. developed a new dueling system called ď Solid SystemĒ. Anyway, Anzu gets kidnapped so Yugi must accept Tenmaís challenge. Yugi summons the God Cards, but Tenma has something more powerful, The Devilís Avatar. I think it can copy the gods or something because when Yugi plays Osiris, he attacks a monster and the monster turns into a black ball. The black ball turns into a black Osiris, and Yugi is scared. I canít read Japanese, so I donít know exactly what happens. Tenma duels Yugi this time in a VR kind of thing, I think. Yugi must defeat 13 Duel Professors to reach Tenma.
Viz may publish YGOR in English Jump. This may be why the are jumping straight to the Memories arc. Thatís just a thought though, donít quote me on it.