The Room of Fate returns from the previous Dead Ops Arcade games. It is a bonus room where you can select between 4 different fates that each provide a upgrade for your character for the rest of the run. In this iteration of DOA, the Room of Fate is found after you complete Round 20 and head into the 2nd Wild area. Get to the top of the mountain in this new lava location and you'll find a hole you can fall down which leads to the Room of Fate. For further context, refer to the video below that shows the entire 2nd Wild area and where to go to find the Room of Fate.