In episode 3 of House of the Dragon, there isnt a lot of consensus over who should be next in line for Prince Aegon's second birthday, while others insist the throne is still Rhaenyras (being the actual firstborn and named heir). Poor Viserys, father and king, wants a clear sign of the right path and the mention of a white stag running around the Kingswood.
When Viserys (Paddy Considine) is called to a stag, it isn't what he imagined; it's, as one of the helpers notes, still a big lad, but the animal isn't white. This moment, though staged, and without the clear symbolism he so clearly seeks, provides no clarity about who the gods want to show their favor to.
Rhaenyra (Milly Alcock) is the one who spots the enormous white stag on a cliff in the morning. By design, she stares it down, prevents Ser Criston (Fabien Frankel) from killing it, and lets it go. The whole scene feels a bit mystical, tapping into the type of magic Game of Thrones used to employ to keep its high fantasy characters guessing about the future.
The world of A Song of Ice and Fire is unpredictable and randomly spread across the world. No religion had a clear grasp on magic, but none of them had a clear grasp on it either. Changed faces, reanimation, and ghost demon babies all existed with the same degree of predictability as lightning or a vision from looking into a fire.
House of the Dragon is based on Fire & Blood, which is a fairly brief account of the events as told by three people who witnessed (or witnessed) them. While George R.R. Martin brought whole characters back to life in the A Song of Ice and Fire books that the show left dead, Fire & Blood reads more like a textbook, leaving out the more otherworldly details of Martin's world.
The stag hunt in episode 3, like Aegon the Conquerors' dream from episode 1, is a step back toward the more strangely otherworldly world of Thrones. This time the story may be one we know the end of, but the signs along the way are more ambiguously otherworldly. The Iron Throne seems to reject certain occupants, and the white stag appears to those who may be worthy. But is any of that the greatest indicator of good ruler?