The chance of receiving a pharaoh's sceptre scales depending on the floor level, upon a successful theft from a grand gold chest or sarcophagus (meaning no scarabs or mummies appear).
Players often choose to loot the Grand Gold Chest instead of the Sarcophagus (lootable item that can be found in Pyramid Plunder), since looting the sarcophagus grants Strength experience rather than Thieving experience. The sarcophagus also takes significantly more time to loot, thus being less efficient to loot for players aiming to get an as high as possible Thieving experience rate.
The chance of successfully looting the chest (no scarab appears) decreases by 1/256 every room. The following are the rates in the first room:
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These drop rates assume that the chest is looted succesfully, i.e. no mummy or scarab swarm appeared instead.