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The valuable wand of speed monster is a wand that will make monsters (including your character) speed up.
Zapping a peaceful creature with this wand (accidentally or otherwise) will anger it. While pets won't be angered, they do have a chance to resist: when zapping a pet successfully, you will get the message "(Pet's Name) is suddenly moving faster!" If there is no message, the pet probably resisted. You can check to see if a pet has intrinsic speed (fast) by applying a stethoscope to the pet.
Once you have identified this wand and zap yourself with it, the intrinsic speed is permanent. Thereafter, these wands are mostly useful for enhancing pets and steeds.
Engraving with a wand of speed monster will give the message "The bugs on the floor speed up!". Even though the message is unambiguous, the wand is not auto-identified. This is left up to the player.
Wands comprise 4% of all randomly-generated items in the main dungeon, 6% in containers, 5% on the Rogue level, and 8% in Gehennom. There is a 5% chance that a randomly-generated wand will be a wand of speed monster.