For pet displacement, see Pet#Speed
Displacement causes your image to appear a tile or two away from where you actually are. This makes it very difficult for monsters to hit you. The cloak of displacement, which is currently the only way this property can be obtained, is prized in the early game for it.
The exact effects are as follows: Displacement will make any given monster think you are at a random square within a 5x5 area centred on the player (read: 2 squares to either side). If you do not have a clear line of sight to the monster, it will only generate the image in a 3x3 square around you (read: it will think you are adjacent to where you are). This is presumably to prevent monsters being alerted to your presence from well around corners, or from the other side of a closed door.
As the observant reader will have figured out from the last paragraph, displacement is done per-monster, so your displaced image will generally be in two different locations for two different monsters. This means it is possible for one monster to see your image in the square of another monster. This will not cause the monsters to damage each other in melee-- such attacks still produces the "wild miss" message-- but they may still harm each other with breath weapons, ranged weapons, and the like.
If a monster knows where you are, displacement has no effect, unlike Invisibility which still grants a -2 to-hit bonus when a monster knows your location. However, when a monster does not know your location, it only has a 1/4 chance per turn of figuring out where you actually are, as opposed to 1/3 for invisibility. Like invisibility, each time you move, you must be "found" again by the monster in question. This makes having displacement or invisibility invaluable when you are running like hell from a fight you are ill-equipped for.
If a lawful demon prince mistakenly demands a bribe from your displaced image, he will become hostile without a chance of being pacified.
Displacement vs Invisibility
For those trying to decide whether to use a cloak of displacement or invisibility, important points have been outlined below:
- Displacement is not invisibility. Unlike invisibility, displacement still allows monsters to see you, and cannot be used as a tool for sneaking past monsters.
- Invisibility provides a -2 to-hit bonus if your adversary cannot see invisible. This is equivalent to 2 points of AC without any damage reduction.
- Invisible players will not be let into shops, but this is a minor inconvenience if the source of your invisibility is your cloak, as you may simply take it off.
- As noted above, your displaced image will not cause one monster to attack another in melee. This is most likely a result of the difficulties inherent in implementing a "hostile state" between two monsters, the equivalent to "It gets angry!" for the player.
- While moving while invisible will cause monsters to attack the square you once occupied, displacement generates your image somewhere within two squares to either side; meaning there is a very small chance of the monster moving in the wrong direction entirely. This chance is, however, very small: from 0% to 28%, depending on your surroundings and movement, but it will generally be 8.7% in an open room if you're moving away from the monster; which you probably are if you're hoping it will run away from you.
- While invisible, each turn, a given monster will have a 1 in 3 chance of discovering your position. With displacement, this chance is only 1 in 4 (non-stacking), making it easier to survive when running one's ass off. This "chance of discovery" is per MONSTER turn, so fast monsters like soldier ants will find you a lot faster no matter which you are using.
- Plenty of things can see invisible, very few can see through displacement
- There are many ways to become invisible (cloak of invisibility, spellbook of invisibility, ring of invisibility, potion of invisibility, wand of make invisible, and stalker meat), whereas displacement may only be gained with the cloak.
In summary, the biggest advantage of invisibility AND displacement are the 66% and 75% chances respectively that a monster will not know where you are if you have moved. For this reason, displacement and invisibility are quite evenly matched. However, the other advantages, like the to-hit penalty for invisibility, are trivial. Furthermore, if you have both displacement and invisibility, invisibility's lesser stay-hidden chance of 66% will be used instead of displacement's 75%, and invisibility will nullify the effects of displacement. Therefore having both displacement and invisibility simultaneously is just invisibility, and therefore entirely pointless, unless you are fighting monsters that see invisible.
In SLASH'EM, monster displacement exists. Therefore, monsters can be displaced, resulting in amusing remarks such as
- "You displace the displacer beast."
Only displacer beasts have displacement; (baby) shimmering dragons, whose scales give displacement, merely have a much lower AC than other dragons, making them harder to hit (thus simulating "displacement").
The cloak of displacement grants MC2, rather than MC1 as in Nethack 3.6.0.
In Dungeons and Dragons, a displacer beast appears several feet away from where it truly stands.