An ogre that displays quantum properties.
3 HD, 11 hp, AC as chain, attack at +3 for d10, saves as fighter 3.
A quantum ogre exists as a wave function distributed across all locations in the dungeon. When you map the place out, assign each room or corridor a chance for the ogre to be there: they should all add up to 1. Maybe some rooms have 0 chance for the ogre to be in them, to help things add up nicely.
An quantum ogre can exist in two states: wavelike and particle-like. It starts out in its wave-like state.
A wave-like ogre partially exists in all rooms at once (IE the ogre is 1/10th present in a room with 1-in-10 assigned to it as its chance for ogre). It can tell what happens in all of them, with a sort of dim awareness proportional to its chance for that location. A wave-like ogre cannot interact physically. Those that encounter it percieve it as a sort of hazy probability cloud of potential-ogre. They can tell that there might be an ogre here.
A particle-like ogre exists in only one place, where it fights normally like any other physical creature.
Collapsing the wave-function: when somebody tries to attack the ogre (or similarly interact with it in a way that would require it to be in its particle-like state), roll to collapse the wave function. IE make the chance roll to see if the ogre is present in that room. If it's not, assign that chance to another location that hasn't yet been proved not to contain the ogre. Eventually, either the ogre shows up or the chance is condensed into one place with 100% certainty (where the ogre then achieves particle-like form).
When the ogre is in its particle-form, whenever it wants to it can try to revert to wave-form, with its probability remaining distributed across various locations. The chance for this is the opposite of the chance to pop into particle form (so if a room has a 1-in-6 chance of ogre, the ogre has a 5-in-6 chance to go back to wave form in it). If the room has 0 chance of ogre, it reverts to wave form automatically. Becoming wave-like again doesn't alter the probabilities for each room.
The ogre can also try to collapse its own wave-function by making an attack: roll to see if it's actually there. If it is, the wave-function collapses and the ogre becomes particle-like enough to bash its victim with a club. Otherwise, it's not there and the probability gets shunted to another location.
Once the Ogre's location is known with 100% certainty, it immediately automatically takes particle form without needing a roll. When it next reverts to wave-form, the probabilities go back to their starting state (before they started getting condensed).
A three room complex, with rooms A, B, C and D. Each is given a 2-in-8 chance of ogre.
The PCs enter room A and try to stab the ogre. The wave-function is collapsed, and gets a 5 (no ogre). The ogre is not in room A, and the probability is distributed so that room B has a 4-in-6 chance and room C and D a 2-in-6 chance.
The PCs enter room B and the ogre tries to hit them with its club. The wave-function is collapsed, and a result of 3 (yes ogre) means the ogre becomes a particle and is able to bash them with his club.
The PCs flee to room C, and the ogre pursues them out. It decides to pursue them in wave form, and rolls a 5 (no ogre): thus itreturns to wave-like state, with a 4-in-6 chance for room B and a 2-in-6 chance for room C and D.
The ogre tries to hit them with its club again, and the collapsing wave-function rolls a 4 (no ogre). The ogre is not in room C! The probability is assigned to room D, so now B and D both have a 4-in-8 chance of ogre.
The PCs go back to room B, and the ogre once again tries to leap out at them, but gets a 7 (no ogre). So it is now definately not in room B. The probability is assigned to the last possible room - room D - where it has an 8-in-8 chance and so pops out immediately.
The PCs arrive in room D, and the ogre flees! The ogre takes wave-like form and the wave-function returns to its original state (2-in-8 for each room).
Edited bonus content: Interferance!
If there are more than two quantum ogres in a dungeon, track the chances of each seperately. HOWEVER! The many ogres interfere with one another when nobody is looking (fnar fnar). Track the interferance like this:
When one ogre fails to pop into particle form in a room, then all the other ogres also Don't Exist In That Room and must redistribute their probabilities appropriately.
When an ogre successfully pops into particle form in a room, every other ogre MUST test to see if they pop into particle form too (simultaneously): those that pop in appear in particle form and those that fail must redistribute their probabilities as normal.
Where there are exactly two ogres, the ogres are entangled (it's not my fault quantum physics was written by perverts). One begins in particle form. When one pops into particle form, the other immediately pops back to wave form.