1: The classic locally deterministic quantum: Once the players commit to a path, the Ogre appears on that path.
This is illusionism, which is a form of railroading. It completely negates player choice. To me, it's the worst form of railroading as it is harder to see than the blatant, "No, you can't do that, you have to do this instead."
2: The local evenly random quantum: Once the players commit to the path, the GM flip a coin to see if the Ogre is on that path.
3: The global evenly random quantum: Once the players commit to the path, the GM flip a coin to see which path the Ogre is currently guarding.
4: The local uneven random quantum: Once the players commit to the path, the GM rolls D20. If the players chose path A the Ogre is there on a 5 or lower, if they chose path B the ogre is there on a 15 or lower.
5: The global uneven random quantum: Once the players commit to the path, the GM rolls D20. If the result is 5 or lower, the ogre is on path A, otherwise it is on path B.
6: The oversaturated local random quantum: Once the players commit to the path, the GM rolls D20. If they chose path A the Ogre is on the path on a 15 or lower. If they chose path B the ogre is on the path on a 10 or lower.
I don't like any method where the ogre's location is rolled after the players make their choice. If the path is random, because the ogre wanders and could be on either path, that roll should happen before the players get to the fork in the road and have to pick a path. That way their choice means something. Either they will 100% encounter the ogre or they will 100% avoid it, depending on the path picked.
7: The weirdly entangled local quantum: If a character is declared to “be alert” while moving through the forest, the player rolls a D20. On a 6 or higher the Ogre is on the path. If no one makes such a declaration it is not on the path.
I would never use this method, nor would I stay in a game that did. Encounters should not be present or not depending on whether a PC is alert.
8: The ultra local random quantum: While the party is traveling through the forest, roll D6 every hour. On a 1 they encounter the ogre.
This is only quantum to the DM who is effectively opening the box when he rolls the 1 and determines the encounter. To the players/PCs, it's not quantum.
This is clearly the wandering monster variant.
9: The even random stocking: Before the session the GM flip a coin to determine which path the Ogre is on.
10: The uneven random stocking: Before the session the GM roll D20. On a 5 or less the Ogre is on path A, otherwise it is on path B.
11: The deterministic stocking: Before the session the GM decides where the ogre is.
and as a bonus
12: The anticlimax: There is no Ogre to encounter, as the last party passing through already has slain it, and its remains have been consumed by forest beings.
All of these are quantum only the the DM. To the players, the location of the ogre and the fact that it is an ogre is pre-established and not quantum.
Which of these do you find acceptable? Which are unacceptable? Why?
For me, only the methods that are not quantum to the players are acceptable. If players encounter quantum situations, their agency is damaged to a greater or lesser degree, and that's not acceptable to me.