The extra item will be pulled from the current room's item pool, even if the original item is from a different pool (ex. Beggars or items from Alabaster Box).
After Isaac gets hit once with the item activated, at any time with only a brief warning, the sword may fall, instantly killing Isaac regardless of his health. The sword has a 1/10000 chance every 4 frames to fall, so on average, 50% of all Damocles runs will not drop the sword until after at least 15 minutes and 24 seconds have passed.
The chance for the sword to fall does not increase beyond the first hit taken.
Items from Chests will not be doubled, which greatly limits Damocles' benefit in Chapter 6.
The exception to this is Mega Chests, which will spawn one extra item alongside the 2 original items for a total of 3 items.
In scenarios that have multiple items to choose from (such as rare double Treasure Room layouts and Boss Rush), an additional set of items for Isaac to choose from spawns. Only one item from each set can be taken.
Having multiple Damocles active at once does not spawn additional items.
The only way Isaac can survive the falling sword is if he's invincible at the time it falls or, by technicality, with a respawn item. After the sword falls, extra items will no longer spawn.
Losing a life before the sword falls does not remove the sword or its threat.
Items with associated costs, like those in Devil Room or Shop, will not create additional items. This severely limits this item's benefit when used as Tainted Keeper, since most items that are normally created as pedestals are instead Shop items.
This can cause items that are in inaccessible spots in certain room layouts to be moved to a more convenient location due to not having space for two pedestals in that spot.
Blood Oath: Getting stabbed by Blood Oath does not trigger the chance of falling.
Book of Virtues: Spawns a wisp on the middle ring, looking like a sword. The wisp's tears look like Spirit Sword's beams, but there are no other effects. Likely not fully implemented.
Dark Arts: When in the shadow state, Isaac can survive the instant kill of Damocles, though this requires precise timing and can be impossible if Dark Art's charge is empty as the sword is falling.
Gnawed Leaf: If in the form of the statue, Isaac will be immune to the falling sword.
Tooth and Nail's statue form can also save Isaac, but the statue transformation time lining up with the sword falling is unlikely.
Lazarus' revival mechanic allows him to continue the run after dying to Damocles.
This extends to other extra-life items such as 1up! or Dead Cat.
The Lost / Tainted Lost: Any damage the Lost would take is likely to kill him instantly, meaning that the item's downside is greatly mitigated. Dying and respawning, however, will still trigger the chance of falling.
Magic Skin: Spawns 2 items on every use instead of 1.
Given the 1/10000 chance for the sword to fall every 4 frames (0.133 seconds), Isaac has a ~4.4% chance to die for every minute of gameplay that passes after he takes damage with Damocles active. The following is a table for times Isaac could survive to after getting hit, along with the chances of reaching them:
Chance of Survival
2 Minutes 20 seconds
4 Minutes, 57 seconds
7 Minutes, 55 seconds
11 Minutes, 21 seconds
15 Minutes, 24 seconds
20 Minutes, 21 seconds
26 Minutes, 45 seconds
35 Minutes, 40 seconds
51 Minutes, 9 seconds
Damocles originates from the Antibirth mod. In Antibirth, the more times Isaac would get hit, the higher the chance of Damocles falling became.
The item's appearance and effects are a reference to [the] Sword of Damocles, a story in which Damocles frequently praised King Dionysius's life of wealth and luxury, and is offered to switch places with Dionysius on the throne for a day to have a taste of his power. Damocles accepts, only to find that Dionysius had a sword hanging over his throne by a single horse hair to remind Damocles of the never ending threats to both themselves and their country that a ruler must deal with during their reign, causing Damocles to beg to give the throne back to Dionysius
Damocles can be seen hanging over Isaac's head on the Antibirthalbum cover.
There are actually two different Damocles items in the game: one (item ID 577) is the active item that Isaac can encounter, and the other (item ID 656) is a hidden passive item that is given when the active Damocles is used and that carries out the item's effects. The passive Damocles cannot be encountered through any normal means, even via Spindown Dice or Death Certificate, nor does it appear in the collection grid. If spawned on a pedestal via the Debug Console, collecting the passive Damocles will immediately put the sword above Isaac's head as if the active Damocles were used.