Level generation in this challenge works very differently than normal. Tainted Jacob begins in a starting room without doors, and other rooms are generated in small clusters that are disconnected from each other and must be located by using the Red Key. Each floor generates like an XL Curse of the Labyrinth floor with one Shop and two Boss and Treasure Rooms, each connected to a group of normal rooms. Defeating either Boss will spawn a trapdoor that leads to the next chapter. Chapter 4, however, will not have special rooms other than the single Boss room where Mother resides. All rooms may be from any floor in the current chapter (for example, in Chapter 1, rooms may be from the Basement, Cellar, Burning Basement, Downpour, or Dross). This applies to both pre-generated rooms and new rooms made using the Red Key.
The Red Key also works differently than normal. It starts in Jacob's pill/rune/card slot, and can be used any number of times with no recharge. The Red Key can not be used to create a door to the I AM ERROR room.
After using the Red Key 20 times in a single floor, Dark Esau will spawn. The Red Key's charge bar displays how many uses it has left until this happens, rather than the item's actual charge. Another Dark Esau will spawn every 5 additional uses of the Red Key, as long as Jacob is not in his The Lost form. If he is, no more Dark Esaus will spawn.
Try to avoid depleting Red Key's charge without covering a lot of ground. Each red room entered will be able to check the adjacent three rooms to see if they are normal rooms, so spacing apart paths of red rooms in straight lines, at least two rooms apart, will grant the most information per use of the key.
This challenge is like Blackjack, as it's preferable to visit as many rooms as possible, as they give you consumables or even extra items, while making sure you don't go over the allotted amount of uses of the Red Key given per floor before Dark Esau spawns.
Most special rooms have at least one normal room next to them that are free to go into. Mapping abilities will show you the locations of either the special rooms or the clusters of rooms where they can be found, allowing you to minimize aimless wandering and potential Dark Esau encounters.
The Compass, Crystal Ball, and Treasure Map are the most useful items for this purpose, allowing an optimal route to be planned on every floor to visit as many rooms as possible to get more items and therefore a greater chance of winning.
Book of Secrets is also useful to help find where the regular rooms, item rooms, shops and boss rooms.
Sol acts like a weaker version of The Compass for the purposes of this run, as it reveals one boss room, and beating the boss will show the rest of the rooms on the floor.
It is very risky to take unidentified Pills during this challenge, as getting an Amnesia will make it much harder to find your way around.
Due to the fact that starting items in this challenge cannot be changed, rerolling your character through the use of the D4, the D100, or other means such as a Dice Room will completely refresh your Red Key charges and allow you to use it freely to explore without the worry of Dark Esau spawning for as long as it lasts. This means that the aforementioned items can be invaluable to a given run, as your active item will recharge much faster than the Red Key depletes itself.
Any means of teleportation works surprisingly well in this challenge: random teleportation will NOT teleport you to any red room, including already opened ones. This will almost guarantee that you will teleport into either special rooms themselves (treasure, shop, boss, etc) or rooms adjacent to them, saving lots of red key charge in the progression. Teleport and Teleport 2.0 both work, while Broken Remote is the most efficient while in combination with certain active item that can be infinitely used (like Guppy's Paw).
Alternatively, if you're comfortable playing as The Lost, you can keep using the Red Key once the first Dark Esau has spawned. More Dark Esaus will spawn each five uses of the Red Key, and they will actively damage each other until one of their health reaches zero, at which point they will all die simultaneously. Once this point is reached, you'll be stuck as Dead Tainted Jacob for the rest of the floor, but Dark Esau will not spawn anymore, leaving you free to explore every room. Be careful before entering any room, since if you end up entering a Curse Room, you'll have no way of leaving without taking damage unless you have any effects that prevent damage or teleports, though it is still possible to know which room it is before you enter.
Obtaining the Eraser can remove almost all the difficulty from this run. Getting Dark Esau's health down and then landing the killing blow using the Eraser will permanently remove him from the run, allowing unlimited usage of the Red Key without any penalties on all future floors.
If you are okay with Dark Esau chasing you, you can use it 5 more times before another one spawns, as well as an extra means of damage for the boss of the floor.
Before going to the next floor, be sure to kill Dark Esau(s) first, or they will follow you into the next floor.
You do not need to fight Mother to finish this challenge, it is enough to fight any boss on the last floor. Using Book of Revelations might turn Mother into Conquest or Death, and the fight will still drop a trophy. The same strategy can be used with a IV - The Emperor? card; it also drops a trophy while having the boss be any available for Chapter 4. It is also possible to find a trapdoor from a dirty bedroom or a Rune of Ehwaz to go to Sheol and fight Satan, where the challenge will end.
Although you cannot get Angel or Devil Rooms from bosses, it's still possible to encounter them as red rooms.
Do not transform into other characters during this challenge, as this will remove the Red Key and eventually make you unable to progress through floors.
Using Mama Mega! is a potential full clear of a floor, but is risky once you are the lost, especially on the caves, where mushroom explosions may kill you on the room instantly.
Crystal Key is very useful in this challenge because it has a chance to open red rooms after a room is completed, saving Red Key uses.
If possible, try not to let Dark Esau spawn on the last floor because otherwise you'll have to fight Mother while he annoys you. Since Mother is a bullet hell boss, you'll have a hard time surviving.