The Binding of Isaac wiki's got a pretty comprehensive (if slightly generalized, and minorly inaccurate) list. Remember that all cards are a single use item, so once they are used they vanish.
- O The Fool: Teleports the player to the starting room for that floor.
- I The Magician: Gives you the use of Spoon Bender (homing shots) until you leave the current room.
- II The High Priestess: Summon's Mom's foot stomp on a random enemy. Can also hit the player, and will do so if there are no enemies in the room.
- III The Empress: Gives you the use of Whore of Babylon until you leave the room. Whore of Babylon is Eve's curse, but unlike her version, this just hurts you half a heart then increases your damage.
- IV The Emperor: Teleports the player to the Boss Room.
- V The Hierophant: Spawns two soul hearts.
- VI The Lovers: Spawns two hearts.
- VII The Chariot: Acts as a single-shot use of My Little Unicorn.
- VIII Justice: Spawns bombs, hearts, coins, and keys around the player.
- IX The Hermit: Teleports the player to the Mini-boss Room, or the shop if a mini-boss room is not available.
- X Wheel of Fortune: Spawns a Slot Machine.
- XI Strength: Makes the player bigger, increasing maximum health and damage until the player leaves the room.
- XII The Hanged Man: Gives you the use of Transcendence (flight over gaps, rocks and spikes) until you leave the current room.
- XIII Death: Gives you a single use of The Necronomicon (massive damage to all enemies in the room).
- XIV The Tower: Gives you a single use of Anarchist's Cookbook (spawns multiple bombs around the room at random).
- XV The Devil: Gives you a single use of Book of Belial (increased tear damage) until you leave the current room.
- XVI Temperance: Spawns a Blood Donation Machine.
- XVII The Stars: Teleports the player to the Item Room, or acts as Telepills if there is no item room (i.e. in The Womb and Sheol).
- XVIII The Moon: Teleports the player to the Secret Room.
- XIX The Sun: Completely heals the player, does damage to all enemies on screen and acts as a Treasure Map and Compass for the current level only.
- XX Judgement: Spawns a beggar. If you have no money, spawns 1 heart, coin, bomb and key instead.
- XXI The World: Acts as a Treasure Map and a Compass for the current level only.
Tarot Cards II, III, XVII, and XIX were added in a patch on November 1 2011.
After several careful playthroughs taking notes, I believe I can answer my own question.
Enemy waves are indeed set, but this is only 95% accurate. The enemy waves for each zone (Basement, Caves, The Depths, etc.) are always the same (two for each zone, other than basement, where I've only ever seen a challenge room on the second floor and Sheol, which only has one floor). However, there is no set association between floor and wave, meaning that if we have floors 1 and 2 and waves A and B, the association of floors to waves could be either 1-A, 2-B or 1-B, 2-A (though this loose association might be new in light of the Halloween update, as prior to this I've have always had the same wave on the same floor in the same zone). So why 95%? It's almost always 1-A and 2-B from my experience (even after the update).
So here are the waves for each zone (check the wiki for monster and boss names):
- Basement:
- Wave A:
- 5 x Fly (the blinking red ones, not the docile black ones)
- 5 x Pooter
- 5 x Gaper (pretty sure either kind can spawn, usually the ones with shut eyes)
- Caves:
- Wave A:
- 5 x Charger
- 4 x Globin (usually the slow kind, but fast ones can spawn)
- 4 x Maw (either kind, but usually 3 white and 1 red)
- Wave B:
- 5 x Spity
- 3 x Hive
- 3 x Host (both kinds, but usually it's 3 armored ones)
- The Depths:
- Wave A:
- 4 x Baby
- 5 x Hopper
- 4 x Knight (the faster version new to the Halloween update can also spawn)
- Wave B:
- 3 x Vis
- 4 x Leaper
- 4 x Globin (always the fast ones, as far as I have seen)
- The Womb:
- Wave A:
- 3 x Larry Jr. (each just a head and one segment)
- 1 x Chub
- 2 x Monstro
- Wave B:
- 1 x Fistula
- 1 x Loki
- 1 x Chub
- Sheol
Seeing how Sheol is rather new and also a pain to walk around needlessly, I've only been to the challenge room one time. I got The Womb's wave A, and if I had to guess you simply get one of The Womb's waves. If I find out otherwise I'll be sure to update this answer (and feel free to shed some light on this point yourselves).
Best Answer
Looks like somebody on Steam forums decided to answer this question and to use SCIENCE! while doing it.
To put it simply he divides the room in four categories(he calls hidden rooms those that in my other answer I called Top Secret Rooms):
they come from the future and have a funny Austrian accentonly one exit, all of the special rooms are terminators(shops, treasure rooms, bosses and mini bosses). The hidden room is a terminatorSo, basically, every floor is generated randomly, then the hidden room takes the place of one of the normal terminators, then the secret room is put into place, AFTER all of the other rooms have been placed. Please note that the floors have a size limit: the map will never be bigger than 9x6 tiles (width x height). Also every floor has its specific room number:
While I disagree with the completely random placement of the secret room (he says that every wall is rolled randomly to see if it connects to a secret room), his theory is pretty sound, and applies quite well with what we already know about the behaviour of hidden and secret rooms.
To summarize:
HIDDEN ROOMS:
are terminators. This means they cannot be placed near more than one other room. They also cannot be placed near other terminators, and this includes every other special room(treasure, shop, arcade, curse, challenge). Be aware however that a room that looks like a terminator may be a corridor leading to a hidden room.
will never fall out of the normal 9x6 grid. If you have a potential wall candidate that would bring you out of the grid, it means that there's no hidden room back there.
they're intentionally hard to find. No tarot card and no item (with the exception of X-ray Vision and Spelunker Hat) will help you in finding them. Anyway they're potential teleport destination, so you may be lucky and find them this way. Other than that, you have to use your bombs and your brain.
Secret rooms instead are generated in a completely different way from the other rooms. Secret rooms are placed after the rest of the level has been created. Vimescarrot, the creator of the post on Steam forums, proposes the idea that ANY wall can lead to a secret room:
However, I disagree with this idea. In ~400 runs I have NEVER found a secret room near a single wall, and the only times I've found them near only two walls was when there were no available 3 or 4 rooms spaces. This seems to me a big enough sample to be quite sure of what I've found.
Whichever idea you'll follow anyway, it will be more likely to find secret rooms in spaces surrounded by many other rooms.
The secret rooms too will follow the 9x6 rule, so any wall leading out of the grid can be safely left unbombed.
Differently from hidden rooms, there are many items that can help you find secret rooms: the Sun and the World tarot cards, the Map and the Crystal Ball show you the current level map layout, including the secret room. Spelunker hat and X-ray Vision work as well.
PAY ATTENTION: Curse of the Labyrinth completely messes up all these rules. To put it in Vimescarrot words:
Until now nobody has been able to find a pattern in level generation with Curse of the Labyrinth. If you happen to find by chance a secret room in one of those levels, it can be filled with enemies(from my experience I can tell that it WILL be). If you're low on bombs and don't have X-ray Vision get the hell out of there through the exit you came in: if you bomb one of the other walls you may find yourself on the other side without a way to end the level.
By the way, basing on a small sample(2 runs), it looks like that, similarly to shop rooms, an XL level will only have one secret and one hidden room each.