Binding of Isaac Observations

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BINDING OF ISAAC: WRATH OF THE LAMB (1.48) OBSERVATIONS
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Pastebin SECOND "FINAL" REVISION - March 2, 2013

This is probably going to be the final revision, unless errors are pointed out or
particularly interesting things are discovered.
 -Color Printer

Questions? Complaints? Corrections? Interesting things to add? Etc? Direct them to:
printer (dot) of (dot) color (at) gmail (dot) com

---ITEM POOLS---
(Signifies that an item must be unlocked first.)
*Signifies that an item is not always available. See ITEM DROPS for more information.

REGULAR DROPS
---Sad Onion, The Inner Eye, Spoon Bender, Max's Head, My Reflection, Number One, Blood of the Martyr,
   Brother Bobby, Brother Bobby, Halo of Flies, Magic Mushroom, The Virus, Roid Rage, <3, Boom!, Boom!,
   Wooden Spoon*, The Belt*, Mom's Underwear*, Mom's Heels*, Mom's Lipstick*, Mr. Boom, Mom's Bra,
   Kamikaze, Mom's Pad, Teleport!, Doctor's Remote, Cupid's Arrow, Shoop-Da-Whoop, Magneto, Mom's Eye,
   Lemon Mishap, Distant Admiration, Book of Shadows, Wiggle Worm, Charm of the Vampire,
   Anarchist's Cookbook, The Hourglass, Sister Maggy, Chocolate Milk, Growth Hormones, Mini Mush,
   Rosary, PhD, X-Ray Vision, My Little Unicorn, Deck of Cards, Ouija Board, Odd Mushroom Thin,
   Odd Mushroom Large, Dead Sea Scrolls, Bobby-Bomb, Forever Alone, Bucket of Lard, Best Friend,
   Remote Detonator, Stigmata, Bob's Curse, Scapular, Speed Ball, Bum Friend*, Infestation, Ipecac,
   Tough Love, Mulligan, Technology 2, Mutant Spider, Chemical Peel, Peeper, Bloody Lust, Crack the Sky,
   Ghost Baby, Harlequin Baby, Polyphemus, Mitre, Portable Slot*, Holy Water, Black Bean, Tooth Picks,
   3 Dollar Bill, Telepathy For Dummies, (D20), (Celtic Cross), (Abel), (Sacrificial Dagger),
   (Rainbow Baby), (Blood Rights), (SMB Super Fan!), (Spider Butt), (Daddy Long Legs),
   (Guppy's Hairball), Skeleton Key*, (The Necronomicon)*, Technology*, (The Book of Belial)*,
   (Yum Heart), (Lucky Foot)*, (A Quarter)*, (Dr. Fetus), (The Poop), (Spelunker Hat),
   (Monstro's Tooth), (Loki's Horns), (Lil' Chubby), (The Relic), (Sack of Pennies), (Robo-Baby),
   (Gamekid), (The Book of Sin)*, (Little Steve), (Little Gish), (Little Chad), (The Halo),
   (Mom's Bottle of Pills), (The Common Cold)*, (The Parasite)*, (D6),
   (Mr. Mega), (Pinking Shears), (The Wafer), (Money = Power)*, (Mom's Contacts), (The Bean),
   (Mom's Knife)*, (Dead Bird), (Whore of Babylon)*, (Razor Blade)*, (Guardian Angel), (Bomb Bag),
   (Demon Baby)*, (Forget Me Now)*, (Monster Manuel)*
BOSS DROPS
---Lunch, Dinner, Dessert, Breakfast, Rotten Meat, Wooden Spoon OR The Belt,
   Mom's Underwear/Heels/Lipstick (Any 2 of the 3), Wire Coat Hanger, Pentagram, Pageant Boy,
   Cat-O-Nine Tails, Stem Cells, MEAT!, Magic 8-Ball, Mom's Coin Purse, Squeezy, Jesus Juice, BOX,
   (Super Bandage)*
SECRET ROOM PRIZES
---1-Up, 1-Up*, My Little Unicorn, My Little Unicorn*, Raw Liver, Bob's Rotten Head, Ankh, Pyro*,
   (Dad's Key), We Need To Go Deeper!*, (The Book of Belial)*, (Transcendence)*, (Spider Bite),
   (Epic Fetus)
SHOP ITEMS
---Treasure Map, Treasure Map, Ladder, Ladder, Compass, Compass, Steam Sale, Mom's Purse,
   Mom's Coin Purse, Habit, Notched Axe, (The Candle), Bum Friend*, Portable Slot*, 9-Volt*,
   Battery*, (The Book of Revelations)
GOLD CHEST CONTENTS
---Tammy's Head, Wooden Spoon OR The Belt, Mom's Underwear/Heels/Lipstick (only one), Rotten Meat,
   Sad Onion, Steven, Fate*
DEVIL ROOM DEALS
---Brother Bobby, Sister Maggy, The Mark, The Pact, Dead Cat, Ouija Board, Brimstone, Guppy's Paw,
   Guppy's Head, Spirit of the Night, (Bloody Lust), (Guppy's Tail), (The Necronomicon)*, Technology*,
   Lord of the Pit*, We Need To Go Deeper!*, (The Book of Belial)*, (Lucky Foot)*, (The Nail)*,
   (A Quarter)*, (The Book of Sin)*, (The Common Cold)*, (The Parasite)*, (Money = Power)*,
   (Mom's Knife)*, (Whore of Babylon)*, (Razor Blade)*, (Demon Baby)*, (Forget Me Now)*,
   (Monster Manuel)*
ARENA "PRESENTS"
---Rotten Meat, Skeleton Key, Boom!, The Compass, Teleport, Growth Hormones, Roid Rage, The Virus
LIBRARY BOOKS
---Book of Shadows, Anarchist's Cookbook, Telepathy For Dummies, (The Necronomicon),
   (The Book of Belial), (The Book of Revelations), (The Book of Sin), (Monster Manuel)
GOD ROOM GIFTS
---Blood of the Martyr, The Bible, Halo, Prayer Card, Scapular, Mitre, Sacred Heart, Holy Grail,
   Holy Grail*, Dead Dove, (The Relic), (Guardian Angel)

SLOT MACHINES ONLY: A Dollar
SHELL GAME ONLY: Skatole
BLOOD DONATION MACHINES ONLY: Blood Bag, IV Bag
FORTUNE MACHINES ONLY: Crystal Ball
HORSEMEN ONLY: Cube of Meat
HEADLESS HORSEMAN ONLY: Pony
CONQUEST ONLY: White Pony
KRAMPUS ONLY: Lump of Coal
BLUE ROCKS ONLY: The Small Rock

---ITEM DROPS---
*Anything that can be dropped by a boss, be found in a shop or a gold chest can never be found as a Regular drop, because all the contents of those three pools are removed from the Regular drop pool. However, only one instance of each item is removed, so the Sad Onion can still be found as a regular drop.
*Brother Bobby and Boom! are in the Regular Drop pool twice.
*The Wooden Spoon OR the Belt can be found as a Boss Drop, but never both; the game randomly chooses one of the two and puts it in the Boss Drop pool. The same applies for Gold Chests, but the same item can be in both pools. Both items are also in the Regular drop pool, but due to the effect above, if either of them can be found as either a Boss Drop or a Gold Chest drop, it will be removed from the Regular drop pool.
*The game picks two random Mom range items (Lipstick, Heels, Underwear) and adds them to the Boss Drop pool, and also adds one random Mom range item to the Gold Chest pool. These three items do not have to be unique. Any item not found in those pools can be found as a Regular drop.
*There is a 50% chance the 1-up Mushroom and My Little Unicorn will be in the Secret Room pool twice.
*If you find the Bum Friend in a Shop, Holy Grail is in the Angel Room item pool twice. If you find the Portable Slot in the Shop, the Holy Grail is only in the Angel Room item pool once. Each possibility has a 50% chance of occuring.
*There is a 50% chance that Fate will be available in a Gold Chest and Pyro will be available in a Secret Room. Yes, these are in the same "if" condition. No, you cannot find them anywhere else.
*There is a 50% chance Skeleton Key will be added to the Regular item pool. It can still be found in the Arena either way.
*The Necronomicon has a 33% chance of never being added to the item pools. If it is added, there is a 66% chance it will be available as a Regular drop, and a 33% chance it will be available as a Devil Room drop. Either way, it gets added to the Library pool.
*The 9-Volt and the Battery are only available in the Shop Item pool, and there is only a 50% chance each that they will be available.
*There is a 20% chance that Technology will be a Devil Room item instead of a Regular item drop.
*There is a 33% chance that Lord of the Pit will be available in the Devil Room pool.
*There is a 33% chance that We Need to Go Deeper! will be avaiable in the Devil Room, a 33% chance it will be available in the Secret Room, and a 33% chance it won't be available at all.
*There is a 33% chance that the Book of Belial will be avaiable as a Regular drop, a 33% chance it will be available in the Secret Room, and a 33% chance it will be available in the Devil Room. It will always be available for a drop in the Library.
**However, the Book of Belial is never in the item pools when you're playing as Judas. No other character's starting items have this condition.
*There is a 66% chance that Transcendence will be available in the Secret Room.
*There is a 66% chance that The Nail will be available in the Devil Room.
*There is a 66% chance that Super Bandage will be available as a Boss Drop.
*There are several items that have a 33% chance of being available in the Devil Room instead of a Regular drop: Lucky Foot, Quarter, Book of Sin, The Common Cold, The Parasite, Money = Power, Mom's Knife, Whore of Babylon, Razor Blade, Demon Baby, Forget-Me-Now, and the Monster Manuel.
*The Book of Sin and the Monster Manuel will also always be available in the Library.
*Unlocking Bloody Lust adds it to the Devil Room pool...but it is always available as a Regular drop, even before you unlock it.
*If five or less items are left remaining in the Regular item pool when it goes to fetch an item, the entire item pool system is reset.
*The Rosary adds the Bible to the Shop Item pool seven times.
*Dr. Fetus adds Bobby-Bomb and Mr. Mega to the Regular drop pool six times each.
*There's a missing item pool that never actually seems to ever exist, for drops sometimes in treasure rooms.
*Library pool never empties unless you pick up the books. If you've collected them all, bam, it turns into two free items.
*You won't see the IV bag from a blood machine if you've picked it up before.
*Seeing an item from a regular drop, Arena, Boss Arena, Devil Room, Demon Beggar, Gold Chest, Shop, Beggar (Shop Pool), Secret Room, or Boss Drop will remove one instance of it from its respective pool UNLESS the item pool is refreshed.
*Seeing an item from a God Room (or a Demon Beggar giving a God Item) or Library, however, will not temporarily remove it from play.
*Picking up an item will (with the exception of special cases like the Cube of Meat) remove all of it from play. Period. (Unless lol bugs)
*Demon Beggars drop Devil Items. If they drop a God Item however, there's a God Room on the floor instead.
*God Rooms and Demon Beggars on floors with God Rooms won't drop a God Item if the Devil Room pool is empty!
*Demon Beggars drop Shop Items like ordinary Beggars if it can't drop a Devil/God Item.
*Boss Rooms (and Boss Arenas) bug out when empty (because they don't check to see if the boss pool is empty) and won't refresh the item pools. They'll drop an undefined item instead.
*The above applies to Secret Rooms, too.
*Libraries won't refresh the item pools, but since they never empty they'll start dipping into the Regular pool if you've touched all the books. They might refresh the item pools...but they crash the game when it tries.
*Shop Rooms (and Beggars) won't dip into their pool when there's one item left and go into the Regular pool instead.
*The Fallen drops Devil Room items if there's any available, but doesn't remove them from the Devil Room pool. Pick it up to remove it.
*If a Beggar (either type) fails to find an item to drop the very first time, it'll just drop whatever.
*Normal Beggars have a random chance of dropping a basic health up item.
*Red Chests can drop Dead Cat, Guppy's Head, Guppy's Paw, or Guppy's Tail.

--DROPPING AN ITEM--
Let's walk through the greatest mystery of this game: dropping an item.

First the game walks through the checks in this order:
-Are you in a Library? Find a book and drop it.
-Are there items left in the Arena pool? Are you in an Arena, and not a Boss Arena? Pick an Arena item from the pool, drop it and remove it.
-Are there items left in the Devil Room pool? Are you in a God Room, or in a Curse Room or dealing with a Demon Beggar on a floor with a God Room? Find a God item that hasn't been picked up and drop it.
-Are there items left in the Devil Room pool? Are you in a Devil Room, or in a Curse Room or dealing with a Demon Beggar on a floor with a Devil Room? Pick a devil item from the pool, drop it and remove it.
-Are there items left in the Gold Chest pool? Did you just open a Gold Chest? Are you not in The Chest? Pick a gold chest item from the pool, drop it and remove it.
-Are there at least two items left in the Shop pool? Are you in a shop or dealing with a Beggar? Pick a shop item from the pool, drop it and remove it.
-(The game talks about some pool that's never created here. It's a 50% chance of taking from it if in you're in a treasure room, but it's nonexistant and empty so it never accesses it.)
-Are you in a secret room? Pick a secret item from the pool, drop it and remove it.
-Are you in a boss arena? Pick a boss item from the pool, drop it and remove it.
-Are you in a boss room? Did you beat...
--The Fallen? If there's a Devil item left in the pool, drop one.
--Conquest? Drop the White Pony if it hasn't already been picked up.
--Headless Horseman? Drop the Pony if it hasn't already been picked up.
--C.H.A.D.? Drop Little Chad if it hasn't already been picked up.
--Gish? Drop Little Gish if it hasn't already been picked up.
--Steven? Drop Little Steve, or Steven if Little Steve has been picked up. (Steven has a 1/6 chance of Dropping anyway.)
--A Horseman Of The Apocalypse? Drop a Meat Cube. Period.
--Any other boss? Pick a boss item, drop it, and remove it. (This also happens if you already have a boss drop from above.)
-Do none of the above apply and you just need an item? Pick a regular drop item, drop it and remove it.

Items are only removed if it doesn't get thrown out and actually gets chosen. What determines if an item gets thrown out? Good answer! Let's find out.

-If you've got at least three firing familiars following you, firing familiars will get thrown right out the window.
--The firing amiliars it checks for are: Brother Bobby, Sister Maggy, Robo-Baby, Little Gish, Little Steve, Demon Baby, Ghost Baby, Harlequin Baby, Rainbow Baby, and Abel.
--Level 2 Meat Boy doesn't count. Little Chub doesn't count either.
-If you've picked up the item at least once, throw it out.
-If you've collected the item in a previous run, there's a 20% chance it will get thrown out. That's right, the game favors new items.
-Is the item not an "Upgrade"? Then it's good.
-Is the item an "Upgrade"? Randomly throw it out.

As previously said, if an item gets thrown out, it's still in the pool. It just doesn't get dropped.
If the item generator goes all the way through and manages to not get a valid item, it tries again. And again. And again.
In fact, it tries to drop a relevant and valid item 100 times!
If it takes over 100 tries, it picks an item from the regular pool and removes it. It will drop it if it's valid. If not, it'll try again until it finds
an item or bugs the hell out.
Also! When it dips back into the regular pool and sees that the regular pool has 5 or less items remaining, ALL ITEM POOLS will get regenerated anew.

But wait, what's this about "Upgrades" and randomly throwing them out? Well, there's a collection of items that the game considers to be very good.
They're either straight upgrades, or the benefits it gives outweigh the negatives. Spacebar items are (usually) not "Upgrades".
Items that can be found in places other than the Treasure Room are not considered to be "Upgrades".
The game keeps track of the number of upgrades you pick up. Every time you pick up a new one, it increments a counter.
When a game generates an upgrade, it randomly throws it out depending on the Upgrade Counter value. The more upgrades, the higher the value.
The higher the value. The more likely it is an upgrade item will be thrown out! The RNG may hand you a game sometimes, but it really needs luck to be on your side.

List of Upgrades:
The Sad Onion, The Inner Eye, Spoon Bender, Max's Head, My Reflection***, Number One, Blood of the Martyr, Brother Bobby, Magic Mushroom, Raw Liver, Cupid's Arrow,
Steven, Pentagram, Mom's Eye, Distant Admiration, Dr. Fetus, Wiggle Worm, Sister Maggy, Technology, Growth Hormones, Loki's Horns, Spider Bite, Lil' Chubby, The Small Rock,
Super Bandage, Robo-Baby, Little Gish, Little Steve, The Halo, The Common Cold, The Parasite, The Wafer, Money=Power, Mom's Contacts, Ouija Board, Stigmata, Speed Ball,
Prayer Card, Ipecac, Tough Love, The Mulligan, Technology 2, Chemical Peel, Bloody Lust, Epic Fetus, Daddy Long Legs, Fate, Black Bean, Sacred Heart, Tooth Picks, Holy Grail,
Dead Dove, Guppy's Hairball, SMB Super Fan, Pyro, 3 Dollar Bill, Jesus Juice

***Even Ed and Florian know My Reflection can be terrible. That's why this item only adds .2 to the Upgrade Counter.

You'll notice this list is most of the non-Spacebar items in the game. This means picking up more and more upgrades means you are more likely
to find Spacebar items further down. A few items are missing from this list, however, most notably Mom's Knife and Polyphemus.

Here are the odds of getting an Upgrade thrown out when chosen for a drop.
***These are not the odds of NOT getting an Upgrade, only the odds of getting an Upgrade passed over during item generation.***

Upgrade Counter		Chance of Throwing Out Upgrade
0					16.66%
1					76.19%
2					86.11%
3					90.20%
4					92.42%
5					93.83%
6					94.79%
n					100 * (1 - (1 / (1.2 + 3n)))

This is why Spacebar items can because much more common later on, especially if you haven't been getting many.

--ITEMS--
*The 3-Dollar Bill can give you one of the following effects: Sad Onion, Inner Eye, Spoon Bender, My Reflection, Number One, Magneto (bug?), Mom's Contacts, Ouija Board, Speed Ball, Tough Love, and THE LUCKY FOOT.
*The Monster Manuel can give you one of the following familiars: Brother Bobby, Level 2/3 Meat Boy, Halo of Flies, Distant Admiration, Sister Maggy, Lil' Chubby, Robo-Baby, Little Gish, Little Steve, Guardian Angel, Demon Baby, and Forever Alone.
*The Dead Sea Scrolls can activate one of the following effects: Book of Belial, Necronomicon, Mr. Boom, Tammy's Head, Mom's Bra, Kamikaze, Mom's Pad, Bob's Rotten Head, Teleport, Yum Heart, Lemon Mishap, Shoop-Da-Whoop, Book of Shadows, Wiggle Worm (Doesn't do anything), Anarchist's Cookbook, Hourglass, My Little Unicorn, Book of Revelations, The Nail, We Need To Go Deeper, Deck of Cards, Monstro's Tooth, The Gamekid, The Book of Sin, Mom's Bottle of Pills, and The Pinking Shears.
*9-Volt has no effect on the Candle.
*Using the Bible on Satan or Isaac removes all of your Soul Hearts and hits you for 1000 damage. You can survive the damage with the Wafer, but you still lose your soul hearts.
*Using the Bible on ??? is fine.
*The Rainbow Baby has seven different tear effects: Sister Maggy, Robo-Baby, Little Gish, Little Steve, Demon Baby, Ghost Baby, Harlequin Baby.
*Pageant Boy spawns exactly 7 coins.
*Celtic Cross has a 20% chance of activating Book of Shadows upon taking damage.
*The Book of Shadows lasts for 300 frames. The Celtic Cross protects you for 200 frames, and the Polaroid protects you for 150.
*Ipecac, Polyphemus, and Mutant Spider decrease the effect of Inner Eye if you have it, so as to not make your fire rate absurdly low.
*The Book of Sin can spawn one of the following seven pickups with equal probability: a whole Heart, a soul Heart, 1 Bomb, a Key (2% chance of it being golden), a Pill, a Tarot card, or a random Coin.
*Justice spawns: one random Heart, one random coin, one Key (2% chance of it being golden) and one random bomb.
*The Necronomicon, The Missing Page, and Blood Rights damage all enemies for 40 damage. The Death card deals 60 damage, and Spider Butt deals 10. The Sun card deals 100 damage.
*My Little Unicorn and the Chariot card's effect lasts for 180 frames. Gamekid's effect lasts for 200 frames.
*Mom's Bra freezes enemies for 220 frames. Mom's Pad freezes enemies for 160 frames, and scares enemies away for 180 frames.
*The Sun, Magic Mushroom, <3, and Raw Liver all heal only 1000 hearts of your health, if you somehow managed to have that much.
*Sacred Heart heals 15 hearts when you pick it up. The Blood Bag heals 5 hearts. PhD, 2 hearts. Stem Cells, 1.5. Bucket of Lard, half a heart.
*The Nail's effect lets you damage enemies on contact, like the Virus or My Little Unicorn.
*The Halo boosts Health, Damage, Speed, Range, and Fire Rate. The Magic Mushroom boosts Health, Damage (more so than Halo), Speed, and Range. It does NOT boost fire rate.

--THE D20--
*The D20 rerolls: hearts, coins, keys, bombs, chests (closed or open), pills, tarot cards, and trinkets.
*The game will first turn every object into either a heart, a coin, a key, a bomb, a regular chest (possibly a red chest?) or a golden chest.
*If it rolls it into a gold chest, there is a 50% chance it might become a heart instead.
*If it rolls it into a regular chest, there is a 33% chance it might become a coin instead.
*There is a 10% chance it might turn into a key instead (and a 50% chance that key will be golden).
*There is then a 6.66% chance it might turn into a tarot card instead.
*There is then a 6.66% chance it might turn into a pill instead.
*Finally, there is then a 5% chance it might turn into a trinket instead.
*(Not sure if regular chests and/or gold chests have a chance of being red, needs more research)
*Heart		18.62%
*Coin		16.55%
*Key		16.55%
*Bomb		16.55%
*Chest		 8.28%
*Pill		 6.33%
*Gold Chest	 6.21%
*Tarot Card	 5.91%
*Trinket	 5.00%

--TAROT CARDS--
*There is a 20% chance a Playing Card (The 2s, Joker) will spawn instead of a Tarot Card.
*The Empress is more powerful than the standard Whore of Babylon effect.
*The Strength card gives the Magic Mushroom effect.

--KEYS--
*A key has a 2% chance of being golden.

--HEARTS--
*Anything that drops a random type of heart follows this procedure:
**First, it is either a normal heart or half a heart. Both possibilities have equal chances.
**There is then a 2% chance the drop becomes an eternal heart.
**There is then a 10% chance the drop becomes a soul heart.
***If you're playing as Eve and the above fails, try again with a 6.25% chance of success.
***If you have Mom's Pearl and the above fails, try again with a 10% chance of success.
***If you have the Mitre and the above fails, try again with a 50% chance of success.
*Random heart drops in the Womb-themed dark secret room with all the whole hearts will ALWAYS be whole hearts.
*Random heart drops in the Cathedral-themed dark secret room with the lonely eternal heart wll ALWAYS be an eternal heart!
**Bring the Justice card to the Cathedral-themed dark secret room and you get a free heart container!

--BOMBS--
*Anything that drops a random type of bomb follows this procedure:
**It starts out as just a regular bomb.
**There is a 14.29% chance the drop will become a 1+1 Free Bomb.
**There is then a 2% chance the drop become a Super Troll Bomb.
**There is then a 10% chance the drop become a regular Troll Bomb.

--COINS--
*For random coin drops, it will start as a penny. There is a 5% chance it will become a nickel and a 1% chance it will become a dime.

--MACHINES--
*The Blood Donation Machine has a 6.66% (1 in 15) chance of exploding on each donation, revealing either a Blood Bag or an IV Bag (equal chances).
*Blood Donation Machines spit out 1-3 coins on each donation, with the PhD awarding 1 extra.
*Slot Machines have a 33% chance of being Fortune Teller Machines.
*Slot Machines spawned in the Dark Secret Room will always be Fortune Teller Machines.
*The Fly "reward" on the Slot Machines have a 33% chance of awarding a shield fly. Otherwise it spawns an enemy fly.
*The Shell Game has a 1 in 13 chance of offering Skatole as a prize, if you don't already have it.

--CHESTS--
*Regular Chests have a 5% chance of becoming a Red Chest.
*Regular Chests spawned in the Curse Room or the Dark Secret Room will always be Red Chests.
*Gold Chests will never become Red Chests, unless you have the Left Hand.
*Regular Chests have 2 pickups in them.
*Gold Chests have 2-6 pickups in them.

*Red Chest Outcome Percentages
*Spiders		17%
*Soul Hearts		14.51%
*Troll Bombs		14.51%
*Pills			14.51%
*Super Troll Bombs	13.6%
*Blue Flies		10.87%
*Guppy Item		10%
*Devil-port		5%

--ROOM DROPS--
*Generate a random real number from 0 to 1.
*If you have the Lucky Foot, multiply it by 0.9 and add 0.1.
*If you have positive Luck, multiply it by 0.9 and add 0.1.
*If you have the Lucky Toe, multipliy it by 0.9 and add 0.1 UNLESS you have all three conditions here met, then multiply by 0.98 and add 0.02.
*If you have negative Luck, subtract your luck stat multiplied by 0.1. (Basically, add 0.1 for each Luck Down pill. If on the 7 Years Bad Luck challenge, add 0.2 for starting luck.)
*Check it against the following ranges:
*Nothing	x < 0.22
*Tarot Card/Pill/Trinket 0.22 <= x < 0.3
*Coin	0.3 <= x < 0.45
*Heart	0.45 <= x < 0.6
*Key	0.6 <= x < 0.8	(Goes down 0.01 each floor. 0.79 on the first floor, 0.69 in The Chest.)
*Bomb	0.8 <= x < 0.95
*Regular Chest	x >= 0.95

*Guppy's Tail effect drops in the following way:
*1 in 6 chance of getting a regular chest
*1 in 6 chance of getting a gold chest
*1 in 6 chance of having the room drop completely nothing
*1 in 2 chance of having a regular room drop (if any)

--BEGGARS AND DEMON BEGGARS--
*Beggars have a 33% chance of being Demon Beggars.
*Beggars are more likely to drop things the more money you give them. They are guaranteed to drop something after 8 coins.
*Beggars check their current coin total against a series of random numbers added up. If it's larger than them, they drop something. See table below.
*After dropping something, the beggar's coin total drops back down to 2 or 3.
*Demon Beggars have a 1 in 4 chance of dropping something every time you donate. If you have the Lucky Foot, this chance goes up to 1 in 3.
*Beggars keep dropping things until they drop a treasure, at which point they leave.

*Odds of a Beggar dropping something after X coins
		(at least one thing dropped)
1	3.125%	39.0625%
2	12.5%	60.9375%
3	28.125%	79.6875%
4	50%	92.1875%
5	71.875% 98.4375%
6	87.5%	100%
7	96.875%
8	100%

*Beggar Drop Rates
*Heart - 16.66%
*Bomb - 16.66%
*Key - 16.66%
*Treasure - 25%
*HP Up - 12.5%
*Tarot Card - 12.5%

*Demon Beggar Drop Rates
*Pill - 25%
*Tarot Card - 25%
*Trinket - 12.5%
*Devil/God Treasure - 37.5%

--PILLS--
*Negative stat pills, except for Luck and Health, do not have an equal opposite effect as their positive counterpart; instead, their negative drop is 20% lower.
*Speed Up has the same effect as the Wooden Spoon or the Belt: a 30% increase in Base Speed.
*Speed Down removes 80% of the Speed Up effect: a 24% decrease in Base Speed.
*Range Up has half the effect of a Mom Range Up item. (Exact effect unknown right now) Range Down removes 80% of the Range Up effect.
*Tears Up has half the effect of the Wire Coat Hanger. (Exact effect unknown right now) Tears Down removes 80% of the Tears Up effect.
*Due to a typo, Explosive Diarrhea pills do not spawn.
*New pill effects are determined when you take the pill (or when PhD identifies it)
*Stat pills, under normal circumstances have equal chances of being good or bad.
*PhD prevents new pills from being I Found Pills/Puberty or Telepills.
*PhD or Lucky Foot prevents new pills from being Bad Trip.
*If you take an undefined pill while you have full health (or 3+ soul hearts as ???) it will never be a Full Health pill.
*If you take an undefined pill while you have 0 keys and 0 bombs, it will never be a Bombs Are Key pill.
*If you take an undefined pill while you have 1 heart or less, it will never be a Bad Trip pill. It could still be a Full Health pill, but it won't add Bad Trip to the pill effects array.
*Range Down pills become Range Up pills if you have Number One and have not yet hit Womb 2.

*Pill Distribution Percentages (This only applies if all pill effects are available)
*Telepills		13.26%
*Full Health		10.00%
*Bombs are Key		 7.46%
*Bad Gas		 6.92%
*Balls of Steel		 6.87%
*Bad Trip		 6.53%
*Range Up		 4.97%
*Range Down		 4.97%
*I Found Pills		 4.90%
*Blue Flies		 4.89%
*Health Up		 3.73%
*Health Down		 3.73%
*Tears Up		 3.73%
*Tears Down		 3.73%
*Speed Up		 3.31%
*Speed Down		 3.31%
*Pretty Fly		 3.09%
*Luck Up		 2.30%
*Luck Down		 2.30%

--TRINKETS--
*Simply seeing a trinket will remove it from play.
*Mom can still drop the Polaroid if you've seen it, and the Polaroid can still be pulled from the trinket pool if you've seen Mom drop it or not.
*If you've seen all the trinkets, the game will start dropping tarot cards and playing cards whenever it would drop a trinket.
*If you completely empty the trinket pool, **Mom WILL NOT drop the Polaroid**.
*The Counterfeit Penny can only be found in Golden Poop; it is not in the regular Trinket drop pool. It is the only trinket to not be in the regular drop pool.
*The Fish Head spawns exactly one blue attack fly every time you get hit.
*Liberty Cap has a 25% chance of giving you a random Mushroom effect when you enter a room. (Odd Mushroom, Mini Mushroom, and Compass (bug?))
*Goat's Hoof and Curved Horn recently had their effects changed and swapped. Originally, Goat's Hoof added Damage and Curved Horn added Speed.
*Isaac's Fork has a 10% chance of healing half a heart on clearing a room.
*The Tick will suck up 15% of the health of enemies that spawn with greater than 60 Health. This applies to pretty much anything that isn't a standard enemy.
*Child's Heart/Rusted Key/Match Stick/Safety Cap/Ace of Spades have a 10% chance of changing the room drop to a random heart/key or chest/bomb/pill/tarot card.
*Those trinkets also have a 1 in 3 chance of adding their respective item to a chest.

--LUCK--
*The Lucky Foot, Lucky Toe, and Luck stat are all independent, though sometimes they overlap.
*The Lucky Foot increases room drops by 10%.
*Positive Luck increases room drops by 10%. (Taking any Luck Up pills past the first only helps with Tough Love.)
*The Lucky Toe increases room drops by 10%. (If you have both the Lucky Foot, and positive Luck, it increases it by 2%, making room drops 100%.)
*The Lucky Toe also has a 2 in 3 chance of adding an item to a chest.
*Negative Luck is broken; each Luck Down pill increases room drops by 10%, and makes chests 10% more likely.
*The Luck stat affects the chance of Tough Love turning tears into teeth. The higher the luck, the more likely. (At 10 Luck, all tears are teeth.)
*Lucky Foot gives you another 1 in 3 chance at winning the Shell Game.

--STATS--
*Speed Ball boosts Tear Speed by 20%. Cat-O-Nine-Tails, 23%. Stem Cells, Tooth Picks, and Magic 8-Ball increase tear speed by 16% each.
*Samson naturally gets a 31% increase in Tear Speed.
*Sacred Heart decreases your Tear Speed by 25%.
*Your Tear Speed can't go any higher than 140% (increase of 40%).
*Maggy is the slowest character, with a base Speed of 85%. Cain is the fastest character, with a base Speed of 130%.
*Eve has a Speed of 123%, while ??? and Samson have a Speed of 110%. Judas has the same speed as Isaac: a flat 100%.
*Your speed cannot be boosted past 200%. However, the following exceptions can boost your speed past this limit:
**While using My Little Unicorn (and other related items), your base speed is increased by 28%.
**Goat's Hoof adds 15% base speed.
*The Pony and the White Pony boost your speed to 150% if you're not already faster.
*Picking up all the speed dropping items would decrease your speed to 30% base speed. If you were Maggy, that would decrease your speed to a sluggish 15%.
*Technically, getting a 0% Speed through Speed Down pills and other nonsense would not render you immobile, as there is a small amount that the Base Speed is added to.
*Speed can sometimes be bugged on the stat screen; it can be lower but the screen still reports a rating of 2.
*Jesus Juice boosts Range AND Damage.
*Sacred Heart multiplies your base damage by 2.3. And then adds another point of damage.
*Technology 2 multiplies your base damage by .65.
*Suicide flies deal twice your base tear damage.
*Max's Head, Magic Mushroom, or both the Belial effect and Blood of the Martyr add a bonus 50% tear damage (tear damage only).
*Tough Love teeth do 320% base damage.
*Coal can boost tear damage by up to 21 points.
*When Parasite tears split, the size and damage boost from coal is transfered to the new tears.
*Pinky Eye has double the strength of the Common Cold's poisonous damage. Pinky Eye does 4 damage, Common Cold does 2. Farts do 3.5.

--MONSTERS AND BOSSES--
*All colored champions (NOT alternate versions!) are the same for each enemy.
*Enemies have a 5% chance of being a champion.
*Champion enemies are 15% bigger, have twice as much health, and do a full heart of damage.
*Bosses have a 10-20% chance of being a champion, depending on the boss.
**If Everything is Terrible, bosses have a 20-40% chance of being a champion.
**Champion bosses cannot spawn until Mom's Heart is defeated and Judas is unlocked...
**...UNLESS the room location ID is divisible by four.
*Krampus has a 10% chance of spawning in a Devil Room. If you've made at least one deal with the devil this goes up to 33%.
*Krampus cannot spawn in floors that would have a God Room, nor can he spawn more than once.
*Each Deadly Sin has a specific item or a type of pickup they can drop. Super Deadly Sins have a different item.
*Deadly Sins have a 25% chance of dropping their item, while Super Deadly Sins have a 14.3% chance.
*Sloth drops Bob's Rotten Head or a tarot card. Super Sloth drops Bob's Curse or a tarot card.
*Lust drops The Virus or a pill. Super Lust drops the Yum Heart or a pill.
*Wrath drops Mr. Boom or two random bombs. Super Wrath drops Mr. Mega or two random bombs.
*Gluttony drops <3 or two random hearts. Super Gluttony drops a Bucket of Lard or two random hearts.
*Greed drops Steam Sale or 4-8 coins. Super Greed drops a Quarter or 4-8 coins. (If you don't have the Quarter unlocked, Steam Sale drops instead.)
*Envy drops Shoop da Whoop! or a troll bomb. Super Envy drops Forever Alone or a troll bomb.
*Pride drops Anarchist's Cookbook or a tarot card. Super Pride drops Dead Cat or a tarot card. Ultra Pride always drops The Left Hand.
*The Deadly Sins, The Fallen, Krampus, and The Headless Horseman all get stronger the deeper you go.
*Wrath has the highest health of all the Sins (except maybe all of Envy's heads combined).
*Most of the Super Sins have 150% the health of their regular counterpart.
*Super Gluttony has 160% the health of Gluttony (same health as regular Wrath), and Super Wrath has 130% the health of Wrath.
*Super Envy and Super Pride have the same health as their regular counterparts (but technically, Super Envy splits into three heads which adds overall health).
*Ultra Pride has twice the health of most of the Sins.
*The Headless Horseman has about twice the health of the average Sin.
*The Fallen has about three times the health of the average Sin. (Krampus has a little more health than The Fallen.)
*Ultra Pride has a 10% chance of replacing any Sin (except Greed).
*Greed cannot spawn until Caves/Catacombs 2/XL.
*Greed cannot spawn in the secret room until the Depths/Necropolis.
*Greed cannot spawn two floors in a row (with the exception of XL floor(s)).

--ROOMS AND FLOORS--
*Any floor (with the exception of the Arena) past the first will have an Arena if it can place one. Basement/Cellar 2 have a 50% chance of attempting to place an Arena.
*Treasure Rooms and Shop cannot spawn past Depths/Necropolis 2. Period.
*In addition, The Chest cannot have a sacrifice room, a library, a curse room, a mini-boss room, an arena, or an arcade.
*The Chest cannot have any curses, not even Curse of Darkness.
*The chance of finding a Devil/God room without any modifiers is a flat 1%.
**Having the Pentagram increases the chance of finding a Devil/God Room by 20%.
**Holding the Book of Belial increases the chance of finding a Devil/God Room by 25%.
**Holding the Book of Revelations increases the chance of finding a Devil/God Room by 35%.
**Killing the Beggar increases the chance of finding a Devil/God Room by 35%.
**Beating the boss without taking damage increases the chance of finding a Devil/God Room by 35%. Soul Heart damage does not count.
**Beating the entire floor without taking damage increases the chance of finding a Devil/God Room by 99%. Soul Heart damage does not count. Does not work on the first floor.
**Having the Devil/God room opened up two floors ago cuts your chances in half. This also always happens on Basement/Cellar 2.
**Having the Devil/God room opened up the previous floor cuts your chances in half twice. (If you're on a labyrinth floor, the previous floor SHOULD be two floors ago. Needs testing.) This also always happens on Basement/Cellar 1.
*On the 7 Years Bad Luck challenge, the treasure room has a 33.3% chance of not spawning.
*Telepills have a 1 in 15 chance of taking you to the Error Room (except in Sheol/Cathedral).
*Teleport! cannot take you to the Error Room.
*A Curse Room has a 1 in 12 chance of having a God/Devil Item.
*An Arcade has a 1 in 6 chance of containing a free heart, and a 1 in 6 chance of containing a free coin.
*The Shop has a 50% chance of having 3 items for sale, a 16.66% chance of selling 2 items, a 16.66% chance of selling 4 items, and a 16.66% chance of selling 5 items.
*The Error room will have, in addition to one free treasure, either one extra item, 9 pills, 13 coins and 3 buyable things, or 4 treasure chests.

--OTHER--
*When characters have less than 1 heart, they leave a pee stain on the ground whenever the enter the room. However, Eve leaves a blood stain instead, presumably because at half a heart she enters the Whore of Babylon mode.
*The following sources of damage do NOT count against "No Damage" achievements: blood donations, using the Razor Blade, and Bad Trip pills.
*The three new pill colors in Wrath of the Lamb are randomly mixed in with the old pill colors. There is a 50% chance of a new color replacing an old color for every new color.

----SPEED BOOSTERS----
Speed Stat starts at 1.
Cannot be boosted past 2,
unless otherwise noted.
Goat Hoof			.15 (can go past maximum)
The Mark			.2
Unicorn-like effect	 	.28 (can go past maximum)
Blood Bag			.3
Wooden Spoon		 	.3
The Belt			.3
Magic Mushroom		 	.3
Mini Mushroom		 	.3
The Halo			.3
Whore of Bablyon	 	.3
Odd Mushroom, Thin	 	.3
Speed Ball			.3
Lord of the Pit		 	.3
Speed Up Pill		 	.3
WoB, room activated	 	.36
Growth Hormones		 	.4
The Empress Card	 	.45
Roid Rage			.6
Pony/White Pony			Speed is set to 1.5 if lower
The Virus			-.1
Odd Mushroom, Large		-.1
The Nail			-.18
The Small Rock			-.2
Bucket of Lard			-.2
SMB Super Fan!			-.2
Speed Down Pill			-.24

---FIRE RATE BOOSTERS---
Fire Rate calculation is really, really weird.
These numbers don't really mean anything
except for relative comparisons.
The Halo				.2
The Small Rock		 		.2
SMB Super Fan!		 		.2
Squeezy					.4
Wiggle Worm				.4
Wire Coat Hanger	 		.7
The Pact				.7
Sad Onion				.7
Number One				1.5
Odd Mushroom, Thin			1.7
Samson					-.25
Sacred Heart				-.4
----
Chocolate Milk		Multiplies final fire rate by .80 (increase)
The Inner Eye		Multiplies final fire rate by 2.1, then adds 3 (decrease)
Cancer			Subtracts 2 from final fire rate (increase)
Other things like Polyphemus and Mom's Knife handle/effect fire rate differently.

---SOME FINAL NOTES---
If you make a 1,000 line function without breaking it up
into smaller functions I WILL HUNT YOU DOWN AND FIND YOU

Please remember basic arithmetic. If you subtract a
negative number from a positive number the positive
number gets bigger. One wrong symbol can screw
everything up.

Clever programming tricks are fine but people reserve the
right to look at it and go "wow that looks terrible"

And finally...

Just because a game is coded enough to run well
and give the initial illusion of a well-programmed game
does NOT mean it is actually a well-programmed game!

Thanks,
Color Printer