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"I Am Error" is a rare, special room that only has a 6.66% chance of being accessible when using telepills. The name and appearance of the character in the room references Zelda II: The Adventure of Link.
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The item "Bible" can not only give you wings for usage of one room, but can also kill Mother during the fight with her, or you if you decide to use it while fighting Satan.
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The character "???" also known as the Blue Baby, is a reference to both Edmund McMillen's Newgrounds username, BlueBaby, and one of his earliest Newgrounds submissions, "Dead Baby Dressup".
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The fez on Judas' head is a referential jab at FEZ creator Phil Fish, who voted against Edmund McMillen and his team at the Independent Games Festival. The name "Judas" likely was intended to evoke Judas Iscariot of the New Testament, and suggests that the character Judas represents Fish's betrayal of Edmund.
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Completing the Chest with any character is supposed to unlock an item and an achievement after the first attempt. While the in-game award is correct, the Steam achievements are glitched, where beating the Chest with one character will unlock the achievement of another. This goes for all characters excluding Maggy and Isaac.
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According to developer Edmund McMillen, the working title for The Binding of Isaac was "Love Sick" and was later changed to "Mom" before it eventually became The Binding of Isaac.
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As recently as the game's third update, the passive item "Money=Power" contained a typo that made it appear as "Monkey=Power". This would be patched out in a future update.
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