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Color identity is a concept expanding the color of cards. This is primarily relevant for the Commander format, in which players are not allowed to use any cards whose color identity isn't encompassed by that of their commander. The Brawl "format" available in Magic: The Gathering Arena and Magic Online also make use of the concept (because Brawl is technically a Commander format variant, not a format of its own).

Description

While in game play mechanics, the color of a card is always determined exclusively by the colors used in its casting cost or its color indicator (including some color indicators retroactively applied to cards like Ancestral Vision, which previously specified the card's color in the rule text), the color identity of a card is specified by all mana symbols that appear in its casting cost, color indicator, and rules text.

For example, while Fires of Undeath is a {R} card, and Silver Knight has protection from it and White Knight does not. It can't be used by a player who uses Kumano, Master Yamabushi as their General in a game of Commander. This is because the color identity of Fires of Undeath is {R}{B} and is not a subset of the color-identity of Kumano ({R}).

Another example is General Tazri, which is a {W}{U}{B}{R}{G} General for the Ally tribe due to her activation cost in the rules text.

Phyrexian mana is considered to be the mana of the color it replaces, e.g. Dismember is a {B} card. Hybrid mana is considered to be both colors, thus Kitchen Finks has a color identity of {W}{G}.

A special case is the hybrid {W/B} mana symbol on creatures with the Extort ability. It is considered part of the reminder text, not part of the rules text, so it doesn't determine color identity.

It is worth noting, that only mana symbols define color identity. Cards like Mad Ratter, which only use a color as wording, do not inherit that color in their color identity. Therefore, Mad Ratter could be included in a mono-red commander deck.

Lands

Lands are colorless, but they may still have a color identity. Basic lands have the intrinsic rules text: {T}: Add [mana symbol of land's type]—establishing their color identity by their basic land type. So, for instance, Mountain has a {R} color identity, because it has the rules text, {T}: Add {R}—even if this isn’t printed on a particular Mountain. Wastes only has the {C} symbol printed on it, and has no basic land type; thus, it has no color identity. (In Commander format rules, cards like Wastes with no color identity can appear in any deck, regardless of its commander.)

On nonbasic lands, mana symbols usually appear in the rules text; if present, they will determine the card’s color identity. So for example, a dual land such as Tundra has the {W}{U} color identity, even though the card itself is colorless. Blighted Woodland is also colorless—like all lands—but it has a color identity of {G}, because a {G} appears in its rules text.

However, in cases such as City of Brass, even though its printed text reads, {T}: Add one mana of any color, the card has no color identity, because no mana symbols appear.

Rules

From the glossary of the Comprehensive Rules (July 23, 2021—Adventures in the Forgotten Realms)

Color Identity
A set of colors that determines what cards may be included in a deck for the Commander casual variant. See rule 903.4.

From the Comprehensive Rules (July 23, 2021—Adventures in the Forgotten Realms)

  • 903.4. The Commander variant uses color identity to determine what cards can be in a deck with a certain commander. The color identity of a card is the color or colors of any mana symbols in that card’s mana cost or rules text, plus any colors defined by its characteristic-defining abilities (see rule 604.3) or color indicator (see rule 204).

    Example: Bosh, Iron Golem is a legendary artifact creature with mana cost {8} and the ability “{3}{R}, Sacrifice an artifact: Bosh, Iron Golem deals damage equal to the sacrificed artifact’s mana value to any target.” Bosh’s color identity is red.

    • 903.4a Color identity is established before the game begins.
    • 903.4b If a commander has a static ability that causes a player to choose its color before the game begins, that choice applies during deck construction and throughout the game, even as the commander changes zones. That choice affects the commander’s color identity. The player reveals that choice as they put their commander into the command zone before the game begins. See rules 103.2c and 607.2n.
    • 903.4c Reminder text is ignored when determining a card’s color identity. See rule 207.2.
    • 903.4d The back face of a double-faced card (see rule 712) is included when determining a card’s color identity. This is an exception to rule 712.4a.

      Example: Civilized Scholar is the front face of a double-faced card with mana cost {2}{U}. Homicidal Brute is the back face of that double-faced card and has a red color indicator. The card’s color identity is blue and red.

    • 903.4e If an ability refers to the colors or number of colors in a commander’s color identity, that quality is undefined if that player doesn’t have a commander. That part of the ability won’t do anything. Costs that refer to that quality are unpayable.

From the Comprehensive Rules (July 23, 2021—Adventures in the Forgotten Realms)

  • 305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words “basic land type,” it’s referring to one of these subtypes. An object with the land card type and a basic land type has the intrinsic ability “{T}: Add [mana symbol],” even if the text box doesn’t actually contain that text or the object has no text box. For Plains, [mana symbol] is {W}; for Islands, {U}; for Swamps, {B}; for Mountains, {R}; and for Forests, {G}. See rule 107.4a. See also rule 605, “Mana Abilities.”