White creature A have protection against Blue, and opponent is a full multicolor deck with all blue & green. (creature and sorcery, everything are all green & blue)
Does the "protection" here still protect the white ?
if yes, doesnt this mean there is no way for the blue & green deck to destroy the white creature(with protection) at all?
Protection affects only four specific things. If a white creature has protection from blue:
It can't be the target of blue spells or abilities from blue sources (C.R. 702.16b).
It can't be attached to by blue permanents (C.R. 702.16c-d).
All damage blue sources would deal to it is prevented (C.R. 702.16e).
It can't be blocked by blue creatures (C.R. 702.16f).
Protection from blue doesn't affect green sources at all (unless they're also blue) (C.R. 608.2i). Protection, by itself, though, doesn't keep the creature from being destroyed (although a creature is usually destroyed due to damage [C.R. 704.5g-h] and due to abilities that target it, this is not always the case).
EDIT (Dec. 24, 2020): One rule was renumbered with Commander Legends.
A multicolor card that's green and blue is fully green and fully blue. Protection from blue will fully work against it, because it is a blue card. The creature with protection can't be targeted, enchanted, damaged or blocked by it.
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It can't do any of the four things protection cares about, but that's not synonymous with nothing. Depending on what the creature is doing, it can still affect a creature with protection from it. For example, a Reiver Demon can still destroy a problack creature (if it isn't also black or an artifact) with its trigger.
so that mean a multicolor creature cant do anything to a creature with a color protection which he himself also own that color right?
The multicolor creature can't block the protected creature when the later attacks, its abilities can't target the protected creature, and any damage it would deal to that creature is prevented.
There are ways the multicolor creature could affect the protected creature as long as it's not targeting or damaging or blocking it (or somehow becoming an aura or equipment and enchanting/equipping it).
so that mean a multicolor creature cant do anything to a creature with a color protection which he himself also own that color right?
If a permanent has protection from a certain color (for example, blue), any source that has that color (for example, a blue creature or a green and blue spell) will be affected by that protection ability. For example, in your scenario, a green and blue creature can't block a creature with protection from blue (C.R. 702.16f), since the green and blue creature is blue (C.R. 608.2i). Note, however, that it's not necessarily true that such a source "can't do anything" to that permanent; protection touches on only four specific things, as I mentioned in comment 3. For example, the blue spell Upheaval will return all permanents to their owners' hands, even creatures with protection from blue, since it doesn't deal damage or target any permanents this way (review C.R. 702.16b, 702.16e, 115.10a, 115.1a; C.R. 702.16c-d, 702.16f don't apply to Upheaval here).
EDIT (Dec. 8, 2017; Jun. 24, 2018): Add rule citations.
EDIT (Mar. 27, 2019; Dec. 9. 2019): Correctness edit.
EDIT (Jun. 23, 2019): Edited.
EDIT (May 26, 2020): Edited, including because some rules were renumbered with Core Set 2020.
EDIT (Dec. 24, 2020): One rule was renumbered with Commander Legends.
situation:
White creature A have protection against Blue, and opponent is a full multicolor deck with all blue & green. (creature and sorcery, everything are all green & blue)
Does the "protection" here still protect the white ?
if yes, doesnt this mean there is no way for the blue & green deck to destroy the white creature(with protection) at all?
EDIT (Dec. 24, 2020): One rule was renumbered with Commander Legends.
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The multicolor creature can't block the protected creature when the later attacks, its abilities can't target the protected creature, and any damage it would deal to that creature is prevented.
There are ways the multicolor creature could affect the protected creature as long as it's not targeting or damaging or blocking it (or somehow becoming an aura or equipment and enchanting/equipping it).
If a permanent has protection from a certain color (for example, blue), any source that has that color (for example, a blue creature or a green and blue spell) will be affected by that protection ability. For example, in your scenario, a green and blue creature can't block a creature with protection from blue (C.R. 702.16f), since the green and blue creature is blue (C.R. 608.2i). Note, however, that it's not necessarily true that such a source "can't do anything" to that permanent; protection touches on only four specific things, as I mentioned in comment 3. For example, the blue spell Upheaval will return all permanents to their owners' hands, even creatures with protection from blue, since it doesn't deal damage or target any permanents this way (review C.R. 702.16b, 702.16e, 115.10a, 115.1a; C.R. 702.16c-d, 702.16f don't apply to Upheaval here).
EDIT (Dec. 8, 2017; Jun. 24, 2018): Add rule citations.
EDIT (Mar. 27, 2019; Dec. 9. 2019): Correctness edit.
EDIT (Jun. 23, 2019): Edited.
EDIT (May 26, 2020): Edited, including because some rules were renumbered with Core Set 2020.
EDIT (Dec. 24, 2020): One rule was renumbered with Commander Legends.