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I read from the comprehensive rules guide that there is a damage assignment order, but I've always played the game as if there was a blocking order. Here is the relevant text:

509.2. Second, for each attacking creature that's become blocked, the active player announces that creature's damage assignment order, which consists of the creatures blocking it in an order of that player's choice. (During the combat damage step, an attacking creature can't assign combat damage to a creature that's blocking it unless each creature ahead of that blocking creature in its order is assigned lethal damage.) This turn-based action doesn't use the stack. Example: Vastwood Gorger is blocked by Llanowar Elves, Runeclaw Bear, and Serra Angel. Vastwood Gorger's controller announces the Vastwood Gorger's damage assignment order as Serra Angel, then Llanowar Elves, then Runeclaw Bear.

My interpretation of this is that I can attack with a 3/3 and the opponent can block with a 1/1 and a 4/4. I could make it deal the damage to the 1/1 first, and there is no blocking order such that the opponent can't say the 4/4 blocks first and 1/1 blocks second.

Is this accurate?

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    Semantics aside, I tend to conceptualize the damage-assignment order as the blocking-order, just that the attacker chooses that order. I could be in the minority on this opinion. – corsiKa Nov 6 '14 at 17:13
  • @corsiKa Yes, I've heard plenty of people refer to this as "[the attacking player] ordering blockers". – Cascabel Nov 6 '14 at 20:03
  • "Ordering blockers" is far more accurate. It necessarily implies you already have blockers. While "blocking order" could also mean that, it would require using a different definition of blocking than MTG does. The far more obvious implication of "blocking order" is that you are choosing the order in which things will block, which is incorrect. – ikegami Nov 7 '14 at 4:57
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By the very rule you quoted (and the one directly following it):

  • You choose the damage assignment order of attacking creatures you control. (CR 509.2.)
  • Your opponent chooses the damage assignment order of blocking creatures he controls. (CR 509.3.)

Simple Example

You: "I attack with Centaur Warrior."
Opponent: "I block with Jeskai Student and Disciple of Phenax."
You: "I will assign damage to Jeskai Student first, followed by Disciple of Phenax."
You: "Damage?"
Opponent: "Sure."

Note: There was no need for your opponent to declare a damage assignment order, because each of his blockers are only blocking one attacker. Centaur is assumed to be first in line.

Centaur Warrior must deal at least lethal damage to Jeskai Student before dealing any damage to Disciple of Phenax. You are not allowed to change the order at this point. Therefore, Centaur deals all 3 points of damage to Student. Student and Disciple each deal 1 point of damage to Centaur.

Centaur and Disciple live. Student dies.

Intermediate Example

You: "I attack with Ash Zealot."
Opponent: "I block with Elvish Mystic and Runeclaw Bear."
You: "I will assign damage to Runeclaw Bear first, followed by Elvish Mystic."
You: "First Strike Damage?"
Opponent: "Sure."
You: "Bear dies. Second Strike damage?"
Opponent: "I'll cast Giant Growth on my Elvish Mystic."
You: "Ok it resolves. Second Strike damage?"
Opponent: "Sure."

Ash Zealot deals damage in the first damage phase. Zealot must deal at least lethal to Runeclaw Bear before moving on to Elvish Mystic. Therefore, Zealot deals all 2 points of damage to Runeclaw Bear.

At this point, you both get the chance to play spells and activate abilities. Your opponent takes this chance to make his Elf larger with Giant Growth. We then move to the second damage phase. Runeclaw Bear is already dead and so cannot deal damage. Ash Zealot already dealt its damage. Elvish Mystic is the only creature than will deal damage, and so it deals 3 point of damage to the Zealot.

Mystic lives. Zealot and Bear die.

Special Notes

Some abilities modify, or provide exceptions to, the rules for attacking and blocking. For a particularly complicated example, read about an old mechanic called Banding.

  • You said earlier that Banding deserves to be a footnote as opposed to the entire answer; I recommend adding a footnote here mentioning that Banding can change the normal rules that you describe here. – GendoIkari Nov 6 '14 at 17:29
  • @Gendolkari I probably should have said "At best, it deserves to be a footnote." But I'll mention it anyway for completeness. – Rainbolt Nov 6 '14 at 18:02
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Yes, it is accurate. There is no blocking order, only damage assignment order. Since you declare how your attackers damage will be assigned to it's blockers, your opponent can't change it.

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You're correct in your assumption. but the Banding rule provides an exception to this, as below.

702.21j During the combat damage step, if an attacking creature is being blocked by a creature with banding, or by both a [quality] creature with “bands with other [quality]” and another [quality] creature, the defending player (rather than the active player) chooses how the attacking creature’s damage is assigned. That player can divide that creature’s combat damage as he orshe chooses among any number of creatures blocking it. This is an exception to the procedure described in rule 510.1c.

In your example, if the 4/4 and the 1/1 were banding and blocked your 3/3, then the defending player could put the 4/4 first in the damage assignment order and thus prevent his 1/1 being dealt any damage.

(Side note: Unless you're playing with really old cards, you probably won't come across Banding)

  • Not sure why this was downvoted. Banding is a thing and is relevant to this question. – Ellesedil Nov 6 '14 at 15:53
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    @Ellesedil I guess the downvote was because the answer had fundamentally false information in it: "Between choosing damage assignment order and assigning the damage, players can cast spells and activate abilities, so creatures could gain or lose the Banding ability" I've edited the answer to be a bit more specific in simply pointing out the exception that Banding creates. – Aiken Nov 6 '14 at 16:00
  • @Aiken: Ah, good call. Glossed over that part as I paid attention primarily to the rule text. – Ellesedil Nov 6 '14 at 16:02
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    @Ellesedil The downvote was mine, because the answer was (and still is) primarily about banding, which is an obscure mechanic that sees no competitive play and WotC has officially announced was a mistake to have ever printed. It's so needlessly complicated that it deserves to be a footnote instead of the entire body of the answer. At this point, all I see is the "You're correct" at the top, and the rest of the answer may as well be invisible. – Rainbolt Nov 6 '14 at 16:14
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    @Rainbolt: All of those things about banding is irrelevant. It exists, some cards have it or can grant it, and may come up in casual play. And then there's also things like this, which none of the answers talk about and actually perfectly fits with the asker's question. – Ellesedil Nov 6 '14 at 16:22

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