So, if I successfully cast Lurrus of the Dream-Den from my Side Board, and it resolves, and I have an Emrakul, the Aeons Torn in my hand, does that mean I can now cast it for only 2 colorless mana?
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No one can make you feel inferior without your permission.
You have things exactly backwards. If you are using Lurrus as your companion, that means that you can’t have Emrakul (or any other permanents with CMC 3+) in your deck (or command zone, if relevant) in the first place.
Companion doesn’t change the Characteristics of cards in your deck or hand. Rather, it places a restriction on deck building that must be in place before the game starts and Lurrus is named as your companion.
You seem to confusing mana cost with converted mana cost. The converted mana cost (CMC) is a non-negative integer. The CMC of a card or permanent is calculated by adding 1 for each mana (colored, colorless, generic, or snow), phyrexian mana, and bicolor hybrid mana; 2 for each monocolor hybrid mana; and 0 for each X in the object's mana cost. An object with no mana cost has a CMC of 0. The CMC of a spell on the stack is calculated similarly to cards and permanents except each X is not necessarily 0 but the value chosen for that X as the spell was cast.
I agree completely with Davidb32, but have to ask a about the ruling on Lurrus whic says if you have a X cost creature in your graveyard such as Ugins connjuran it can only be cast for 2. This seems to me to fly in the face of many years of rulings? However if you look up rulings under lurrus on the mtg website it states this is how it works. Why?
Lurrus cares about the converted mana cost of the spell on the stack, not the card in your graveyard. If you have a Stonecoil Serpent in your graveyard and you want to cast it via Lurrus' ability, the largest value you can choose for X is 2. If you pick 3 or more, then the converted mana cost of the spell on the stack is 3 or more, and not castable via Lurrus' ability.
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Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.
Still slightly confused about Lurrus... too much conflicting info online. I understand that as a companion he puts a limit of 2cc on your deck construction, easy peasy. But (as a non-companion) his recur ability still has me confused, since it only cares about the converted mana cost of the spell, so does that mean I can or can't cast Parcelbeast from my grave with Lurrus for 2cc...? Similarly, can Lurrus let me cast Regal Leosaur from my grave for 3cc...? It seems like I should be able to cast Parcelbeast and not Leosaur, but if not, I'm still unclear on why I can't...
Still slightly confused about Lurrus... too much conflicting info online. I understand that as a companion he puts a limit of 2cc on your deck construction, easy peasy. But (as a non-companion) his recur ability still has me confused, since it only cares about the converted mana cost of the spell, so does that mean I can or can't cast Parcelbeast from my grave with Lurrus for 2cc...? Similarly, can Lurrus let me cast Regal Leosaur from my grave for 3cc...? It seems like I should be able to cast Parcelbeast and not Leosaur, but if not, I'm still unclear on why I can't...
The mana cost of Parcelbeast is 2GU.
The converted mana cost of Parcelbeast is 4.
4 is not "2 or less".
Therefore, a Parcelbeast spell would not be a "permanent spell with converted mana cost 2 or less".
The mana cost of Regal Leosaur is GW.
The converted mana cost of Regal Leosaur is 2.
2 is "2 or less".
Therefore, a Regal Leosaur spell would be a "permanent spell with converted mana cost 2 or less".
Using the mutate ability changes nothing about the above.
702.139a Mutate appears on some creature cards. It represents a static ability that functions while the spell with mutate is on the stack. “Mutate [cost]” means “You may pay [cost] rather than pay this spell’s mana cost. If you do, it becomes a mutating creature spell and targets a non-Human creature with the same owner as this spell.” Casting a spell using its mutate ability follows the rules for paying alternative costs (see 601.2b and 601.2f–h).
202. Mana Cost and Color
202.1. A card’s mana cost is indicated by mana symbols near the top of the card. (See rule 107.4.) On most cards, these symbols are printed in the upper right corner. Some cards from the Future Sight set have alternate frames in which the mana symbols appear to the left of the illustration.
202.3. The converted mana cost of an object is a number equal to the total amount of mana in its mana cost, regardless of color.
Example: A mana cost of 3UU translates to a converted mana cost of 5.
118.9c An alternative cost doesn’t change a spell’s mana cost, only what its controller has to pay to cast it. Spells and abilities that ask for that spell’s mana cost still see the original value.
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Why bother with mere rulings when so many answers can be found in the Rules?
Regal Leosaur is a "spell with mana value 2 or less", because the amount of mana in its mana cost is 2, even if you pay more than two mana to cast it, but
Parcelbeast is not a "spell with mana value 2 or less", because the amount of mana in its mana cost is 4, even if you pay two mana or less to cast Parcelbeast (whether as a mutating creature spell or otherwise)
(C.R. 202.3). A spell's mana value is determined regardless of what was spent (or will be spent) to cast the spell (C.R. 202.3). The only thing that can change a spell's mana value is the value of X chosen for the spell, and then only if the spell has X in its mana cost (C.R. 202.3e), which neither Parcelbeast nor Regal Leosaur has. See also this thread.
EDIT (Jun. 9, 2021): Edited to conform to rule changes in the meantime.
Thank you both, that clears it up! I was hooked on thinking what you actually pay will be the spell's converted mana cost (which to me sounds more logical). So I can recur creatures/cards with alternative costs higher than 2, so long as their original casting cost was 2 or less (with X cost spells at 2 or less in total), allowing me to cast the Leosaur for 3cc with Lurrus...
Companion doesn’t change the Characteristics of cards in your deck or hand. Rather, it places a restriction on deck building that must be in place before the game starts and Lurrus is named as your companion.
Scientists have calculated that the chance of anything so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules
The mana cost of Parcelbeast is 2GU.
The converted mana cost of Parcelbeast is 4.
4 is not "2 or less".
Therefore, a Parcelbeast spell would not be a "permanent spell with converted mana cost 2 or less".
The mana cost of Regal Leosaur is GW.
The converted mana cost of Regal Leosaur is 2.
2 is "2 or less".
Therefore, a Regal Leosaur spell would be a "permanent spell with converted mana cost 2 or less".
Using the mutate ability changes nothing about the above.
(C.R. 202.3). A spell's mana value is determined regardless of what was spent (or will be spent) to cast the spell (C.R. 202.3). The only thing that can change a spell's mana value is the value of X chosen for the spell, and then only if the spell has X in its mana cost (C.R. 202.3e), which neither Parcelbeast nor Regal Leosaur has. See also this thread.
EDIT (Jun. 9, 2021): Edited to conform to rule changes in the meantime.