Are 7 mash shuffles enough?

An extremely prevalent sentiment among most players is that mash-shuffling is not enough to evenly randomize the deck. They have the strong feeling that cards will not be "separated enough" from each other, and that if, for example (the most common example), they put all their lands on the top of the deck and start mash-shuffling, they will end up with huge clumps of lands, and huge clumps of non-lands (and thus they will either mana-flood or mana-screw). They feel that most certainly 7 mash shuffles (which is the oft-quoted figure) is not even nearly enough. For this reason they will often resort to pile-shuffling to "separate the cards". No matter how they are explained that 7 mash shuffles is indeed enough, and that nothing else is needed, they just can't accept it. They might accept something like 20 or 30 mashes, but certainly not 7.

But I'll try to explain it.

Let's assume that the deck uses decent sleeves (ie. not those cheap transparent thin sleeves intended for double-sleeving that can get sticky and pretty much glue cards together). Let's consider two cards that are adjacent in the deck, and let's examine how their relative separation will behave during mash shuffling.

You'd agree that with one mash, there's roughly speaking an approximately 50% chance that at least one new card will be inserted between them. Question: What are the chances that they will still be adjacent after 7 mash shuffles, on average?

Answer: Approximately 1 in 128, or about 0.8%.

Ok, there's only a very minuscule chance that they will still be adjacent after 7 mash shuffles. But they will still very likely to be very close to each other, right?

No. The thing is, the more separated they are already of each other, the more likely it is that more cards will be inserted between them. If you think about it, you'll realize that, in fact, their distance will, on average, roughly double with each mash shuffle. This means that their separation will grow exponentially with each mash.

What does this mean in practice? On the first mash, their separation will increase on average by 0.5 cards (which is what a 50% chance of a card being inserted between them means). This separation will, on average, double with each mash. Thus their average separation will roughly double the 0.5 seven times, ending up with an average separation of 64 cards. (And this is the average separation between them, not the maximum. The maximum could theoretically be anything.)

Since there is (typically) only 60 cards in the deck, a separation of over that means in practice that the card "wraps around" in the deck, to the other side. In practice this means that it will end up pretty much at a random place within the deck. There's a big chance that the relative order of the two original cards in the deck we were examining will switch (probably somewhere around the 50% figure, which is exactly what should happen.)

Yet, no matter how precisely this is explained, most players will not accept it. They will trust their own intuition more than mathematics. And they will waste everybody's time with useless pile-shuffling, and mash-shuffling dozens of times.

A non-existent mana cost

There's a principle (well, rule really) in Magic that goes like this: A non-existent mana cost cannot be paid.

What does this mean?

Consider this scenario: You have a Living End in your graveyard, and you cast a Snapcaster Mage, and use it to give the Living End flashback. Can you then proceed to cast Living End from your graveyard?

The answer is no, you can't. And the reason for this is the principle: A non-existent mana cost cannot be paid.

Living End has no mana cost. This is not the same thing as having a mana cost of 0. (If its mana cost were 0, then it would have a mana cost symbol with 0 on its upper right corner.) It has no mana cost at all. This means that it can't be cast in the normal way (because paying its mana cost is part of the casting process, and in this case that step cannot be done, because it has no mana cost.)

(Note that Living End has a converted mana cost of 0. However, this is a completely different and unrelated thing. That value is used only for effects that look for converted mana cost explicitly. Casting does not look at converted mana costs.)

Snapcaster Mage adds flashback to the card when it's in your graveyard, and it states that the flashback cost is its mana cost. However, as stated, the card has no mana cost! This means that it has no flashback cost either, and a non-existent cost can't be paid. Therefore you can't cast it using Snapcaster Mage either.

So how exactly is Living End cast, then? Using its suspend ability. Suspend works like this: If the card is in your hand, any time you could cast the card (ie. obeying timing restrictions for the card type) you may pay the suspend cost, which moves the card into exile with the specified number of time counters. At the beginning of your upkeep you remove one time counter from it, and when the last time counter is removed, you may cast the card without paying its mana cost.

That last part is the crucial difference: The effect allows you to cast the card "without paying its mana cost". Any effect that uses that wording bypasses completely the mana cost of the card, and thus we don't even look at what it is (or, like in this case, whether it even exists.) The effect instructing you to cast the card doesn't require paying any mana cost, and thus the card can be cast.

Consider Living End with these two cards:

Act on Impulse exiles the top three cards of your library, and allows you to cast them (from exile) until end of turn. Even though the cards are in exile rather than in your hand, the casting process is identical. Therefore you can't cast Living End this way, because you can't pay its mana cost. (Incidentally, you can't suspend it either, because the suspend ability can only be used if the card is in your hand.)

Chandra's third ability exiles the top ten cards of your library. You then choose an instant or sorcery card among them, copy it three times, and then you may cast these copies without paying their mana costs. This, thus, does allow you to cast (the copies of) Living End, as mana cost is irrelevant.

As an unrelated side note, notice that these two effects behave different with regards to timing restrictions.

With Act on Impulse you have to obey the timing restrictions of the card (in other words, if the card is a sorcery or a creature without flash, you can only cast it whenever you could normally cast a sorcery, ie. in your main phase when the stack is empty.) With Chandra's third ability, however, you cast even sorceries immediately, ignoring their timing restriction (ie. even if the stack is not empty, and even if this somehow wasn't your main phase.)

The reason for the difference is that in the former case the effect allows you to cast the cards during a time period (ie. "you may cast these cards until (some time in the future)"), while in the latter case the effect instructs you to cast the cards immediately, while the effect is resolving. Whenever an effect instructs you to cast a card immediately, you do so disregarding the card's type; whenever an effect allows you to cast a card during a period of time (ie. until end of turn or whatever), you have to obey the timing restrictions of the card type.

The problem with shuffling in MtG

Most competitive card games, where each player has a deck of cards that needs to be randomized, have one very major problem: Experienced cheaters can masterfully manipulate and "stack" the deck while shuffling, without their opponent or anybody else noticing. (This kind of cheating is sometimes caught on camera. With camera footage we have the advantage of seeing the shuffling as many times and as closely as we want, and in slow motion. In a real-life situation it's much harder, especially if we don't know what to look for, and sometimes even then.)

Experienced cheaters can stack the deck by moving certain cards to the top or the bottom of the deck.

To minimize the possibility of cheating, MtG tournament rules require for the opponent to also shuffle the deck afterward. The problem with this is that even though you can't stack your own deck, you can do it for your opponent's deck. For example you can mana-flood or mana-screw your opponent by stacking their deck appropriately.

Poker doesn't really have this problem because if you shuffle the deck, you have to present it to an opponent, and said opponent must only cut the deck once. (In fact, cutting it more than once, or even outright shuffling it, is forbidden at most places. It must be cut, and cut only once.) This way neither player can manipulate the deck. The shuffler can't know where the opponent will cut the deck, so there's no way to make certain cards end up on the top. (The only exception to this is that if both players are working together, and the other player cuts the deck where the shuffler "marked" it. This is a common cheating tactic in poker, but it only works if two players are working together, and only if they are sitting side by side on the table, as the cut is always made by the next player.)

Many have suggested using this same principle in MtG. In other words, shuffle your deck, and then your opponent cuts it once, and that's it. However, unlike in poker, this isn't a very effective anti-cheat measure in Magic. Yes, it prevents you from getting the cards you want on the top (or bottom, in the case of your opponent's deck in some situations), but there's another cheat that a single cut doesn't prevent: Mana weaving.

Mana weaving is distributing the lands evenly in the deck, so that you get a steady supply of lands and do not get mana flooded or mana screwed. An expert cheater can more or less easily mana weave their deck (eg. by shuffling in such a way that most lands go eg. to the bottom of the deck, and then mash-shuffling that bottom part into the rest of the deck once.) This is blatant cheating, of course, because the deck is not randomized.

And the thing is, a single cut to such a deck isn't going to undo any such mana weaving. And that's why the poker way doesn't really work in Magic. The opponent really needs to shuffle the deck in order to undo any possible mana weaving, and make the deck truly randomized. But, of course, when you can fully shuffle a deck, it allows cheating.

This is a dilemma that has no practical solution.

At the highest levels of poker cheating by shuffling trickery is impossible because players do not shuffle nor are allowed to touch the deck in any way. It's shuffled by a neutral dealer, employed by the tournament organizer or the casino.

In MtG tournaments the same could work if judges always shuffled the players' decks. The problem is that a typical tournament has over a hundred players and only a few judges. This solution is just impossible to implement in practice. (This could work on the top-8 matches, but for some reason it's not done that way. Perhaps it's not really needed either. The top-8 matches are always videoed and very closely watched, and it can be fairly assumed that nobody dares to cheat there. Although it does happen from time to time...)

Is color a copyable value?

Simple question: Is the color of a permanent a copyable value? (In other words, if something copies that permanent, will it also copy its color?)

The intuitive answer would be "of course it is!" Naturally it's not that simple.

Copyable values are listed in rule 706.2. They are: "name, mana cost, color indicator, card type, subtype, supertype, rules text, power, toughness, and/or loyalty".

Note that "color" is not among them. "Color indicator" is, but that's not the same thing. To understand the difference, assume that the color of a permanent were changed by something like Thoughtlace (which says "Target spell or permanent becomes blue.") That spell won't add a color indicator to the permanent; it will simply be a continuous effect that changes its color. If that permanent were to now be copied, it won't have that changed color, but the original one of that permanent.

The color of a permanent is derived from its other info. This is actually explicitly explained in the next rule, ie. 706.2a, which says: "A copy acquires the color of the object it’s copying because that value is derived from its mana cost or color indicator."

In other words, to derive the (copyable) color of a permanent, we look for one of these:

1. If it has a colored mana cost.
2. If it has a color indicator. (If it does, it overrides the color derived from the mana cost.)
3. If it has an ability of the form "(this) is (color)". (Very rare nowadays.)

So the next question is: If something creates a token that is, for example, a "1/1 green Snake creature", it will have no mana cost, no color indicator, and no abilities. If now something copies this permanent, will it be green?

From all the information given above, the answer would seem to be "no". After all, the copy has no mana cost, no color indicator and no abilities either, and as rule 706.2a said, those are the ones that would determine its color.

However, the real answer is "yes", but the reason for it is quite unclear and indirect (and, in my opinion, one of the shortcomings of the current rules, as they do not state this very clearly).

The list above was actually incomplete. There is a fourth case, but this additional case is very indirectly implied in a completely different rule pertaining to tokens. This fourth case would be:

4. If it's a token, and the effect that created it specified its color.

A special rule governs this situation. In this case "color" does become a copyable value of the permanent, and it will become copied if something copies it. This fact, however, is currently very unclear, and can only be inferred indirectly. The actual rule where this is inferred from is the following:

110.5b The spell or ability that creates a token may define the values of any number of characteristics for the token. This becomes the token’s “text.” The characteristic values defined this way are functionally equivalent to the characteristic values that are printed on a card; for example, they define the token’s copiable values. A token doesn’t have any characteristics not defined by the spell or ability that created it.

If you are confused, don't worry. So am I. But yes, that rule effectively means that "color" is a copyable value of the token (even though it's usually not for any other permanent).

Can zones be targeted?

There are several things in Magic the Gathering that can be targeted by spells and abilities: Cards, permanents, players, spells (including copies of spells)...

Question: Can zones be targeted?

At first this question might seem silly. After all, what sense would something like "target battlefield" make? (After all, there is only one battlefield, and it would make little sense to "target" it with anything.) However, perhaps a bit surprisingly, the rules of the game support the possibility of targeting a zone. The exact rule that defines targeting is (emphasis mine):

114.1. Some spells and abilities require their controller to choose one or more targets for them. The targets are object(s), player(s), and/or zone(s) the spell or ability will affect. These targets are declared as part of the process of putting the spell or ability on the stack. The targets can’t be changed except by another spell or ability that explicitly says it can do so.

There are some zones that are more sensible to be targeted because they exist per player. Namely graveyards, libraries and hands. Of course normally these are always referred to by targeting the player, not the zone (ie. "target player's graveyard", "target player's library", and "target player's hand".)

To my knowledge, however, there exists one card that targets a zone directly: Circu, Dimir Lobotomist.

It says: "Whenever you cast a blue spell, exile the top card of target library." (Also the second ability targets a library directly.)

The funny thing about this card is that there's no reason why it couldn't say "target player's library", other than that the text wouldn't fit if it said so. Even more curiously, as far as I'm aware, the possibility of targeting a zone was added to rule 114.1 precisely for this one card.

Attacking costs

Question: You control a Floodtide Serpent enchanted with Ordeal of Heliod. You attack with the serpent and return the ordeal to your hand. Does the triggered ability of ordeal trigger?

Most players' intuition would be that it doesn't trigger. In this case the intuition is correct (rare for this blog.) The interesting question is, however, why exactly.

Declaring attackers is a bit more complex of an operation than most players are aware of. It actually resembles the process of casting spells and activating abilities.

Casting a spell technically follows the following procedure (highly condensed here): Announce the spell you are going to cast by revealing it (it moves to the stack), make any possible choices for the spell (possible modes, value of X, alternative or additional costs to be paid, color choice of hybrid mana symbols), choose targets (if it has any), determine the total cost of the spell, activate mana abilities, and finally pay the costs. After all this has been successfully and legally done, the spell is considered successfully cast (and anything that triggers on such a spell being cast triggers now.)

(If at any point it turns out that one of those actions is illegal, everything above is reversed, and none of it is considered having happened.)

Activating abilities is almost identical to the above (with the only difference being that it's not a spell that's put on the stack, but an ability.)

Perhaps a bit surprisingly, but very consistently, declaring attackers (and also declaring blockers) follows a procedure that's very similar. First you announce which creatures are going to attack, then you choose what they are attacking (ie. which opponents or planeswalkers those opponents control), then you determine the possible costs required for this to happen, then you can activate mana abilities, and finally pay the costs (if there are any). After all this has been successfully and legally done, the creatures are considered successfully declared as attackers, and anything that triggers on such a creature attacking triggers now.

(If at any point it turns out that one of those actions is illegal, everything above is reversed, and none of it is considered having happened. This includes in this case checking that no restrictions are broken, and that the amount of requirements that can be fulfilled with a legal declaration has been maximized.)

Note how costs are paid before a creature is considered having attacked, and returning an enchantment to its owner's hand is a cost for Floodtide Serpent to attack. Thus the ordeal returns to your hand before the serpent has attacked, and thus it doesn't trigger.

Abilities and layers, redux

I have touched this subject before, but here's a much simpler case:

1. You control a Bonescythe Sliver, and someone casts Snakeform on it. Will your other slivers have double strike?
2. You control a Stormtide Leviathan, and someone casts Snakeform on it. Will all lands be Islands in addition to their other types?

Instinctively the answer to both questions would be "no", but of course it's not that simple.

In the first case, even though the Sliver's ability has an earlier timestamp than the ability-removing effect created by Snakeform (which normally would mean that all other slivers get first strike before the Snakeform effect removes Bonescythe's abilities), these are dependent effects. In other words, both continuous effects exist on the same layer (the "ability adding/removing" layer, ie. layer 6), and the existence of one depends on the other. This makes them dependent, and for this reason Snakeform's effect is always applied before Bonescythe's, regardless of their relative timestamps. Which means that no slivers get first strike. This makes it intuitive even without knowing about layers, timestamps and dependent effects.

What is much less intuitive is what happens in the second case. One could easily think that it works the same way: Snakeform removes the ability, and thus lands are not Islands in addition to their other types. However, it doesn't work like that.

The Leviathan's effect is not an ability-adding effect, but a type-changing effect. Types are set in a lower layer (more precisely layer 4). This means that the effect is evaluated before any ability-removing effect.

These two effects are not dependent because they are on different layers. Only effects on the same layer can be dependent.

This means that even though Leviathan ends up not having any abilities, all lands will still be Islands in addition to their other types, as unintuitive as that may be.