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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The instruction to roll a die and the effect that occurs because of the result are all part of the same ability. Players do not get the chance to respond to the ability after knowing the result of the roll.

Some abilities, like that of Pixie Guide and Barbarian Class, replace rolling a die with rolling extra dice and ignoring the lowest roll. The ignored rolls are not considered for the effect that instructed you to roll a die, and do not cause abilities to trigger. For all intents and purposes, once you determine which dice count, any extra dice were never rolled.

While playing Planechase, rolling the planar die will cause any ability that triggers whenever a player rolls one or more dice to trigger. However, any effect that refers to a numerical result will ignore the rolling of the planar die.

If you choose to put the card into your hand, you don't need to reveal it.

Dice are identified by the number of faces each one has. For example, a d20 is a twenty-sided die.

An ability that tells you to roll a die will also specify what to do with the result of that roll. Most often, this is in the form of a “results table” in the card text.

Some effects may modify the result of a die roll. This may be part of the instruction to roll a die or it may come from other cards. Anything that references the “result” of a die roll is looking for the result after these modifications. Anything that is looking for the “natural result” is looking for the number shown on the face of the die before these modifications.

Some effects instruct you to roll again. This uses the same number and type of dice as the original roll, and that roll will use the same set of possible outcomes.

An effect that says “choose a target, then roll a d20” or similar still uses the normal process of putting an ability on the stack and resolving it. Choosing targets is part of putting the ability on the stack and rolling the d20 happens later, as the ability resolves.

Dice used must have equally likely outcomes and the roll must be fair. Although physical dice are recommended, digital substitutes are allowed, provided they have the same number of equally likely outcomes as specified in the original roll instruction.

The “otherwise” in the last ability refers to whether or not you put it onto the battlefield, not whether or not it's an artifact card. You may put it into your hand even if it's an artifact card.

Tournament events have more specific rules regarding dice and die-rolling. For more information, please see the most recent version of the Magic Tournament Rules at https://wpn.wizards.com/en/document/magic-gathering-tournament-rules.