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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.

If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. You can't choose a different one.

The second ability triggers whenever a player casts a spell that targets only one creature and no other object or player. It doesn't matter who controls the creature.

The copy is created even if the spell that caused the ability to trigger has been countered by the time the ability resolves. The copy resolves before the original spell.

The controller of a copy can't choose to pay any additional costs for the copy. However, effects based on any additional costs that were paid for the original spell are copied as though those same costs were paid for the copy too. Notably, if the spell you copy was kicked, the copies will also be kicked.

The copy that Ivy, Gleeful Spellthief's second ability creates is created on the stack, so it's not "cast." Other abilities that trigger when a player casts a spell won't trigger.

If the spell that's copied has an X whose value was determined as it was cast, the copy has the same value of X.

If a spell has multiple targets but all of them are the same creature, Ivy, Gleeful Spellthief's second ability will trigger.

If Ivy, Gleeful Spellthief isn't a legal target for the spell, no copy can be created.