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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 multiple players each control Treasure Nabbers, an artifact tapped for mana will make quite a journey. For example, if player A taps an artifact for mana during their turn, and players B and C are the next players in turn order who control Treasure Nabbers, C's ability resolves before B and C gains control of the artifact. Then B gains control of the artifact. B keeps it during their turn, and then C regains control of the artifact once B's effect expires, then A will have it back after C's expires. However, if B or C taps the artifact for mana, one of them will take it from the other. You may need to pay very careful attention to which effects are still in effect, which have expired, and who owns what.

If you control multiple Treasure Nabbers, their effects all expire at the same time. You won't keep an artifact for any longer.

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If that player controls any nabbed treasures, the effect giving that player control of those artifacts ends.

An artifact is "tapped for mana" when a player activates a mana ability of an artifact that includes {T} (the tap symbol). Notably, tapping an artifact to pay for a spell with the improvise keyword is not tapping that artifact for mana.

If the artifact leaves the battlefield, Treasure Nabber doesn't nab it from the zone it moved to.

The artifact remains tapped when you gain control of it.

If an opponent taps an artifact for mana during your turn, you'll gain control of it and keep control of it until the end of your next turn.