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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.

In a Two-Headed Giant game, life gained by your teammate won't cause Bilbo, Birthday Celebrant's first ability to apply, even though it will cause your team's life total to increase.

Bilbo, Birthday Celebrant's first ability applies just once to each life-gaining event, no matter how much life is gained. If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and the ability of Bilbo, Birthday Celebrant applies only once.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Bilbo, Birthday Celebrant's first ability will apply to those two events separately. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, and/or planeswalkers at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will apply only once.

If you somehow control two Bilbo, Birthday Celebrants and you would gain life, you gain that much life plus 2. A third Bilbo, Birthday Celebrant has you gain that much life plus 3, and so on.