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

Some spells or abilities that produce mana restrict how that mana can be spent, have an additional effect that affects the spell or ability that mana is spent on, or create a delayed triggered ability (see rule 603.7a) that triggers when that mana is spent. This doesn’t affect the mana’s type.

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.

If multiple effects modify how damage is dealt, the player being dealt damage, or the controller of the permanent being dealt damage, chooses the order in which to apply the effects. For example, the ability of Decorated Griffin says “{1}{W}: Prevent the next 1 combat damage that would be dealt to you this turn.” Suppose you control a Decorated Griffin, and you and an opponent are the chosen players for a Bitter Feud. If a creature that player controls would deal 3 combat damage to you, and Decorated Griffin’s ability has resolved once, you can choose to either (a) apply the effect from Decorated Griffin first and prevent 1 damage, and then let Bitter Feud’s effect double the remaining 2 damage, for a result 4 damage being dealt to you, or (b) let Bitter Feud’s effect apply first and double the damage to 6, and then apply the effect from Decorated Griffin to prevent 1 damage, for a result of 5 damage being dealt to you.

If there are two Bitter Feuds on the battlefield, and the same two players were chosen for each, damage dealt will be doubled for each. So, two Bitter Feuds will end up multiplying the damage by four, three will multiply the damage by eight, and four by sixteen.

The source of the damage doesn’t change. A spell that deals damage will specify the source of the damage. This is usually the spell itself. An ability that deals damage will specify the source of the damage, although it will never be the ability itself. Usually the source of the ability is also the source of the damage.

Bitter Feud applies to damage dealt by any source controlled by one of the chosen players, not just combat damage.