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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 target player is an illegal target when Jace’s first loyalty ability tries to resolve, it doesn’t resolve. You won’t draw a card.

If for some reason you can’t win the game (because your opponent controls Platinum Angel, for example), you won’t lose for having tried to draw a card from a library with no cards in it. The draw was still replaced.

If two or more players control Jace, Wielder of Mysteries and each player is instructed to draw a number of cards, first the player whose turn it is draws that many cards. If this causes that player to win the game instead, the game is immediately over. If the game isn’t over yet, repeat this process for each other player in turn order.

Follow the instructions in the order listed on Jace’s first loyalty ability: if you target yourself, you’ll put the top two cards of your library into your graveyard and then draw a card.

If your library has fewer than seven cards in it while resolving Jace’s last ability, and Jace has already left the battlefield, you’ll draw as many cards as you can and then win the game before state-based actions would cause you to lose the game for trying to draw from an empty library.