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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.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as an escape cost), add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was and no matter whether an alternative cost was paid.

If you cast a spell with its escape permission, you can't choose to apply any other alternative costs or to cast it without paying its mana cost. If it has any additional costs, you must pay those.

If a card with escape is put into your graveyard during your turn, you'll be able to cast it right away if it's legal to do so, before an opponent can take any actions.

Once you begin casting a spell with escape, it immediately moves to the stack. Players can't take any other actions until you're done casting the spell.

Escape's permission doesn't change when you may cast the spell from your graveyard.

If the target creature is an illegal target when Polukranos's activated ability tries to resolve, the ability doesn't resolve. If Polukranos is no longer on the battlefield, the target creature won't deal or be dealt damage.

If an amount of damage would be dealt to Polukranos greater than the number of +1/+1 counters on it, all of that damage is prevented, and all of those counters are removed. In most cases, this will result in Polukranos having 0 toughness, so it will be put into its owner's graveyard.

After an escaped spell resolves, it returns to its owner's graveyard if it's not a permanent spell. If it is a permanent spell, it enters the battlefield and will return to its owner's graveyard if it dies later. Perhaps it will escape again—good underworld security is so hard to come by these days.

If a card has multiple abilities giving you permission to cast it, such as two escape abilities or an escape ability and a flashback ability, you choose which one to apply. The others have no effect.

If damage that can't be prevented is dealt to Polukranos, the damage is dealt and you'll simultaneously remove that many +1/+1 counters from it, all before the game checks for lethal damage.