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.