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As far as I understand, Cipher works like so: when a card that contains Cipher is cast, you encode it onto a spell on the battlefield, like a creature for example. Every time that creature attacks and deals damage to a player, a copy of the encoded creature is made.
If the opponent does not have anything to block a flying creature I've encoded, and for 3 turns straight I can deal damage with the creature that was encoded, does it result in 3 copies? Can you only make one copy?
Cipher copies the encoded spell, not the creature - have another look at the reminder text:
Then you may exile this spell card encoded on a creature you control. Whenever that creature deals combat damage to a player, its controller may cast a copy of this card without paying its mana cost.
"This card" is referring to the card it's printed on, the spell with cipher. So if for example you cast Last Thoughts (allowing you to draw a card) and encode it on a creature, each time that creature deals combat damage to a player, you get to re-cast Last Thoughts for free (and draw another card). This can happen as many times as you can manage to deal combat damage to a player with the creature.
I should also point out: you can only encode it onto a creature, not anything else on the battlefield. (And, I know it sounds pedantic, but there's no such thing as a spell on the battlefield - things on the battlefield are called "permanents", a word you'll see on some cards.)
Hopefully this makes more sense to you than copying the creature - you're encoding the spell onto the creature, tying them together, so that the creature can cause the spell to be cast again.
