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The Wizard's Sign is placed on a specific stack for half the initiative cost, and then it can be moved, or it is removed when the stack is destroyed. When a mage casts a spell, it is duplicated on the stack under the Sign, but this costs the same amount of mana.
Therefore, if you cast damage spells on a stack under the Sign, the damage will be doubled, but the mana cost will also increase by 2 times, or you can simply hit two stacks at the same time. Before version 3.0, the Sign did not affect spells that hit an area, but now it does. That is, by placing the Sign correctly, you can, for example, cover 2 Meteor Showers over the entire enemy army in one turn.