I have Thespian's Stage in play copying Raging Ravine. I animate Thespian's Stage, give it vigilance in some way, and attack. My opponent flashes in Ambush Viper and blocks. I decide I don't want to trade. Can I activate Thespian's Stage to copy a non-animated land and get out of combat that way? What happens to the damage?
Gatherer doesn't say anything about this - only that I need to activate the animation costs after Thespian's Stage has copied a land.
No, you cannot turn it into another land to remove it from combat. The issue is due to layers.
Layer 1 is copy effects (Thespian's Stage).
Layer 4 is type changing effects (Raging Ravine's ability).
Since it is still the same object, both layers are applied in order. So, for layer 1 you have a Thespian's Stage that is copying a Raging Ravine that is copying a land (say, a Forest). Then you apply the type changing effect in layer 4 that turns it into a 3/3 creature.
So, you'd end up with a 3/3 Creature Land - Forest (with a +1/+1 counter from attacking as Raging Ravine)
613.1a Layer 1: Copy effects are applied. See rule 706, “Copying Objects.”
613.1b Layer 2: Control-changing effects are applied.
613.1c Layer 3: Text-changing effects are applied. See rule 612, “Text-Changing Effects.”
613.1d Layer 4: Type-changing effects are applied. These include effects that change an object’s card type, subtype, and/or supertype.
613.1e Layer 5: Color-changing effects are applied.
613.1f Layer 6: Ability-adding effects, ability-removing effects, and effects that say an object can’t have an ability are applied.
613.1g Layer 7: Power- and/or toughness-changing effects are applied.
