Wait, so it works in opposite right? If we buy a card in WoE, how do we use it, if we don't have it in the actual card game?
You can't. Players are responsible for fielding decks they are able to play.
You could however sell it, trade it, or convert it using a skill to a different card. Or keep it for bragging rights/discard fodder. Or turn it in as part of a quest reward, or use it as part of the requirements for a skill.
If you fight a battle with a card from your WoE personal vault in your WoE deck, but that card is not actually in the real deck you use to fight that battle, then you have fielded an illegal deck the same as if you used a card in your real deck that you don't have in WoE.
This does advantage veterans, but since the rarest cards in Elements will also be relatively hard to get ahold of in WoE we don't see this as so much of a problem. Also, WoE is relatively slow-paced, meaning that it should be relatively easy to get ahold of cards you'll need to use for WoE even if you're an absolute newbie.
