I think it would be really cool if there were leagues that were drawback cards only, or restricted to lower level characters, or only one combination of race/class, like the quests. (Clearly, 1 HP leagues would be problematic, at best. Lots of Flash Of Agony, Firestorm, etc)
They would have to be constructed leagues I assume? I think handicap leagues would be the best of the lot, and probably quite fun. But if you want a real handicap match, try Danger Wizards! http://forums.cardhunter.com/threads/danger-wizards.6501/
Let's look through the list of quests, shall we? No Team Deaths: Seems really dangerous, lots of targeted spells and such. Could be an interesting dynamic. 1 HP: Lolnope Only Certain Class and/or Certain race: Could be interesting, I would love to see all elf wizards duking it out. Level set to "X": I want this so badly. The dynamics alone would be fascinating to watch. Drawbacks Only: Round Start! EVERYONE TRIPS AT ONCE! End of Round. Needless to say, yes yes yes yes yes.
