The Loop Troupe

Rogue can recur events more flexibly than most other heroes in the game, using Superpower Adaptation. So as long as she touches a Leadership ally, she can get Mutant Mayhem in hand pretty consistently. So I put together a deck that abuses this.

• Two copies of Children of the Atom, so this you can quickly broaden the targets for Mutant Mayhem. Caliban and Hope Summers are here, though, so Mutant Mayhem will have targets even if you cant find CotA for some reason.
• Utopia can ready a character (usually Rogue herself) when you play an X-man ally
• Beast "refunds" Mutant Mayhem by grabbing a resource
• M can delete a low-health minion
• Kid Omega can have immediate impact
• Caliban tutors another ally
• Hope Summers can tutor any of Rogue's events
• Cyclops can make the Villain vulnerable to attacks
• Phoenix can heal and ready another ally so they can activate again
• because you want to have allies out and then re-play them with Mutant Mayhem, Band Together will usually be a double if not a triple resource, even from pretty early in the game. Makes a good target for Beast to grab.
• The X-Jet and Deft Focus and Ingenuity and X-Gene and Uncanny X-Men to make it easier to play more cards (which is how you win the game)
• The eponymous Loop Troupe = If you have Beast and Hope Summers in play, along with one other Leadership ally, you can loop Mutant Mayhem as many times as you have Superpower Adaptation still in your deck. (using Beast to get Band Together and Hope to get Superpower Adaptation, which you immediately use to get Mutant Mayhem back)
• Once you've run out of Superpower Adaptation, use the last tutor to get Southern Cross or Goin' Rogue. Even better if you have Energy Transfer or Bulletproof Belle in your hand, use the last tutor to get the other and switch Touched to the Villain to negate the next attack(s).

Keep in mind that to use Superpower Adaptation to recur Mutant Mayhem, you have to put Touched on a leadership ally, but if you target that same ally with Mutant Mayhem, Touched falls off and cannot be re-applied to any character (unless you use Energy Transfer)