Dark World Purrely
The synergy between these decks are fairly simple, Purrely needs good cards to discard so that they don't run out of advantage, and Dark world needs additional cards to discard themselves. Dark worlds provide near-infinite discard fodder for your purrely quick plays, as well as link material for an Apollousa or Muckracker, rank 8 material for 38 or 90, or to make a fusion that can negate 1 card, then get rid of 2 cards in the opponent's hand. The Dark worlds also provide a great drawing engine so you can get access to your Purrely quick-play spells without relying on the randomness of Purrely (25550531). The new Purrely card, Purrely Lily (79933029), gives a great boost to the deck. It allows you to play less copies of My Friend Purrely (56700100) since it can search any Purrely non-quick-play spell Purrely, which can turn almost any purrely card into a one-card combo for Expurrely Noir (83827392).
In order to play the deck, you will have to be familiar with Dark World with the new support, as there are some nice techs that have been given with the new support, like returning a summoned Genta, Gateman of Dark World (77895328) to hand with Grapha, Dragon Lord of Dark World (34230233) or Reign-Beaux, Overking of Dark World (41406613).
The deck is very explosive, but it is possible to brick, unlike Danger Dark world which doesn't brick but relies on luck with dangers. There are pros and cons between using Purrelys in Dark World, and using Dangers in Dark World. Here's some of them.
Pros:
Purrely gives control over your discards, where as dark worlds can either win you the game immediately or lose you the game immediately.
Purrely has amazing access to rank 1 xyz monsters like Lyrilusc - Ensemblue Robin (72971064).
If you don't want to use your purrelys for xyz material, they can still be used as Link Material for Apollousa, I:P, or Muckracker.
They can set up a 2 or 3-activation Zeus very easily, which can win the game on its own.
Expurrely Noir is an Arrival Cyberse @Ignister that also can be interuption, draw you cards, attack multiple monsters with over 7000 attack, or attach opponents monsters to it as material. (These effects mostly come from the quick play spells.)
They're Cute!
Cons:
Purrelys don't give you access to a mass amount of rank 8s, so you lose out on making 38, 90, Felgrand, or Coach King Giantrainer, which draws 3 cards.
Dangers can give you access to as many discards as you need for your darkworlds, but in purrely, you get a limited amount of summons with your quick plays.
Dangers provide many of your draws so that you can get your powerful dark worlds like Snoww or Genta.
You don't have access to Dugares the Timless in this version of the deck. You could make it theoretically by using a genta and a normal summoned level 4, but I've never had a situation where I could do that, or it would be better to do that.
Despite the number of cons that the Purrely version of the deck has, I think the Pros outweigh them by a landslide. Of course, feel free to edit the deck to your liking. The side deck is the preference for the upcoming format, though I do recommend Lancea since it can stop some of the Kashtira, floo, and sword soul tenyi cards, as well as shifter and bystials. Unfortunately it doesn't stop shifter on your turn, but it can prevent an otk against some decks.