Alright, I know the doctor is most likely winning, but does Rick have any wincons?
Rick has Wincons, but it depends on how much "COMPOSITE" the Death Battle crew makes their Rick, and how they interpret some feats, although I speak from the perspective of someone who doesn't even know much about Doctor Who
-Precognition and personality: Rick is more bloodlusted than the doctor and could see all the chances of his deaths (C-137)
-Possible advantage in speed: Rick was able to move in literal nothingness without time or space, after stealing the mathematical laws of an entire universe ("C-137" comics)
-The above could be an advantage if most of Doc's feats are based on following some mathematical logic.
-The universe-destroying bomb: The ricks of the citadel have access to a universe-destroying bomb, from how you describe the doctor he can surely avoid that, but when this bomb was activated it prevented any being from that universe from being able to teleport to another ( comics)
-The timeline destroyer machine and the save and load machine:
The machine that destroys timelines destroys those where an unfavorable event for Rick happens, leaving the good one for him (C-132 comics), the saving machine creates new timelines in the same dimension to have access to multiple points save files that can later be merged (C-137)
-Physical immortality via Phoenix Project and spiritual immortality via multiple Dogmas + Multiple selves:
According to Dan Harmon's comments, due to the phoenix project Rick could not die in a conventional physical way, since there are an infinite number of universes like the ones he revived in S4ep1 (C-137). In the Comics, Rick died physically and simply came back to life in the afterlife dominated by different deities by momentarily believing in them, this got to the point where he was able to come back from literal nothingness, simply by believing that there was nothing else, after That came back to life when he became an angel from heaven cartoon ("C-137" Comic) his soul in itself also managed to withstand the heat of the sun of hell, which would have destroyed the soul of common people (Go to hell) Rick Prime has the mention of "Existing in multiple points" at once, probably each with regen
Multiple selves onekill:
According to the commentary on one of the episodes, Rick was going to use a liquid capable of eliminating all the possible versions in the infinite multiverse of whoever drinks it.
BFR: In Rick and Morty the "Central Finite Curve" is a barrier that separates "all the infinite universes where Rick is the smartest" "from all the infinite universes where he is not" Maybe in the context of the fight Rick could use the curve to enclose the doctor within that infinity or to protect himself from the rest of the infinity
-Warping: After killing the devil, Rick rebuilt hell to his liking, and re-created his universe after it was destroyed in the previous run by the universe-destroying bomb, he did it in such a way that not even his family noticed that They died (go to hell) Rick also had a ring that allowed him to have 3 wishes, to the point of being able to apply reality warping from his reality to one outside the finite central curve (DnD2)
-Meta narrative skills:
Rick was able to cross the fourth wall, from which both its curve and the rest of the infinity were nothing more than a show with seasons, he was also able to make a shield that protected him from the metanarrative abilities of characters who inhabited the fourth wall (C-137 ) Rick was able to travel with his common portal gun to a "real" universe that was reading his actions at the time as a comic, as mere fiction, and kill the reader, and then return to the comic ("C-137" comics). Rick mentions that he inspired himself after traveling with Jerry to a Rick and Morty convention in the "real" world (C-132 comics)
-Other possible Wanks:
Anti toon force for the cameo holding Taz back in Space Jam 2 (Rick mentions this cameo when breaking through the fourth wall of his own series)