"So if A beats B. B beats C. C beats A.
If I make a plan to go A, A, C, A. That's a strategy?"
Yes, but there are more than just A, B and C in UR. Ultimately it comes down to chance/luck, yes - undeniably; But how you play your hand against a known hand can make victory less reliant on luck.
In my opinion the first turn is the most luck based, because you don't know what your opponent plays like, you can just guess what your opponent might try to do depending on his cards and yours. Second is the most important one, because you are either at a disadvantage (less life/pillz, poisoned, etc) or have the advantage so you have to play according to that. The last 2 turns depend on the outcome of the second one: your opponent might be on a checkmate position where you just have to play your pillz correctly to win; you are dead and all you can do is hope your opponent makes a mistake because you have little or no chance to win; or you 2 are even, then it becomes most of the time a 50/50 guess.