I am fairly sure that for any non-trivial game that would boil down to a solution to the halting problem, though I lack time to prove it.

(Or possibly what I think of as the "finite halting problem" somewhat colloquially; a system that isn't actually Turing Complete because it's finite and bounded, but shares "enough" aspects of Turing Completeness that it still means that it's completely computationally infeasible to "prove" the property in question in the real world. Technically the halting problem on real computers falls into this class, a program running without IO is technically on a finite state machine but you're still not going to solve even that halting problem in a world where the bidding opens at 4GB of RAM.)

This is going to be like the second half of a joke about a mathematician and an engineer walking into a bar....

... but, to objectively evaluate whether a game has a degenerate winning condition, make it good enough that twelve-year-olds want to play it, then wait a month or two. ;)