I think it makes sense to combine Nick Bostrom's simulation argument with the many worlds interpretation.
While Copenhagen tells us that some outcomes are very unlikely, the m.w.i. assures us that every possible world actually exists. So we can be sure that there are worlds which contain the necessary equipment to simulate your conscious experience - and since there are (infinitely) many different ways to simulate the same experience, we can follow Bostrum's argument to finally conclude that it is almost certain that you are experiencing The Matrix right now (*).
If you believe the m.w.i. then you must believe that your experience is just a fake (x).
(*) There are N ways how your experience can be simulated and only 1 how it would be real, since you cannot distinguish them they have equal probability and for (infinitely) large N the conclusion follows.
(x) Of course, my argument will probably not convince you, which is just what The Matrix does to you ...