This system does not pay rent, first of all. In fact, if anything, it's several years behind in its mortgage payments. If the universe is completely non-deterministic with infinite random events happening, shouldn't the odds of my living in the specific sub-universe that appears fully deterministic be almost indistinguishable from zero? This can't even cheat with the anthropic principle, since there should be a greater proportion (to the extent that proportions are intelligible in this context) of universes where the laws of causality do not appear to hold.

Perhaps most significantly, we don't know enough about how the universe works to say that it is in any sense possible for billiard balls to turn into pink elephants; we can't rule it out, but we can't say with any certainty that such a universe could actually exist.

Second of all, Hume's paradox (if I understand you correctly) is the fundamental problem of predicting the past from the future. If I did something a hundred times and the exact same thing happened, then I anticipate the same thing to happen on the hundred and first time. This does not appear logically necessary; the only reason we have to expect the future to conform to the past is because the future has always conformed to the past, which is circular. This is a sort of attack on the concept of evidence itself, and I haven't seen a good knock-down counterargument.

Indeed, we cannot be certain that the future will in fact conform to the laws of the past - our Simulation's causality algorithm gets corrupted, perhaps, or something else far "weirder" happens. As Hume says (paraphrasing), it's not like we can stop believing in causality, as the results aren't pretty, so even if we don't understand precisely why, we should probably go on believing that. It seems a bit presumptuous to say we will never understand causality, as other responders have indicated.