A poster on a Usenet group:

I have a math question for you. What are the chances of a magical creator being having always existed yet which is completely undetectable?

Ken:

It's surprising what mathematicians write books about... The terms "magical", "creator", and "undetectable" don't really come within the province of probability theory.

However they do come within the area of mathematics known as game theory - not games in the common sense of that word, but games as in "war games", involving various strategies to achieve certain ends.

Steven J. Brams wrote "Superior beings: if they exist, how would we know? : game-theoretic implications of omniscience, omnipotence, immortality, and incomprehensibility" (Springer-Verlag, New York, 1983).

I won't even try expounding this 200 page book here, but Mrams considers how various aspects of "superior beings" as he calls them might be allocated strategies in two-person, non-zero-sum games. One of these is whether the "superior being" might prefer to conceal his/her/its existence, so that followers base their views on faith, and not on proof of any sort.

Dr Ken Smith - Christian, husband, unpaid mathematician, skeptic, ... "It can hardly be said that hectic passion has been the keynote of my married life with She Who Must Be Obeyed, although I remember a holiday in Brittany when She showed an unwonted enthusiasm for the stuff." Horace Rumpole