For any event that has some episolon>0 probability of happening, it's gonna happen eventually if you give it enough chances.

This is not true (and also you mis-apply the Law of large Numbers here). For example: in a series (one single, continuing series!) of coin tosses, the probability that you get a run of heads at least half as long as the overall length of the series (eg ttththtHHHHHHH) is always >0, but it is not guaranteed to happen, no matter how many chances you give it. Even if the number of coin tosses is infinite (whatever that might mean).

Interestingly, I read the original quote differently from you - I thought the intent was to say "any bloody thing will be brought up in a discussion, eventually, if it is long enough, even really obscure stuff like G.I.T.", rather than "Gödel is brought up way too often in philosophical discussions". What did you really mean, nsheppered???