[Physicist]

The law of statistical averages and science of probability comes into play here.

Of course. What do you think I meant by "long enough"?

You tell me the probability of a thing occurring, and the precision to which you wish to measure the thing, and I can calculate "long enough" for you.

[exmarine]

Of course. What do you think I meant by "long enough"?

The problem is that the universe is finite (15 billions years?) - you do not have infinite time for all special cases. Some "special cases" cannot possibly occur even within the timeframe of the age of the universe, e.g. the self-assembly of a protein molecule for example.