[cristianpascu]

A billion years is a very long time if you wait in a railway station. But in milliseconds, for instance, as powers of 10 is a blink of an eye compared to the magnitude of the search space of configurations of a single protein.

[MrQuincle]

The context here is the lifetime of the universe. If that is 13 billion years, 1 billion is a considerable chunk.

If I interpret you right, you state that we might be extremely lucky hitting on a valid configuration so fast. In other words, the distribution might be at average at e.g. 1000 billion years. What shape would the distribution have?