[ThinkDifferent]

a claim that, given enough time, things which have never been observed in the history of the world and which cannot be made to happen in controlled experiments, are gauranteed to happen

Which can often be true. Flip 30 coins, and note that they will not come up all heads (technically, there's less than a one in a billion chance). You could repeat this every day for the rest of your life, and you would almost certainly never get all heads. But if you could do this every day for a billion years, you would be virtually guaranteed of eventually getting 30 heads. So yes, over long periods of time rare events are more likely to occur than over short periods, and over a sufficiently long time rare events can be "guaranteed" to happen.

[gore3000]

There is no common sense involved in making up a story about how things happened,

Okay, the genetic code of the smallest bacteria has more 'letters' than a Shakespeare play. How long do you figure it would take a monkey to type Hamlet?

[kinsman redeemer]

virtually guaranteed

Ignorance.

[Frumious Bandersnatch]

I can flip a coin any amount of times you want and can guarantee with an extremely high degree of accuracy which side it lands on.  It's a simple parlor trick.  In fact, I can, flip a quarter in my hand, and without looking at pretty much guarantee that whatever side you call, the other side will show up.