Hello there folks!

I was in a pretty serious debate with my friend about probability:

You have 2 cards: 1 red and 1 blue.

You have 1 chance to pick blue, then you mix the cards.

It's either: you always pick blue, you pick blue n-times, you never pick blue.

Let's say that time is infinite.

How can I proove that you MUST pick blue at least once in infinite time?