One of the most persistent, and difficult, types of arguments that atheists tend to run into is the dreaded personal anecdote. This is the story that a person of faith tells you that sums up for them why they are absolutely certain that their faith is correct. It will be a story of some incredible coincidence or miraculous recovery. It "couldn't have just happened that way." There was clearly a "greater force at work". And nothing you could ever say will convince them otherwise.
It won't help to point out that personal experience is not the same thing as observation (in the rigorous sense). No matter how many times you say, "The plural of anecdote is not data," most people don't realize a simple, fundamental fact of existence:
The least likely outcome is the one in which nothing unlikely occurs.
Think about that for a moment. I don't intend to make this a post about probability theory or anything so complex. Simply put, what the Law of Truly Large Numbers states is that any system with many outcomes will inevitably produce the unlikely (less probable) outcomes and that, more importantly, they will be noticed more because they are unusual.
As an example, consider the Jesus on a tortilla / grilled cheese sandwich / potato "miracle" that seems to occur every three years or so. The markings on these objects are essentially random. This means that there is a slim, but non-zero, possibility that these markings will resemble a face*. Say that in a year a billion tortillas are fried (the actual number is much, much higher than that. The average Mexican consumes close to 150 lbs. of corn tortilla yearly). In this scenario, assuming there's a greater than one-in-a-billion chance of a "face-like" tortilla being fried then it is statistically likely to happen. Even more, it very unlikely to not happen. Of course, because it is an unusual outcome it gets noticed more than the remaining millions of banal, faceless tortillas.
This particular failing of the human intellect happens constantly. Consider all the stories you've heard of dreams literally coming true. Your friend dreams a particular event, and then it happens! Inexplicable! Take that, science!
Well, no. Of course not. First off, your dreams have a fairly narrow set of permutative elements -- the people you know, the places you've been, and things on your mind. Therefore, your dreams must be necessarily close to your actual life -- they're populated by the same concepts. If your dreams then combine these elements in different ways (and are affected by your desires, fears, hopes for the future, etc.) then it is an inevitability that you will dream an event that will occur at a later time. There's nothing magical going on, it's just math. Looked at from the reverse, it seems obvious. How many thousands upon thousands of dreams have you had that have not come true?
Strange, coincidental, and downright spooky things have to happen. There will, inevitably, be those times when lives are saved by freak accidents. Twins will die minutes apart. Taking a detour seen in a dream will save someone's life. These are not evidence of the supernatural or the paranormal, they are just the probabilities playing out exactly as we should expect them to.
* And by "face" I mean, "maybe if I squint and assume Jesus looked like Jeff Spicoli."
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