If there is one thing that people should know does not work, it is prayer. Religious people pray for things all the time and they almost never get what they ask for. Even members of Congress hold prayer sessions to drive Satan out of power in the Capitol, though the best way to have that prayer answered would be if they just left the building instead.

So why do people keep doing it? Valerie Talerico has a four part series on prayer and part 2 looks at why people persist.

[H]umankind has outgrown countless superstitious beliefs that our ancestors treated as knowledge. We have discarded thousands of rituals for currying supernatural favor and talismans for warding off harms, each of which failed to precisely the same degree as prayer requests.

So why is it that intelligent, compassionate educated adults—folks who would laugh if you suggested they carry a lucky rabbit’s foot or sacrifice a small goat or cross the street to avoid a black cat—still pray?
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One of our mental super-powers is that we can represent other minds as “introjects” within our own, creating virtual copies of other people that allow us to anticipate their thoughts and preferences, and to act accordingly. If I want to know whether my husband will like an anniversary present, I can call up my virtual Brian script, run the possibilities, and make some good guesses.

Our capacity to represent other human minds within our own also lets us create imaginary beings.
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Prayer makes sense when we understand that humanity’s multi-millennial interest in supernatural beings and powers is actually a means to an end. As humans, a huge part of our energy goes into trying to figure out the cause and effect relationships that govern our lives and wellbeing. To that end, the gods that interest us are gods who care how we think and feel and behave—because otherwise we have no way to manipulate what they do. Our interest in God is not actually about God, per se; it is about us.

But it may also be that in the minds of believers, they think that prayer actually works. It may be a matter of simple statistics. If one prays a lot, then purely by chance one might experience something random that looks remotely like the answer to a prayer. It is like those small lottery winnings that regular players get that keep them hooked to the habit even though the prize is too small to be life changing for them.

I discussed the role of large number statistics in this post from 2013 about preachers with huge followings in Africa who promise miracles to their congregations, if they donate money of course. These preachers say that miracles do seem to occur regularly, strengthening the faith of their followers.

So let us say that the 500,000 people come to church and pray for something special. Let us assume that it is for something like getting a job or passing an exam or getting some sorely needed money or recovering from some illness or finding love or resolving some personal conflict in their lives. Suppose the probability of that happening purely by chance within a week of praying at one of these services is 0.001% (or one chance in 100,000). This is rare enough that if it happens, a gullible religious person would likely consider it a miracle, a direct response to prayer.

What are the chances that at least one person in the congregation will experience such a miracle? It is not a hard calculation. There is a 99.999% chance (probability 0.99999) that for any given person nothing will happen in response to their prayers within the next week. However the probability that nothing will happen for all the half million people is 0.99999^500,000. This number is actually very small, equal to 0.0067. In other words, the chance of no miracles happening to anyone in the congregation is only about 0.67%, or alternatively there is over 99% chance that there will be at least one miracle the following week. In fact, there is a good chance that several such miracles will occur.

Given that people who experience such an event are likely to be overflowing with gratitude (“It’s a miracle! Praise the Lord!”) and broadcast their good fortune far and wide, stories of such miracles will spread like wildfire. No wonder people believe that these mega-preachers can deliver the goods. In fact, once the size of your following gets large enough, you are assured of such miracles routinely occurring, which explains the success of televangelists who confidently promise that good things will happen to those viewers who give money to them, and can truthfully tell stories of people whose prayers were answered thanks to their intervention.

Thus thanks to the general ignorance of probability, anyone can become a miracle worker. All you have to do is plant the seeds of belief in enough people to enable you to take credit for random chance events.

This woman who eats pounds of goldfish crackers each week and who says that she discovered a sign from her god on one of them would have benefited from this knowledge of probability.

If you eat a lot of those crackers after examining each one carefully, at some point you are likely to stumble upon an unusual one that, if you are prone to see such things, is likely to seem miraculous. It was amusing to see her pastor trying to avoid claiming too much for such a trivial thing while not wanting to dismiss the idea of a miracle either.