I believe in prayer.
Prayer moves people and situations intricately and without us thoroughly understanding how that happens. But that’s ok.  But if you haven’t felt or seen the effects of prayer, then me telling you this will not change our opinion about prayer.  Even though prayer is a gift from God, still life goes on without it, so it doesn’t make much difference to many people.

Mostly people who don’t pray have an understanding that prayer should be a simple machine: pull the lever, and a pellet will come out (the prayer is pulling a lever). I’ve not experienced that.

Prayer is more complex, at least in terms of its operations. So it is once simpler but also more difficult than you would imagine. Simpler because it’s fundamentally about simple trust. And more difficult because when can we simply trust God? People are designed to orchestrate their lives. And prayer gets dragged into this.

Children pray well because they are built trusting and live dependently. When they pray it’s an expression of their lives–they have no interest in the “mechanics” of how He would work out answering prayers. This explanation does not dismiss the questions that sceptics or adult believers have about prayer’s efficacy, free will and God’s timing which really ought to be considered.

CS Lewis weighs in (from his book, Miracles):
“When we are praying about the result of… (something, say) a medical consultation the thought will often cross our minds the event is already decided one way or another. I believe this to be no good reason for ceasing (to) pray. The event certainly has been decided – in a sense it was decided ‘before all ages.’    But one of the things taken into account in deciding it, and therefore one of the things that really cause it to happen, may be this very prayer that we offer. Thus, shocking as it may sound, I conclude we can at noon become part causes of an event occurring at ten o’clock. The imagination will, no doubt, play all sorts of tricks on us at this point. It will ask, ‘Then if I stop praying can God go back and alter what has already happened?’ No. The event has already happened and one of its causes has been the fact that you are asking such questions instead of praying. It will ask, ‘Then if I being to pray can God go back and alter was has already happened?’ No. The event has already happened and one of its causes is your present prayer. Thus something does really depend on my choice. My free act contributes to cosmic shape. That contribution is made in eternity ‘before all worlds’ [ages]; but my consciousness of contributing reaches me at a particular point in the time series.”