I believe prayer moves people and situations more intricately than we know. I can give example after example of answered prayer. But I usually don't bother to do that, at least not in the context of talking about the efficacy of prayer. Why? Because if you've not experienced its efficacy, my talking about it will not convince you or any sceptic. My telling you that it makes a difference doesn't make it true for you for your mind has been made up about prayer. It is our our best gift from God, but life will go on without it and so it doesn't make much difference to many people.
Let's ask why this is the case. It seems to me that people don't pray much or well because they believe prayer should be a lever-push the lever and a pellet will come out, where praying is analogous to pushing the lever. Prayer is more complex than that, at least in terms of its operations. It's also simpler and more difficult than most people imagine. It's simpler because it has to do with simple trust. It's more difficult because most people would prefer to orchestrate their lives, including their prayer lives and/or are unwilling to do the actual work and responsiblity that comes as a result of answered prayer.
Children pray most efficaciously because they are most trusting and dependent faith in our Lord’s willingness to answer our prayers, and least interested 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:
“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.”
- CS Lewis, Miracles