I don't think prayer works. We have some studies done on intercessory prayer and the results are negative.
What I see a lot is this kind of a back pedaling. When a child dies of leukemia it is part of God's plan. When a person is on time to work despite a late start then prayer works. Either way prayer works, but it depends on God's mood. What you have is this ultimately: the efficacy of prayer is indistinguishable from a world where there is no God who answers prayers as a world where this is a God who answers prayers in his own time and way.
Maybe praying gives a person a pleasant feeling. That is subjective, but who am I to begrudge a person the equivalent of rubbing a lucky rock?
No matter how you cut it, the world acts as if there isn't a prayer answering God. Positive results are often pretty far stretches to make it a positive result.
Another thing is what kinds of a prayers seem to be answered most often. Amputee children never get their prayers answered, and you'd think they were the most deserving, but Nikki here doesn't drink anymore and her husband's business is doing well. I think the working force is her desire to stay sober and her husband's busienss skill. Why did God answer Nikki's prayers, but not that of thousands upon thousands of broken children. They aren't sinners. They're just kids. It makes God look very... let's just say that omnibenevolent isn't the word I'm looking for here.