Most people's minds are sponge that absorb whatever bombards it the most. This is why commercials work. This is how culture works. People tell each other what they believe and whatever message is most repeated becomes dominant. Note that reason has almost nothing to do with what most people believe.
Prayer is just auto-persuasion through repetition. If your prayer is "I like peanut butter" and you repeat this often enough, then your consumption of peanut butter will likely increase. Prayer can influence behavior.
I now understand why no religion can survive in the modern world without prayer. Without prayer, all that you are bombarded with are the messages of modern culture. Prayer offers an antidote, a brief but intense bombardment by a contrary message that supports the religion against modern culture.
For a prayer to work, it must be fully understood by the person who is praying. Repeating a prayer mindlessly without understanding has no impact.
With this in mind, I did a purely secular translation of my prayer. The main difference was replacing "Yehovah" with "Reality" to make it absolutely clear what this is all about.