Many times we pray to God with the hope that he answers according to what we have asked, sometimes, it happens just as we have asked, most times, it doesn't. When our prayer is not answered according to the way we asked God, we begin to question yourself if prayer really changes God's mind.
No human being has ever had a more profound understanding of divine sovereignty than Jesus. No man ever prayed more fiercely or more effectively. Even in Gethsemane, Jesus requested an option, a different way. When the request was denied, He bowed to the Father’s will.
So if you ask me whether prayer changes things, I answer with an unhesitating “Yes!”
The very reason we pray is because of God’s sovereignty, because we believe that God has it within His power to order things according to His purpose. That is what sovereignty is all about—ordering things according to God’s purpose. So then, does prayer change God’s mind? No. Does prayer change things? Yes, of course.