Some people think that if prayer does not sway God then it has no value and thus prayer must have swaying power over God. I would like to argue against this. I think the bible clearly teaches that God is sovereign (in charge of all things and thus he is not swayed, but you will have to decide what it says for yourself. I will just address the philosophical objection.) If we come to God as empty vessels then prayer is like stooping down with great thirst to drink of the joy the flows from God then it is of great value. For when we come to God empty we display Gods great worth. We thus glorify God by our dependence and are thus fulfilling our purpose.
The bible clearly teaches that the Lord smiling on us is better than any earthly treasure. And God clearly smiles on the humble who rely on coming to him empty handed. He does not smile on arrogance that believes it can force his hand and make him into a puppet if we merely had enough faith to sway him as they wish. We are like children who trust our father to help us in times of trouble. Children do not glorify their father by coming to them demanding that something be done to make them happy. They glorify their fathers by trusting in him when they are weak. Their father’s assurances that he gives to them strengthen their children’s trust and make them more willing to obey when their father commands them.
Since we are not trying to sway God we must remember that all prayer is to glorify God. Thus all pray is about asking God to do what is just and praising him for his excellences and great goodness to us. One never does not have opportunity to praise God. We deserve eternal hell and God has set himself and the whole creation to be our inheritance. The gift is so immense that in any physical or emotional agony we may endure we still would be right to praise God for the brilliance of the blessings that he has bestowed upon us. And how gracious he is to us and how much better he is being to us now then what we deserve.
Prayer also keeps our eyes on God. As such it is of great value. We tend to take our eyes off God. Sin makes us wish to take our eyes of God. To deceive us into wasting our lives on trivial, petty, insignificant things instead of the all encompassing glory and beauty and significance that can be found in God. As such it has great value.