Prayer is much more than asking for things, though that's part of it, prayer is for praising God, thanking Him and for growing in a relationship with Him. I have heard it said if your prayers only benefit you then you are not living a Christian life. Praying for others shows us that we actually care about others, we are giving part of our time to God for others. Prayer has many different benefits when it is done correctly, when it's not one shouldn't expect much.
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God loves those who believe and those who do not and the same goes for me, you have no choice in this matter. That puts the matter of total free will to rest.