What is the logic behind prayer?

[Astrid]

It really depends on who you're asking. Some people pray to feel connected to a higher power. Some people pray to attempt to change a situation that is out of their control. And some people pray for show.
The philosophy behind prayer in the Judeo-Christian, American context has been marred by the popular culture of "what I want is right, all pain is bad" and the fallacy of the prosperity gospel.
Prayer is meant to be a conversation between you and the divine. Prayer can be supplication, as you see constantly on facebook (i.e. "i have a job interview/big test/date/surgery/etc tomorrow. Pray it goes well!"), but when prayer is ONLY attempting to turn one's situation to outcomes that boost the social standing and ease of one's life, the point is missed.
Prayer is talking to God. It can be yelling or thankful or pleading or questioning or conversational. There is a large debate between free-will and predestination (feel free to look that up if you want...it's much to complicated to answer here), but if we take the concept of free-will then you are correct: we make our choices and deal with the positive or negative consequences of those decisions. That does not cut out the possibility of God intervening should we make the decision to pray for a certain situation. While everything may have meaning if we take the time to determine what the event brought to us, that does not mean that everything that happens was for good.
If you are truly curious about these sorts of questions, I would suggest either taking a few religious studies courses or speaking with pastors/priests/rabbis/seminarians/yogis/etc. You will probably get a better understanding or at least have a real conversation where you can come to your own conclusions.