Does prayer change anything? If so, why so selectivly and sporadically?

Yes, there are seemingly "miraculous" events. But they happen at the same rate among Christians, Muslims, Buddhists, atheists, and all other groups. What evidence is there that prayer has any effect on the outcome of anything? Does God intervene and do good things due to prayer requests? But step aside and refuse to intervene, allowing evil to occur, if not enough people pray? If God does intervene, why is it so sporadic? So rare (hence the meaning of miracle). I hear people find their lost keys and call it a day"God-thing". Meanwhile, God ignores the pleas of child dying of cancer. I've heard it said that God has a plan. What kind of God would create a "plan: that includes killing children with cancer? And why would God call up to heath people, help people, feed and clothe and shelter people, plus promise to answer our prayers for those people... when all along he is undermining our efforts to achieve some grand "plan" that requires killing children? Is it really true that Gods "plan" justifies the suffering of his own children? Does God law say the end justifies the means? Even when the means is killing children?