Does prayer affect God?

Freewill theists say Calvinism nullifies prayer. If every event is predestined, what difference does prayer make? 

I've addressed that objection on multiple occasions, so I won't repeat myself here. Instead, I wish to examine the alternative. The freewill theist believes that for prayer to make a difference, it must affect God. Prayer is not, in the first instance, about changing the future, but changing God's mind. The most consistent version is open theism. On this view, God is making things up on the fly. When we pray to God, he exclaims: "That's a great idea! Why didn't I think of that! I was planning to do something else, but you've give me reason to reconsider my contemplated course of action."

Other freewill theists aren't that crass, yet their own position is implicitly the same. How could our prayers affect God unless God had something else in mind, but once we pray to him, he revises his plans because we gave him a better idea. How could prayer influence God unless we can improve on God's original intentions? 

Moreover, we could recast this in terms of foreknowledge or middle knowledge. Even if God doesn't change his mind, God chooses this particular course of action because he had the benefit of our advice. Left to his own devices, God would act less wisely or justly.