But think again about times recently when you may have been grouchy or unreasonable. We do ultimately choose how to behave, but there are many influences on our moods. Maybe you did not sleep well the night before; maybe you had an upset stomach; maybe you did not know when the mechanic would finish with your car or how much it would end up costing. Such exterior circumstances have nothing to do with free will, but they can make it easier or harder to exercise your will in a good way.
I assume that the good effect of prayer is likely to be (in many cases) some change in these external circumstances. A president who is feeling too tired to deal with complaints that he has not taken action may get better rest; a combatant who feels invincible might experience a sudden reminder of his own mortality; a skillful compromise which no one had foreseen might be suggested. As the saying goes, peace would be given a chance, though that chance may always still be refused.
The other benefit, of course, is the benefit of all prayer: it reminds the one one praying that God is ultimately in charge of this as of all things.