Some freewill theists contend that Calvinism renders prayer otiose. I've discussed that before. It confuses predestination with que sera sera fatalism.
More interesting is whether the objection can be turned around. If freewill theism is true, how often can God answer prayer?
According to one plank of the freewill defense, in order to make rational, responsible choices, our choices must have predictable consequences. The foreseeable outcome of a given choice figures in our deliberations. And that in turn requires a world with a high degree of uniformity. If God were to intervene on a regular basis, it would destabilize the natural order. Because our choices would not have predictable consequences, that would rob us of significant freedom.
Given that framework, does it not pose a severe restriction on God vis-a-vis petitionary prayer? God is not at liberty to frequently answer our prayers, for that would destabilize the uniformity of nature, which is a necessary backdrop for exercising our libertarian freedom. Hence, God could only answer prayer on rare occasion.
That raises the question of how often Christians pray. According to one survey, 68% of Christians pray more than once a day while 16% pray once a day, and 12% pray a few times a week.
Suppose we confine the issue to petitionary prayer. Suppose devout Christians pray 3 times a week. This could be for their own needs or the needs of others. That amounts to about 156 petitionary prayers a year. Suppose a Christian prays for 60 years. That totals 9360 petitionary prayers.
Obviously, the figure is variable from one Christian to the next. Some may pray more often. Some may live longer.
But given the constraints of freewill theism, it would seem that God can only answer an infinitesimal fraction of those prayers. Not only is there the direct effect of divine intervention in case of each answered prayer, but an answered prayer is an event, and most events have a ripple effect or even a snowball effect. A cause produces an effect. And the effect may, in turn, cause another effect. To take a comparison, if a couple has 4 kids, and each of their kids has 4 kids, and so on, the end-result is exponential. Like wave interference, the repercussions of answering one prayer must die down before answering another lest they cancel each other out.
(In Calvinism you don't have the same problem because God is in a position to control and coordinate the variables. God wrote the whole plot.)
And, of course, that's vastly multiplied by hundreds of millions of Christians each praying 3 times a week (or whatever). If God answered prayer on anything like a regular basis, the number of divine interventions–not to mention the domino effect–would be staggering.
If freewill theism is true, then it seems that petitionary prayer is almost always futile. God dare not intercede except on rare occasion. Most of the time we pray in vain–if freewill theism is true.