What good is it??? What good is it to consider coincidences? What good is it to "disbelieve", which I take to exhibit a healthy skepticism?
How about doing something that will actually work rather than wasting our time doing something that is basically useless?
And notice how the questioner worded the problem? She is only concerned about the positive outcomes, not about all the negative outcomes that one has to go through to get there. Even if we suppose that prayer actually worked sometimes, don't you think we'd be better off trying something that stood a better chance of success first?
Of course, this is classic. And an interesting animal behaviour problem. A quick Google search of "random reinforcement" yields a number of interesting results. It highlights the fact that superstitious behaviour can be manifested even in rodents simply by reinforcing desired behaviour in a random (and infrequent) fashion. Indeed, these experiments can lead laboratory animals to do some truly strange behaviours. And we have similar problems with prayer. Once one prays--or does any other particular behaviour like carrying a rabbits foot or not taking a shower--and it ever seems to "work" even once, then one is going to keep doing it in the hope that one'll be able to find some combination of behaviours that will guarantee the desired outcome. But since the behaviours and the reinforcement are essentially random, it's all really meaningless. And it's the same reason why baseball players are so superstititious, because it's more likely that'll they get an out than a hit, so they are set up exactly into this kind of pattern of random reinforcement. And not changing your socks for three weeks, an objective person can tell, is not going to make anyone a better hitter.
If we can't examine prayer for coincidence and with healthy skepticism, we end up wasting our time and fall into the mindset where we will waste more and more time as time goes on trying to makes sense out of the randomness.
And frankly, given how infrequently prayers are "answered", god either enjoys messing with people's heads, or he simply doesn't exist. Now, since we are perfectly capable of inducing this kind of behaviour in rats, our "god" could very well just be a smarter lifeform.
For my money, I'm gonna put my faith in my critical thinking and problem solving skills. And if you want to break yourself of your prayer superstition, you should either keep a log of every time you pray and the outcome (to get a good statistic on how often it really works and how long you spend doing it), or just give it up altogether!