Many of us do not care about friday the 13th or serial-killers organs but as a matter of fact, our most common beliefs are not usually irrational or have nothing to do with magic or religion. In fact they are very reasonable and part of our normal functioning, let me give you two examples.
For example, when you go to mall for shopping or out at night, you have a belief that you will get back home alive. Otherwise it's like going for a suicide mission. Life would be very hard without this healthy belief.
When you are choosing a product, your lunch in a restaurant for example, you don't sample and review each meal but choose the meal according to your beliefs. Even if you know it was good last time, it doesn't actually mean it always is so it's a belief.
So is a magical belief really more useful than non-magical? Not necessarily - only if it still serves some beneficial purpose for the believer.