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Magi compose a very small percentage of the population. It is unclear how this ability to control magic is passed on, but it is more common for the children of magi to inherit it. Regular humans can also have a magi child, it is just slightly more rare.
Most magi are not very powerful. They can make small things happen and enchant things in uncomplicated ways, like making something completely water-resistant, or making your house the perfect temperature all the time, or occasionally talking to animals. Magi also specialize in different things, some more powerful than others.
Every now and then, however, a very powerful magi is born. Most come from long lines of magi or, oddly enough, a magi mother and a normal father. These have the capabilities to become very dangerous if not taught properly, but more often than not, they put their abilities to good use.
Magi are always welcome in towns, but most don't settle down until they're older, around their hundreds. (Magi age differently than humans, at 1/4th of the speed. When they are two hundred years old, they appear to be fifty.) Often, while traveling, they'll go to a town with a magi child and take them as an apprentice, teaching them all they know until the child turns about seventy (and appears between fifteen and twenty).