Depending on your state (the state that has issued your current, valid driver's license), reckless driving will carry a differing number of points. In fact, certain states do not adhere to a points system for traffic violations at all, although the vast majorities do. In general, reckless driving will carry a point total sufficient to impose administrative action on one's license for the single violation itself. In other words, upon conviction of the reckless driving offense, a driver will face administrative license suspension regardless of whether his license currently has other points applied or not.
In fact, many to most states treat reckless driving citations as criminal offenses, even in light of traffic violations laws, which can also carry penalties of incarceration, large fines, and of course, the administrative license suspension. In a limited number of scenarios, traffic violations for reckless driving will not carry sufficient points for automatic license suspension based on points, but from a criminal perspective, can carry punishments involving administrative license suspension.
In reality, the only reliable method of determining how many points your reckless driving offense will carry is to consult with your state's drivers manual. It is notable, however, that reckless driving often is a single offense with significant penalties, and in turn, traffic courts may promote the opportunity for a driver to participate in driver education courses or other alternative sentences (which ultimately reduce or dismiss the reckless driving citation, thus allowing a driver to retain his license). However, obtaining these benefits is not guaranteed, and in turn, consulting with a traffic violations lawyer is always in the best interest of a driver.