Abbott was born in St. Louis, Missouri, and attended St. Louis Country Day School. Abbott went to Yale for two years, then attended the University of Colorado for another two, but never graduated. Soon after, Abbott moved to New York, where he and his games were discovered by Martin Gardner. In 1963, after Abbott's book, "Abbott's New Card Games", received only moderate success, he "got tired of being poor" and moved back to St. Louis. There, he became a computer programmer at the Washington University Computer Research Laboratory. In 1965, he moved back to New York, where he continued to work as a computer programmer, mostly with the IBM 360 assembly language.