 In 1950 Sprague received a PhD under Alexander Dinghas at the Freie Universität Berlin with dissertation "Über die eindeutige Bestimmbarkeit der Elemente einer endlichen Menge durch zweifache Einteilung".At the Pädagogische Hochschule Berlin, Sprague was from 1949 Dozent, from 1953 Oberstudienrat (senior teacher at a secondary school), and from 1955 Professor.Sprague is known for his contributions to recreational mathematics, especially the Sprague–Grundy function and its application to combinatorial games, which Sprague and Patrick Michael Grundy discovered independently in 1935 and 1939 respectively.