Turover settled in the Washington area and had a very successful lumber business. He married Bessie Levin and had three daughters: Sylvia, Naomi and Ruth. Turover became a director of the American Chess Foundation. He is also known as a chess patron and philanthropist. He sponsored Bobby Fischer's attendance in the 1962 Stockholm Interzonal. Throughout his life he offered cash prizes and other good for brilliancies in chess games. For instance, in 1930, Turover gave a 500-lire brilliancy prize at the tournament in San Remo. Many years later, in 1973, Turover awarded David Bronstein two magnum bottles of the finest French champagne for a brilliancy in a game against Ljubomir Ljuboevic. In 1974 he established the annual World Brilliancy Prize; the first winner was Michael Stean, who received $1,000 for his win against Walter Browne at the 21st Chess Olympiad in Nice.