He graduated from Stuyvesant High School and studied mathematics at City College of New York, where he discovered bridge.
He wrote several books on the game, and invented various bidding conventions that have become commonplace, including five-card majors, negative doubles, forcing notrump, and the unusual notrump. Roth then took a job as a government statistician in Washington, D.C. He played for the United States or North America in the Bermuda Bowl world team championships of 1955, 1958, and 1967, losing the final each time. Roth was a Grand Life Master of the American Contract Bridge League, and a World Life Master of the World Bridge Federation.
After attending a bridge tournament in Miami Beach, Roth moved there and ran a bridge club for five years. Then he founded the Charles Goren School of Bridge in Washington and ran it for ten years. Roth then purchased the Mayfair Club in New York, which he managed until retiring to Florida in 1995.
Roth married twice, first to Fay Edelstein in 1940. They had a son, but were divorced in 1963, and she died in 1995. Roth died of natural causes in Boca Raton.
Honors Wins Runners-up Bermuda Bowl (3) 1955, 1958, 1967 World Open Team Olympiad (1) 1968 Olympiad Mixed Teams (1) 1972 North American Bridge Championships (23) Vanderbilt (2) 1953, 1975 Spingold (4) 1943, 1945, 1953, 1961 Chicago (now Reisinger) (2) 1937, 1954 Reisinger (1) 1966 Men's Board-a-Match Teams (4) 1952, 1957, 1973, 1977 Master Mixed Teams (5) 1945, 1963, 1966, 1973, 1975 Life Master Pairs (1) 1965 Fall National Open Pairs (1) 1958 Open Pairs (2) 1958, 1966 Master Individual (1) 1955 United States Bridge Championships (1) Open Pair Trials (1) 1967.
ACBL Hall of Fame, 1995Fishbein Trophy 1963, 1965, 1966Herman Trophy 1952North American Bridge Championships (30)Vanderbilt (3) 1943, 1963, 1968Spingold (6) 1940, 1956, 1957, 1963, 1966, 1967Chicago (now Reisinger) (3) 1946, 1952, 1961Reisinger (1) 1967Men's Board-a-Match Teams (4) 1955, 1961, 1969, 1971Master Mixed Teams (4) 1952, 1953, 1955, 1965Life Master Pairs (3) 1956, 1971, 1972Fall National Open Pairs (1) 1942Open Pairs (1) 1960Rockwell Mixed Pairs (2) 1946, 1952Hilliard Mixed Pairs (1) 1959Master Individual (1) 1943.