Jucker was born in Norwood, Ohio. He attended the University of Cincinnati as an undergraduate student and played on the school's basketball teams during the 1938, 1939, and 1940 seasons. He was the captain of the 1940 team. Also, while an undergraduate, Jucker became a member of the Alpha Tau Omega fraternity. Jucker was a professional baseball prospect until he decided to start coaching instead of trying to make it into Major League Baseball. His coaching career began at Batavia High in Clermont County, Ohio, east of Cincinnati. Following service in the Navy during World War II, he joined the college coaching ranks as assistant basketball coach at the United States Merchant Marine Academy in 1946. Two years later, he became head basketball coach at Rensselaer Polytechnic Institute. Jucker returned to the University of Cincinnati in 1953 as assistant basketball coach and baseball mentor. He directed the UC freshmen to a 67–21 record in six years, while his baseball teams were 87–38 over seven seasons. In 1954, Jucker recruited Sandy Koufax at Cincinnati. After watching Koufax in his first practice, Jucker got him a work-study scholarship. Under Jucker's coaching direction in the early 60s, Cincinnati won back-to-back NCAA Basketball Tournament, in 1961 and 1962, defeating Ohio State, who had the great Jerry Lucas and Bob Knight, both years. His 1963 team reached the championship game of the NCAA tournament, where the Bearcats were upended 60–58 in overtime by Loyola of Chicago and All-American Jerry Harkness. Jucker holds the record for the highest winning percentage in NCAA tournament play. In his five seasons coaching the Bearcats, Jucker's team posted a record of 113–28, a.801 winning percentage. Jucker left coaching at UC after the 1965 season. In 1966 he remained at the university as the Intramural Director and spent the summer in Spain coaching their national team. He agreed to coach Spanish national team from 1967 but changed his mind when he received offers from the National Basketball Association. In 1967, he became the head coach of the Cincinnati Royals of the National Basketball Association, a position he held for two seasons. Jucker then went to Rollins College in Winter Park, Florida where he built the school's basketball program into a national contender in NCAA Division II. In 1978, he was inducted into the University of Cincinnati Athletics Hall of Fame. Also, the court that the University of Cincinnati plays on is named after Jucker. The number he wore as Cincinnati baseball coach is one of only two numbers retired by the school's baseball team. Jucker died of prostate cancer on Callawassie Island, South Carolina in 2002 at age 85. He was survived by his wife, Joanne. In 2014, he was inducted into the Ohio Basketball Hall of Fame.