By the late 1960s, Balukas was playing in exhibition matches with top male players. For example, she played with Willie Mosconi and Irving Crane who were together considered between 1941 and 1956 the "best in the world, flat out". In 1975, she again played Willie Mosconi on CBS's "Challenge of the Sexes", playing in games of eight-ball and nine-ball. For the exhibition, the rules were changed to allow Balukas to have an advantage (a practice called "handicapping"). Specifically, Balukas always took the first shot. Then, she also took the next shot, even if she did not put a ball in a pocket on the first shot. Balukas beat Mosconi at both games. She would later play "Battle of the Sexes" matches on television with Rudolph Wanderone (also known as Minnesota Fats) in 1977, Ray Martin in 1979, and with Steve Mizerak in 1986.
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