During the early decades of the 20th century, female chess players were a rarity and Sonja Graf basked in the popularity and attention her sudden fame brought her as much as she exploited the freedom and independence of her new itinerant lifestyle. In 1934, she played against the era's other woman champion, Vera Menchik, in an unofficial match in Amsterdam and, subsequently, in an official 1937 world championship match in Semmering, Austria. She lost both matches (by the scores of 1–3 and 4½–11½), but was invited, along with Menchik, to participate in what would normally have been an exclusive male tournament held that year in Prague. She did not win against any of the champions, and her best result was a draw with the Estonian master Paul Keres.