[1] At fifteen Byvshev entered the chess section of Leningrad Pioneer Palace and after a year of training he reached the first category.
With half a point in the first five rounds, a good tournament result was hardly to be expected, but he won seven out of the next eight games and ended up sharing a decent 12th–13th place.
Among his victims was Vasily Smyslov, Paul Keres and Isaac Boleslavsky, some of the best players in chess world.
Alexander Konstantinopolsky described him as an attacking player who was extremely inventive when he showed his imagination and ability to calculate the complicated variants.
In the friendly matches of the Leningrad team versus Hungary in 1957 and Budapest in 1959, he drew two games against Győző Forintos and won a 2–2 win against Károly Honfi.