His first meaningful chess moves were played at the Sverdlovsk Palace of Pioneers, one of many training schools for talented young players in Soviet Russia.
In 1974, Rashkovsky took part in the team championship of the Spartak Sports Society and along with Albert Kapengut, recorded the tournament's top individual performance, with a score of 5½/7.
Curiously, the full results were censored by the authorities and remained so for many years, because both players had finished ahead of Tigran Petrosian and it was not thought to be in the national interest to disclose even this relatively minor failing of the ex-World Champion.
He was also crowned European Senior Champion in 2007, at Hockenheim, finishing level on points with Algimantas Butnorius but winning on tie-break (ahead of Mark Tseitlin and Wolfgang Uhlmann, among others).
Peter Svidler spoke with high regard of his tenure with the national team, remarking on his optimism and energy and the good spirits that surrounded the Olympiad camp.