Platonov first made a significant mark in competitive chess in 1958, when at age 24 he posted an even score of 6½/13 in the Kiev Championship to tie 8th-9th places; the winner was Yuri Nikolaevsky.
At the 1964 Trade Union Championship in Moscow, there were nine players who eventually became grandmasters in the field, and Platonov scored 9/15 for a share of 3rd-4th place, as the winner was World Champion Tigran Petrosian.
Platonov made his career best score in a Soviet final in the 1969 Zonal at Moscow (URS-ch37), where he finished with 12.5/22, to tie for 7th-9th places; the winners were Petrosian and Polugaevsky.
He got his first international tournament opportunity at Wijk aan Zee 1970, but finished 5.5/15 for a tied 12th-13th place, as Mark Taimanov won.
Platonov's next international chance was the José Raúl Capablanca Memorial at Cienfuegos 1972, where he had one of his best career results, placing second with 13/19, behind only Anatoly Lein.
[3] After that, he appeared less frequently in top events, his results declined, and he did not manage to make another Soviet final, despite several attempts.
Platonov scored wins over top Soviet players[4] such as Mikhail Tal, Vasily Smyslov, Efim Geller, Leonid Stein, Vladimir Savon, Ratmir Kholmov, and Evgeni Vasiukov.