,
Borislav Ivkov,
Andor Lilienthal and
Vasili Smyslov. With his strong result at the 1961 Soviet Championship, he earned the right to play in the 1962
Stockholm Interzonal tournament. His play there was excellent, finishing in a tie for 6th–7th places, but he was denied the right to advance to the
Candidates' Tournament, because of a FIDE rule then in force which limited the qualifiers from any one country to three (in this case USSR). He had finished behind fellow Soviets
Efim Geller, Petrosian, and
Viktor Korchnoi. Despite winning a 3-way playoff against
Pal Benko and
Svetozar Gligorić for the 6th and final spot, due to the aforementioned Soviets finishing ahead of him, Stein was denied the final spot and Benko was awarded it instead. A very similar occurrence was the story of the next Interzonal tournament, in
Amsterdam 1964. Stein took fifth place, sufficient for qualification for any non-Soviet player, with an outstanding total of 16½ / 23, but was blocked from advancement. He had finished behind fellow Soviets
Mikhail Tal,
Vasily Smyslov, and
Boris Spassky, who, along with Danish GM
Bent Larsen, had all scored 17 points. He did represent the USSR at the
Tel Aviv Olympiad that year, scoring a fine 10/13, and winning an individual gold medal on the first reserve board. Again, he was in the Soviet side at the
Havana Olympiad 1966, scoring 9/12, winning an individual silver medal on board four. Both times, the Soviet Union won the team gold medals. Again, in 1967, Stein qualified for the
Sousse Interzonal, scored well, in a tie for 6th–8th places, but had to undergo a further playoff with
Samuel Reshevsky and
Vlastimil Hort, in Los Angeles, which was won by Reshevsky. He was on the Soviet side for the
European team championships at
Hamburg 1965 and
Kapfenberg 1970, both of which were victorious. He served as an alternate on the Soviet team for the
Match of the Century against the Rest of the World team, at
Belgrade 1970. He played one game, losing to Larsen. Stein had already qualified for the 1973
Petropolis Interzonal, and was considered a potential favorite to win the entire Candidates' cycle == Death ==