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Sunnucks represented England several times in Olympiads and team matches, including Great Britain vs. USSR 1954, the Anglo-Dutch match in 1965, and top board for the British Chess Federation (BCF) team at the 1966 Women's Chess Olympiad at Oberhausen.
His 1999 book Secrets of Modern Chess Strategy won the British Chess Federation's Book of the year award as well as the United States Chess Federation Book of the Year.