Purdy only took up chess seriously at age 13 when his friends at school, not his grandfather or father, inspired him and three years later he was good enough to win the 1951 Australian Junior Championship. He was also won the Australian Championship twice. On his first attempt at age 19 he became the first teenager to become Australian champion. He then represented Australia in the 1955 World Junior Chess Championship (won by Boris Spassky).
The 1955 World Junior Championship was played in Antwerp, Belgium and consisted of 24 players. They were split into three groups of eight; the representatives of USSR, Argentina and Yugoslavia (the top three teams at the 1954 Olympiad) were seeded into separate groups, and the remainder were randomly grouped. The top three finishers of each group plus the highest scoring fourth place then went to a final ten player round robin tournament. Surprise casualties at the group stage were Purdy and and Dragoljub Ciric, a future GM, of Yugoslavia. In the final Boris Spassky gave up just two draws to score 8-1 followed by Edmar Mednis who scored 7-2, and Miguel Farre of Spain who scored 6.5-2.5. Future grandmasters Lajos Portisch of Hungary scored 5.5-3.5 and Georgi Tringov of Bulgaria scored 5-4; they finished 4th and 5th.
On his return to Australia, he became involved in chess administration and reporting about chess for The Sydney Morning Herald. In 1962-1963 Purdy won the Australian Chess Championship again and represented Australia at the South-East Asia Zone Tournament in Jakarta which was won by fellow Australian Bela Berger. He also served as President of the Australian Chess Federation in 1971–72.
Seeing how his father struggled to earn a living as a professional chess player, author and journalist he wisely studied accounting part-time, eventually qualifying as an accountant. He worked for the Printing and Allied Trades Employers' Association from 1956 to 1973.
He also took evening courses in law and after becoming an attorney he was employed by the Law Society of NSW in 1978 and eventually became chief executive officer. In 1980 he was appointed as a judge on the NSW Family Court, a position he held until his retirement in 2005. In 1984, Purdy accepted appointment to the newly created Family Court of Australia. He presided mainly at Parramatta but sat on circuit throughout the Commonwealth as a Family Court judge.
Like his father, he was known for a quality rarely seen in chess players today: his good sportsmanship and taking his losses with grace and when he won he always had a kind word for his opponent.
At one time in an attempt to improve his game, he adapted the practice of standing on his head before games. That ended after he fell over, fractured some toes and damaged furniture. Purdy married his wife, Felicity, in 1958 and they had sons, Colin and Michael. He died at age 75 while travelling to attend a funeral.