As a bridge player, Reese won every honour in the game, including the European Championship four times (1948, 1949, 1954, 1963) and the Bermuda Bowl (effectively, the World Team Championship) in 1955—all as a member of the Great Britain open team. He was World Par champion in 1961 and placed second in both the inaugural World Team Olympiad, 1960, and the inaugural World Open Pairs, 1962. He also represented Britain in the 1965 Bermuda Bowl and in five other European Championships. He won the Gold Cup, the premier British domestic competition, on eight occasions.