Enevoldsen won the Danish Chess Championship five times (1940, 1943, 1947, 1948, and 1960). In 1939 he shared first but lost a playoff, and in 1950 he again shared first but lost a lottery.[2]
In a 1933 tournament in Copenhagen, the little known Enevoldsen defeats Aron Nimzowitsch, one of the world's leading players, with an overwhelming king's side attack featuring a rare double knight sacrifice.[6]
Enevoldsen relates that he and Nimzowitsch subsequently became good friends, Nimzowitsch describing him as "the hope of Danish chess". At his request, Enevoldsen was buried alongside Nimzowitsch in Bispebjerg cemetery, Copenhagen.[7]
Enevoldsen authored several chess books in Danish, as well as one book on bridge.
Skak for Viderekomne : det positionelle Angreb [Chess for Advanced Players : The Positional Attack]. Jespersen og Pio. 1940. OCLC468211487.
Lærebog i skak : begyndelsesgrundene, Bind 1: Aabningsspillet [Chess Textbook : First Principles, Volume 1: The Opening Game]. Jespersen og Pio. 1941. OCLC769951094.
Lærebog i skak : begyndelsesgrundene, Bind 2: Midtspillet [Chess Textbook : First Principles, Volume 2: The Middle Game]. Jespersen og Pio. 1943. OCLC774468993.
Lærebog i skak : begyndelsesgrundene, Bind 3:1: Slutspillet [Chess Textbook : First Principles, Volume 3.1: The Endgame]. Jespersen og Pio. 1943. OCLC873291487.
Lærebog i skak : begyndelsesgrundene, Bind 3:2: Slutspillet [Chess Textbook : First Principles, Volume 3.2: The Endgame]. Jespersen og Pio. 1944. OCLC873291499.
Hvermands skakbog [Everyman's Chess Book]. Jespersen og Pio. 1945. OCLC64889433.
Lærebog i skak : begyndelsesgrundene, Bind 3:3: Slutspillet [Chess Textbook : First Principles, Volume 3.3: The Endgame]. Jespersen og Pio. 1949. OCLC873291488.
Tredive år ved skakbrættet [Thirty Years at the Chessboard]. Jespersen og Pio. 1952. OCLC2903985.
Åbningsspillet i skak [Opening Games in Chess]. Dansk Skakforlag. 1961. OCLC469749126.
Tårnslutspillet i skak [Rook Endgames in Chess]. J. Fr. Clausen. 1964. OCLC486140646.
De første trin i skak [The First Step in Chess]. J. Fr. Clausen. 1965. OCLC466922441.
Bondeslutspillet i skak [Pawn Endgames in Chess]. J. Fr. Clausen. 1966. OCLC6985747.
Hyg Dem med skak [Fun with Chess]. Obelisk. 1966. OCLC463514339.
Verdens bedste skak, 1: Romantikken og modernismen [The World's Best Chess, 1:Romanticism and Modernism]. Politiken. 1966. OCLC873099224.
Verdens bedste skak, 2: Hypermodernismen og Capablanca-Aljechin perioden [The World's Best Chess, 2: Hypermodernism and the Capablanca-Alekhine period]. Politiken. 1968. OCLC873099231.
Bobby Fischers vej til VM [Bobby Fischer's Road to the World Championship]. Bramsen & Hjort. 1972. ISBN87-7300-011-6.