Andrew Muir started seriously playing chess while studying at the
University of Glasgow (1975–1979). He won the British Student Chess Championships in 1976 and was the best in Scottish Student Chess Championships in next year. Andrew Muir also won the International Chess Tournament Scottish Open in 1977, and in 1979 in
Manchester won the International Chess Tournament Manchester Open. He was winner of the Glasgow Open International Chess Tournaments Glasgow Open (1982, 1984, 1991, 1995, 2008). In 2007, Andrew Muir became the winner of the
Scottish Chess Championship. In 1990, he was awarded the FIDE International Master (IM) title.
In 1979, at reserve board in the 23rd Clare Benedict Chess Cup in
Cleveland (+2, =0, -2).
Andrew Muir active participated in correspondence chess tournaments between 1982 and 1995. In 1995, he was awarded the International Correspondence Chess Grandmaster (GMC) title.[6]
In recent years, Andrew Muir has devoted much of his time to his
actuary work and less frequently participates in chess tournaments.