Her father was a surgeon and was reported to be fairly strong although he never played tournament chess. He taught his oldest daughters to play and they in turn taught Mary. Even though she was a prominent lady player of her day, she lived a life of poverty and died almost forgotten.
Dr. Rudge died when Mary was 32 years old and she and her sister, both unmarried, went to live with their brother, also unmarried, who served as a curate (a member of the clergy who served as an assistant to a vicar), in Bristol.
After death of her father, Dr. Henry Rudge, she moved to Bristol where she started playing chess seriously. She began playing chess in a correspondence tournament in 1872. The first mention of her in over the board competition was in August 1874 when she played in the second class at the Meeting of the Counties’ Chess Association in Birmingham. According to the Edo rating her highest rating was 2146 in 1883.
Rudge was the first woman to become a member of the Bristol Chess Club which did not allow women to join until 1872 and played board 6 for them in several matches.
By 1889 she was in dire financial straits and gave consent for the club to make a financial appeal on her behalf. As a result, she was befriended by Frideswide Rowland and her husband, Thomas, who was a chess journalist. Mary started alternating between living in Bristol and Ireland. 1889, possibly inspired by Mrs. Rowland, she composed and published a chess problem in the Clontarf Parochial Magazine and gave a simultaneous display, winning all six games. The result was she was soon being hailed as the best female player in the world.
She was a winner of the first Women’s International Chess Congress, under the management of the Ladies' Chess Club of London in conjunction with the Women's Chess Club of New York.
The tournament was played at the Hotel Cecil, in the Masonic Hall, for six days, but the final rounds were decided at the Ideal Cafe, the headquarters of the Ladies' Chess Club in 1897. Her play was described as steady and tenacious and it was said she didn't seem to care so much about how to win, but rather how to make her opponent lose. She never took risks and never indulged in fireworks. Her preferred style was to win a Pawn or get a grip on the position then grind out the win. Rudge was 55 years-old and the oldest of the 20 players and had substantial experience playing chess at the time. She won the event with an overwhelming 18 wins and 1 draw.
Over the next years, she took part in various competitions, playing in Bristol and Dublin. In 1875 she lost a simultaneous exhibition game against Blackburne and in 1876 she was defeated by Zukertort in simul, but in 1898 she played against world champion Emanuel Lasker in a simultaneous display. Lasker was unable to finish all the games in the time available and Mary’s was one of those unfinished. He conceded defeat because he would be lost against best play.
The mid-to-late 1890s saw her health deteriorate and in 1900 her sister died leaving her on her own. In 1912 there was another appeal for funds. The Cork Weekly News published the following announcement by Mrs. Rowland:
Miss Mary Rudge is the daughter of the late Dr Rudge, and after his death she resided with her brother, who kept a school, but since his decease she is quite unprovided for, her sisters are also dead, and she is without any income of any kind. She lived as companion with various ladies, and was for some years resident with Mrs Rowland, both at Clontarf and Kingstown. Whilst at Clontarf, she played in the Clontarf team in the Armstrong Cup matches, and proved a tough opponent, drawing with J. Howard Parnell and winning many a fine game. She was also engaged at the DBC to teach and play in the afternoons. At the Ladies’ International Congress, London, she took first prize (£60), making the fine score of 19½ in 20, the maximum. Miss Rudge held he Champion Cup of the Bristol Chess Club, prior to Messrs H.J. Cole and F.U. Beamish. Miss Rudge is now quite helpless from rheumatism and is seeking admission into a home or (if possible) the Dublin Hospital for Incurables. A fund is being collected for present expenses, pending her admission, and chessplayers are asked to help – either by influence or money. Donations may be sent to Mrs Rowland, 3 Loretto Terrace, Bray, Co. Wicklow, or to Mrs Talboys, 20 Southfield Park, Cotham, Bristol.
In 1918 when her cousin died without a will she claimed to be sole next of kin, but another claimed to be the grandson of her cousin's uncle and appears to have won his case and Mary got nothing.
She moved to the British Home for Incurables, Streatham and died in Guy's Hospital, London, on November 22, 1919 at the age of 77.