Jim Nugent,
From an old article by Laurence Viney, co-editor of The Royal & Ancient Golf Club Golfer's Handbook:
On two occasions in the 1930's a stymie played a vital part in important Championship matches. In 1936 at Garden City, Long Island, in the U.S. Amateur final, Johnny Fischer laid Jack Maclean of Scotland a dead stymie at the 34th hole when Maclean was one up. As a result he lost at the 37th instead of a likely win at the 35th.
In the 1930 British Amateur Bob Jones beat Cyril Tolley in the fourth round at St. Andrews with the help of a stymie at the 19th. Few realize that Bob's memorable Grand Slam might not have been achieved, but for the stymie he laid Tolley.
The author goes on to say that: As the average golfer came to regard returning a good score as more important than the match, so the authorities recognized that if match play was to survive, the "unfair" nature of the stymie should no longer play a part in the game.