A run for your money

From horse racing, specifically the bettor's side of it. The OED dates the literal turf phrase 'a run for one's money' to the late 1830s, meaning a successful race from a horse one had backed, especially one that had seemed likely to be scratched; since a withdrawn horse could settle the wager without any race being run, a horse that actually started gave its backer the minimum he was entitled to - a run for his money - and a genuine contest gave him full value. The Phrase Finder reports the earliest print use as the Sporting Review of 1856 ('owners to have a run for their money, just for the luck'), via Green's Dictionary of Slang. The first recorded figurative use is Hotten's Slang Dictionary of 1874: 'To have a run for one's money is also to have a good determined struggle'. Punch carried it in 1887, the Sydney Bulletin by 1900, and Joyce's 'Ulysses' (1922) blends both senses. The two modern constructions settled by the early 20th century and have barely moved since. The anchor's horse-racing derivation and 19th-century date check out.