Scrub race

a race between scrubs, or between untrained animals or contestants.

See also: Scrub

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
References in classic literature ?
For a long time Billy Kirby would then be seen sauntering around the taverns, the rider of scrub races, the bully of cock-fights, and not infrequently the hero of such sports as the one in hand.
At Tripler, the clinic provided a luncheon for staff and mounted competitions that included teams of dentists and assistants in a three-legged scrub race, PPE exchange race and gold "chipping" contest.