cock, n.⁶ — Green’s Dictionary of Slang

cock n.⁶

[? link to phr. that cock won’t fight, used of someone/something undependable]

a horse, backed as a favourite by the public, which either fails to run or, if running, fails to race hard.

1865		Sporting Gaz. (London) 8 Apr. 4/3: Cock — A horse who is not trying to win [...] a ‘stiff ’un’ .
1873		Sl. Dict.