Green’s Dictionary of Slang

three horses driven in tandem.

1828		High Life in London 27 Jan. 5/1: [D]andies [...] strutting about the city, or shaking the windows of Milsomstreet with tandems and randoms.
1847–81		Halliwell Dict. Archaic and Provincial Words II 666/2: randem tandem A tandem with three horses, sometimes driven by University men, and so called at Oxford.
1860		Hotten Dict. of Modern Sl. etc. (2nd edn) 198: RANDOM, three horses driven in line.
1864, 1867, 1870		Hotten Sl. Dict.
1882		Sydney Sl. Dict. (2 edn) 7: Random - Three horses driven in line.
1895		C. Crowe Aus. Sl. Dict. [as 1882].