Unlike its English sense of a boat rowed by three people, ‘randan’ in Scots has a quite different meaning: some kind of spree or, most commonly, a drinking binge.
Usually the drinker ‘goes on the randan’, or is ‘out on the randan’.
So if you wanted to invite your acquiantances out for a particularly raucous night that is sure to lead to dizzying levels of inebriation, you could ask them: “Gawn oot oan the randan the nite?”
In more recent popular culture, there is an Edinburgh art-rock band called Randan Discotheque.
It’s not to be confused with the town of Randan in the Puy-de-Dome region of France.
See also: ‘bevvy session’