There’s a lot to the troika, it’s been associated with Russia for centuries. Literally means ‘a group of three’.

The configuration of two horses galloping with one horse trotting in the middle allowed for high speeds across vast distances and is commonly referenced in russian literature, particularly authors like Pushkin, Gogol, Dostoevsky, Tolstoy, etc.

It’s also pretty associated with the trinity (troitsa). Triplicity is a major feature of Russian folklore and culture in general; the three brothers, the three trials, three roads, three kisses, etc.

For revolutionaries it was the smallest organizing unit for a number of reasons and was present in both early anarchist and bolshevik cells. Some advantages were that it was agile, hard to infiltrate, and doesn’t need a leader, rather a shared direction. In many ways an anti-hierarchical organizing pattern.

In the Stalin era it got a bit more of a sinister connotation as a ‘troika’ would be the group of officials signing off on sentences.