The compound adjective "three-game" is a modern formation following the productive English pattern of combining a number with a noun to create a descriptive term. The first element, "three," traces its lineage back to the Proto-Indo-European root trei-, a fundamental numeral that evolved into terms for "three" across Indo-European languages. The second element, "game," originates from a Germanic root connoting joy and communal amusement, which narrowed in meaning to signify a contest with rules. The logic of the compound is transparently numerical and categorical, directly specifying a series comprising exactly three contests, commonly used in the context of sports playoffs or match sets.

Structure: three (number) + game (contest) - three: From Old English þrīe, þrēo, from Proto-Germanic þrīz, from Proto-Indo-European tréyes. Functions as a numerical quantifier. - game: From Old English gamen ("sport, fun, amusement"), from Proto-Germanic gamanan ("pleasure, participation"). Functions as the core noun denoting a structured contest or activity.