In English you play a game, but you don’t play a play. In Russian the words for to play and game come from the same root: играть (to play) and игра (game). To play a game is играть в игру.

I already knew the verb играть, but didn’t know that the word for a game was similar, until today.

игра́ть means to play; to act, to perform; to gamble; (of a storm) to rage; (of wine) to sparkle. It comes from the Proto-Slavic *jьgra (play, game).

игра́ means a game; a sport which is played; play (for amusement); acting, performance; role-playing; playing (a musical instrument). [source].

Related words include:

– игра́льный = playing
– игри́вый = playful
– игри́стый = sparkling (of wine)
– игрово́й = game, play, acting, playing
– игро́к = player, gambler

Words for game are the same or similar in other Slavic languages. However they have lost the initial i in most Western Slavic languages: hra (Czech & Slovak); gra (Polish); jhra, hra (Upper Sorbian); gra, igra (Lower Sorbian) [source].