expression, godan verb (-tsu)
play go
The standard expression for playing the board game Go. 碁 is the game, and 打つ is the verb used specifically for playing Go (and some other board games like shogi).
週末はよく父と碁を打つ。
I often play go with my father on weekends.
彼は碁を打つのがとても上手だ。
He is very good at playing go.
将棋 (shogi) uses the verb 指す, while 碁 (go) uses 打つ. Both mean 'to play', but the verb choice is fixed by the game.
The verb 打つ (to hit, to strike) is used idiomatically for playing Go, possibly from the action of placing stones on the board. The exact origin is uncertain.