The maximum number of points that a player can score in one game of basketball is theoretically infinite since there is no cap on points. However, in practical terms, individual players often score between 20 and 60 points in a game. For instance, the current NBA record for the most points scored by a player in a single game is held by Wilt Chamberlain, who scored 100 points in 1962. However, it’s worth noting that achieving such extreme scores is rare and usually involves exceptional individual performances.