Real-time global leaderboard

Design a real-time global leaderboard for a mobile game with 80M monthly players. After every match a player's score updates, and they want to see (1) the global top 100, (2) their own rank, and (3) a small window of players ranked just above and below them, all updating within ~1 second. Scores change millions of times per minute during peak. Computing an exact rank over 80M rows on every read is far too expensive. How do you maintain ranks and serve these three queries cheaply?