Simple solution using CTE, MIN, DATEDIFF
Code
# Code\n```mysql []\nWITH game_analysis As (\n    SELECT player_id, MIN(event_date) AS first_login\n    FROM Activity\n    GROUP BY player_id\n)\nSELECT \n    ROUND(\n        SUM(DATEDIFF(a.event_date, ga.first_login) = 1) / COUNT(DISTINCT a.player_id), 2\n        ) AS fraction\nFROM Activity a\nJOIN game_analysis ga USING (player_id);\n```
['MySQL']