Write SQL to analyze player retention by day, cohort, and game mode.
Use each player's first valid session date as the cohort date and that session's mode as the cohort mode. Retention counts a player when they return in the same mode on a later day.
Output
- One row per observed cohort date, cohort mode, and retention day.
- Columns:
cohort_date, cohort_mode, retention_day, cohort_players, retained_players, and retention_rate_pct.
- Include retention day 0, calculate retention as a percentage rounded to two decimals, and order by cohort date, cohort mode, and retention day.