How the rollout math works
Apple's seven phases are 1%, 2%, 5%, 10%, 20%, 50%, 100%. These are cumulative: on day 3, 5% of eligible users in total can get the update, not 5% more on top of days 1 and 2.
- Cumulative eligible users
- round(eligible base x cumulative %)
- Newly eligible users
- today's cumulative - yesterday's cumulative
For 10,000 eligible users the cumulative counts are 100, 200, 500, 1,000, 2,000, 5,000, and 10,000, so the newly eligible counts are 100, 100, 300, 500, 1,000, 3,000, and 5,000. Half of the base becomes eligible on day 7 alone.