Two part question
I want to start 4,000 games of chess.
Each batch of 500 games will be started on consecutive days.
I never want to timeout and want to play the minimum number of moves per day to avoid the risk of timeout.
I want to move as late as possible in each game, and saving my timebank as much as possible unless the average moves per day exceeds 1000. If timebank is utilised then it will be one day at a time in the game it is required in.
My opponent will always move as follows
3/3 or 3/7 games – the day after I move
7/7 or 7/14 games - two days after I move
14/14 or 21/7 games – four days after I move
21/14 or 21/28 games – 6 days after I move
The games will have the following time controls and be started in the following order
500 games with 3/3
500 games with 3/7
500 games with 7/7
500 games with 7/14
500 games with 14/14
500 games with 21/7
500 games with 21/14
500 games with 21/28
What is the minimum number of moves I must make each day for the first 30 days to avoid any possible timeouts?
Assuming each game lasts 40 moves in total (20 moves each), how long will it take to finish 1000 games?