i) Circle of radius 1 (the map), populated randomly with N players. Each round a new safe zone appears: its radius is half the previous one, and it must be entirely contained within the previous circle. Players outside the new zone die. Players don't move. The first safe zone has radius 0.5. On average, how many rounds until total death for N starting players?
Assuming you figured it out. Good job.
i) N=100 · static · auto-running
mean rounds to total death vs N · 100 trials each
ii) Same setup, but this time, the players may move up to 0.1 times the current radius toward the center. How does the answer change?
ii) N=100 · δ=0.1 · auto-running
mean rounds to total death vs N · 100 trials each