This model assumes each quadrant has an equal 25% chance of being searched first, but that’s just not true on Church. Quads 1 and 2 are on the rebel side and get checked first most of the time because that’s where people drive in from. The caps also aren’t equal, some have better spots to hide and some have more common spots to fight from.
The trials are not independent either, since they will know which gang is capping. They will already know how many players they have and how that gang usually plays (like one person hiding vs. a group holding cap).
Plus, quads 1, 2, and 4 have better hiding spots, while 3 is better for holding cap. So the searches are not random at all.
Definitely a bit oversimplified.