Before revision: We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank ~ 3): - The number of extreme points in an n-point order type, chosen uniformly at random from all such order types, is on average 4+o(1).
After revision: We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank ~ 3): (a) The number of extreme points in an n-point order type, chosen uniformly at random from all such order types, is on average 4+o(1).