Before revision:  }  Second, we study algorithms for determining the order type of a point set in terms of the the number of coordinate bits they require to know.
After revision:  } A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently the space of order types. We present two results on this question. First, we study experimentally the bias in the order types of n random points chosen uniformly and independently in a square, for n up to 16. Second, we study algorithms for determining the order type of a point set in terms of the the number of coordinate bits they require to know.