Dan Asimov noted that I was somewhat unclear when I said
<< It's easy to see that the answer is two thirds of the probability that the convex hull of {A,B,C,D} has four sides. That holds for any i.i.d. selection of the points (consider the points drawn from a circle).
I meant something like "drawn independently from any nonsingular probability distribution on a circle." And I chose a circle (not a disc) just to make the probability of the hull having four sides be 1, so that the probability of forming a reflexive quadrilateral would be 2/3. It's a symmetry argument--the three configurations A---B A---D A C | | \ / |\ /| | | X | X | | | / \ |/ \| D---C C---B D B are equally likely. Also, in my other recent message, I forgot and misquoted the Bayeux Tapestry. The correct phrase is "Isti mirant stella" ("They wondered at a star.") Dan