2008/12/10 John Randall <[EMAIL PROTECTED]>:
> My initial thought is this: Draw the first 3 sides A->B->C.  Let D be the
> other vertex.  Then ABCD is convex iff D lies on the opposite side of the
> line AC from B.  This gives probability at least 1/2 for your question.

ABCD will still be concave if D is, e.g., on the opposite side of BC from A.
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