  We explore free knot diagrams, which are projections of knots into the plane
which don't record over/under data at crossings. We consider the combinatorial
question of which free knot diagrams give which knots and with what
probability. Every free knot diagram is proven to produce trefoil knots, and
certain simple families of free knots are completely worked out. We make some
conjectures (supported by computer-generated data) about bounds on the
probability of a knot arising from a fixed free diagram being the unknot, or
being the trefoil.
