Algebraic tangles have no more figure-eight than trefoil descendants

A resultant knot probability is the proportion of crossing assignments of a free knot diagram that produce a specified knot. An algebraic tangle is a tangle obtained through the algebraic tangle constructions considered in the source. Algebraic-tangle probability conjecture. For a free knot diagram coming from algebraic tangles, the resultant figure-eight probability is less than or equal to the resultant trefoil probability. The conjecture is supported by the enumeration of free knots with at most nine crossings, but the source identifies $9_{40}$ as a counterexample when the algebraic-tangle hypothesis is omitted.