Tangle symmetries preserve resultant-knot probability

A free tangle is a tangle whose crossings are free crossings, and its four anchor points remain fixed on the boundary. The resultant knot probability is the proportion of crossing assignments producing a specified knot. Tangle-symmetry invariance conjecture. Rotating a tangle by $180\degree$, or reflecting it vertically or horizontally in a knot projection, where the reflection fixes none of the four anchor points, does not affect resultant knot probability. The source reports this as an observation and later uses it to explain flype invariance; no proof or resolution of the general statement is supplied.