  In science, as in life, `surprises' can be adequately appreciated only in the
presence of a null model, what we expect a priori. In physics, theories
sometimes express the values of dimensionless physical constants as
combinations of mathematical constants like pi or e. The inverse problem also
arises, whereby the measured value of a physical constant admits a
`surprisingly' simple approximation in terms of well-known mathematical
constants. Can we estimate the probability for this to be a mere coincidence,
rather than an inkling of some theory? We answer the question in the most naive
form.
