An interesting aspect of this is that they use the Flajolet-Martin algorithm to estimate the path length. The paper of Flajolet-Martin deals with a certain correction factor φ, which is defined as follows: φ = 2-½ eγ α-1, where γ = 0.57721... is Euler's constant and α is the constant Πn ≥ 1 (2n/(2n+1))(-1)t(n), where t(n) is the Thue-Morse sequence, the sequence that counts the parity of the number of 1's in the binary expansion of n.
The Thue-Morse sequence has long been a favorite of mine, and Allouche and I wrote a survey paper about it some time ago, where we mentioned the Flajolet-Martin formula. The Thue-Morse sequence comes up in many different areas of mathematics and computer science. And we also wrote a paper about a constant very similar to α: it is Πn ≥ 0 ((2n+1)/(2n+2))(-1)t(n). Believe it or not, it is possible to evaluate this constant in closed form: it is equal to 2-½ !
By contrast, nobody knows a similar simple evaluation for α. In fact, I have offered $50 for a proof that α is irrational or transcendental.