The Pollard Kangaroo algorithm, also known as Pollard's Lambda method, does not rely on the birthday paradox. The birthday paradox is relevant to the Rho method because it depends on finding a collision (i.e., two identical function evaluations).

Gaudry and Schost's algorithm is a hybrid approach for solving the discrete logarithm problem. It combines elements of both the Pollard Rho method—utilizing random walks and the birthday paradox—and the Pohlig-Hellman algorithm, which leverages the factorization of the group order.

I prefer the Pollard Lambda method due to its methodical nature, low memory requirements, and efficiency in cases where the range of possible solutions is known and bounded.