Convert root visit counts into the search policy used to select a self-play move. For positive temperature $\tau$, each legal action $a$ receives

Here $\pi_a$ is the search probability, $N_a$ is the visit count, $\tau$ is temperature, and $\mathcal{L}$ is the legal-action set; $b$ ranges over that set. At positive temperature, if every legal visit count is zero, use a uniform legal policy. At temperature zero, use a one-hot policy at the lowest-index legal action with the largest count. At positive temperature, select the first action whose cumulative probability is strictly greater than the supplied uniform random draw. Return a two-item tuple: the NumPy float64 policy array with the same shape as visits, followed by the selected action as a Python integer.