Section 7.3, paragraph 3 (observed)Observed single-head accuracy 0.768 and recall 0.536 on the finite test set

Single-head baseline. The single-head baseline achieves 0.768 overall accuracy and 0.536 N-position recall. These numbers have an exact theoretical explanation. With $k=4$ bits, an N-position has nim-sum $\sigma \in \{1,\dots,15\}$. Of these 15 values, exactly 8 are odd ($\sigma_0 = 1$: the values $1,3,5,7,9,11,13,15$) and 7 are even ($\sigma_0 = 0$). Head $\pi_0$ detects an N-position only when $\sigma_0 = 1$, so the theoretical N-position recall is $8/15 \approx 0.533$ (observed: 0.536 on the finite test set). All P-positions are correctly classified (since $\sigma = 0$ implies $\sigma_0 = 0$), so on a balanced test set the overall accuracy is $\tfrac{1}{2}\cdot 1 + \tfrac{1}{2}\cdot\tfrac{8}{15} = \tfrac{23}{30} \approx 0.767$ (observed: 0.768). This calculation describes the particular classifier that declares an N-position exactly when $r_0=1$. It is not the winning-move success bound of Theorem 5.12(i), and does not establish a limit on arbitrary classifiers or rollout policies.