What does empirical testing reveal about algorithmic choice? An Empirical Demonstration of the Limits of Algorithmic Selection

This paper empirically investigates the distinction between algorithmic selection, objective optimality, and evidential sufficiency. Using finite MIN/MAX evaluation structures and archived UCT/PUCT search outcomes, I present explicit cases in which an algorithm selects a suboptimal alternative. I also demonstrate that complete information is not necessary to establish strict superiority: incomplete evidence can be sufficient to determine that one alternative is better than another across every completion compatible with the available evidence. Formally, if L_E(a) > U_E(b), then V_γ(a) > V_γ(b) for every γ ∈ Compat(E). Conversely, removing a critical observation can restore comparative indeterminacy. The central result is that an algorithmic choice does not by itself establish optimality, while incomplete evidence may nevertheless be sufficient to prove a strict comparison. Note to reviewers and readers. The empirical claims in this paper are deliberately limited to what the preserved evidence supports. The reported UCT/PUCT cases are presented as explicit counterexamples, not as estimates of population-level error rates or as evidence of the general inferiority of either algorithm. The numerical comparisons and evidential certificates reported in the paper are independently inspectable from the preserved data. Where the original historical executions cannot be reproduced end-to-end from the available artifacts, this limitation is stated explicitly rather than reconstructed or inferred. The purpose of the empirical analysis is therefore not to make broad performance claims, but to test, in concrete computational cases, the distinction between algorithmic selection, objective optimality, and evidential sufficiency.