AlphaBetaPlayer

A generic alpha-beta pruning player. For more information, see https://en.wikipedia.org/wiki/Alpha–beta_pruning

Implements minimax search with alpha-beta pruning to a configurable depth. Alpha-beta pruning eliminates branches that cannot affect the final decision, reducing the effective branching factor from b to approximately √b in the best case — effectively doubling the achievable search depth for the same computation compared to plain minimax.

== Heuristic Convention ==

State.heuristic(s) is positive when the player who just moved to reach s is doing well. This is consistent with the convention used throughout Gambit. At leaf nodes (terminal or depth limit reached), the raw heuristic is returned. The maximizing/minimizing logic correctly accounts for this convention.

== Move Ordering ==

Moves are ordered by heuristic before recursing — highest first for the maximizing player, lowest first for the minimizing player. This shallow search ordering maximises the probability of early pruning, approaching the theoretical best-case performance of alpha-beta.

== Mutable State ==

Alpha and beta bounds are tracked with mutable variables, and boundary/break is used for early termination on a prune. This is intentional: alpha-beta pruning is fundamentally about early exit based on accumulated bounds, and fighting that with purely functional constructs would sacrifice both clarity and performance. Mutable state is appropriate here for the same reason it is appropriate in high-performance sorting algorithms.