We systematically explore the space of greedy heuristics for Wordle, the combinatorial word-guessing game. Starting from pattern-count maximization with answer-set preference, achieving 7,930 total guesses across 2,315 games, we discover that the tiebreaker space has specific low-dimensional structure. A variable hierarchy analysis reveals that dozens of natural partition-shape metrics collapse into two latent families, while answer-set membership operates on a nearly orthogonal axis. Exploiting this structure, we construct an adaptive tiebreaker achieving 7,925 total guesses (average 3.4233), only 5 above the provably optimal 7,920 of Selby (2022), using no lookahead, no entropy, and no search. Exact dynamic programming restricted to the pattern-count candidate class achieves 7,921 (+1 from optimal), proving that the scoring rule identifies the correct candidate pool. The entire 4-guess gap between heuristic and DP optimum is concentrated in exactly two early-game states, arising from two distinct mechanisms. The residual 1-guess gap requires anti-greedy sacrifice. Every tested modification to the global stationary scoring architecture—lookahead, Shannon entropy, depth-conditioned switching, generalized cluster detection—degrades performance. The English answer set exhibits high self-differentiation capacity (0.899 average ratio), quantifying why greedy play succeeds. Code available at: https://github.com/Weber-Braeden-Research/7925-Wordle-SolverWe systematically explore the space of greedy heuristics for Wordle, the combinatorial word-guessing game. Starting from pattern-count maximization with answer-set preference, achieving 7,930 total guesses across 2,315 games, we discover that the tiebreaker space has specific low-dimensional structure. A variable hierarchy analysis reveals that dozens of natural partition-shape metrics collapse into two latent families, while answer-set membership operates on a nearly orthogonal axis. Exploiting this structure, we construct an adaptive tiebreaker achieving 7,925 total guesses (average 3.4233), only 5 above the provably optimal 7,920 of Selby (2022), using no lookahead, no entropy, and no search.Exact dynamic programming restricted to the pattern-count candidate class achieves 7,921 (+1 from optimal), proving that the scoring rule identifies the correct candidate pool. The entire 4-guess gap between heuristic and DP optimum is concentrated in exactly two early-game states, arising from two distinct mechanisms. The residual 1-guess gap requires anti-greedy sacrifice. Every tested modification to the global stationary scoring architecture—lookahead, Shannon entropy, depth-conditioned switching, generalized cluster detection—degrades performance. The English answer set exhibits high self-differentiation capacity (0.899 average ratio), quantifying why greedy play succeeds.Code available at: https://github.com/Weber-Braeden-Research/7925-Wordle-Solver
Braeden Weber (Wed,) studied this question.