Fair expectimax reference (D3/D4)

The strongest dependable public-information policy in this repository. It is the comparator every new candidate must beat, and the teacher behind most label-generation experiments.

The idea

At each move, fair expectimax builds a tree that alternates between player choices (take the best) and chance events (take the average):

"Fair" means the chance nodes average over what can actually happen — every legal next disc, and the possible gray-disc reveals — instead of hoping for the best reveal or fearing the worst. Depth 4 (D4) completes four full max/chance layers; the leaf is a hand-tuned public evaluator.

Why averaging matters

A hidden gray disc can become anything from a 1 to a 7. An optimistic search assumes the reveal you want; a pessimistic one assumes the reveal you fear. Both mis-rank moves, and the ledger confirms it: fair chance handling beats optimistic, worst-case, and tiny reused reveal samples. The price is work — the tree grows by roughly an order of magnitude per ply.

What the evidence showed

Configuration	Games	Mean score	Mean moves	Note
Fair D3	8	235,071	71.0	comparison policy
Fair D4	8	400,675	116.4	won 7 of 8 paired games
Fair D4 (broad cohort)	64	308,296	90.0	the reference mean

• Deeper is not automatically better: selective D5, full D5, and cycle-boundary variants all failed their gates (see the sibling approaches).
• One D4 game scored 1,246,684 points — an anecdote, not an average. The million-point target requires the mean to exceed one million.
• D4 is a strong tactical fallback and teacher, but its average is far below the target. Every serious candidate keeps an exact D4 fallback.

Sources

• fair-only-horizon.cpp — the fair-only depth-3 evaluator.
• fair-only-depth4.cpp — the depth-4 reference build (make native produces build/fair-depth4).
• The TypeScript counterpart used by the benchmark registry is evaluateMoves in src/core/typescript/solver.ts with the combined leaf.