The fair leaf evaluator

The problem

A search that looks four moves ahead still has to guess what happens after the fourth move. If that guess is "how many points did I score", the policy cashes in every chain the moment it can and leaves itself an empty board with nothing prepared; the chance-and-choice walkthrough shows that losing to a quieter move on a real position.

Whatever number the search puts on the boards at the bottom of its tree is the number the whole decision rests on. Every search on the neighbouring pages shares one such number. This page is about where it comes from and what is known about it.

Proposed solution

Write the evaluator in terms of what the board can still do. The heaviest positive term is direct build readiness, structures that will fire soon, weighted 1,600. Latent chain potential, structure one step further away, is weighted 700. Cover access rewards buried gray discs that can still be reached, since revealing them is how the board keeps producing usable numbers. Against those stand penalties for height, for covered discs sitting high up, for low numbers clogging the board, for danger with a rise imminent, and for other public risks (the weights are in the ledger's historical fair-only horizon evaluator section).

One deliberate choice stands out in the recovery notes. The roughness penalty, a tidiness term that discourages uneven column heights, was set to zero. The evaluator is allowed to build spiky, awkward-looking boards, because that is what a board holding a loaded chain looks like. The ledger describes the resulting behaviour as "knife-edge chain-building": able to enter a self-sustaining clear-and-reveal regime, and high variance.

The evaluator reads only the visible board, the visible next disc, and the drops remaining before the next rise. The tuning bench around it has an optional mode that imitates a perfect-information oracle, a planner allowed to read the hidden gray-disc numbers; that mode produces training labels only, its output carries the banner "oracle teacher (UNFAIR, training only)", and no run through it is recorded anywhere.

How it works

1. Read the visible position: the board, the visible next disc, and the drops remaining before the next rise. Nothing in the feature set can see a hidden value, the seed, the score, or the move number.
2. Extract the features: readiness, latent potential, cover access and altitude, height load, low-number congestion, and rise danger.
3. Multiply each feature by its frozen weight and add. The sum is the board's leaf value; a modelled game over is a flat −1,000,000 instead.
4. Hand that one number to the search. The evaluator chooses nothing; the searches on the neighbouring pages consume its values and pick the column.
5. The tuning bench can also play, as a one-move sampled policy, so a coefficient vector can be scored by complete games. Its planner samples are a pure function of the observable position and a fixed policy seed, so neither training nor play can peek at the game's future randomness. A separate sweep tool tests coefficient values the caller names up front, every candidate on the same game seeds, so each comparison is paired.

What happened

The experiment index records these runs as completed, ledger-recorded: "these runs produced the fair reference weights." Nothing more about the fitting is retained. The ledger records the recovery of the resulting weight vector into the native depth-3 evaluator and the gameplay results of the searches that used it; it keeps no result record for the tuning runs themselves, no cohort, no objective value, and no before-and-after comparison. How strong the weights are is answered by the reference search's numbers on the reference page.

The one direct piece of evidence about the leaf's own behaviour is a two-game pilot on two already-used training seeds. The games ran 155 and 160 moves and cleared and revealed discs at rates the task record associates with long games (ledger, historical fair-only horizon evaluator section; the counts are in the results table below). The ledger's own verdict is that two non-independent training seeds show that the mechanism exists and say nothing reliable about a mean.

What we learned

The durable lesson is the shape of the evaluator. It rewards what the board can still do, what can still fire and what can still be revealed, ahead of points already banked, and one conventional tidiness term had to be switched off before the policy would build anything at all.

The provenance of the frozen coefficients is thin. They are recorded as the output of these runs, but the runs' own protocol and cohort never reached the ledger, so anyone re-deriving them faces a fresh fitting problem. They have also never been refitted under corrected scoring or at the depth they are used at, and every later attempt to adjust them (machine tuning, transition rewards, vertical-ladder energy) failed on fresh games. That says the vector is hard to improve by small adjustments. It says nothing about how far it sits from the best possible leaf.

The open question is whether a refit under corrected scoring, at depth 4, on fresh whole-origin data, would keep these coefficients or replace them.