Entombed discs: the 3 that can never clear
Measures how often low numbered discs become impossible to clear, when death follows, and whether the evaluator notices.
On this page
Check an observation made while watching the depth-4 search play: it lets a 3 or a 4 land above its "safe zone": a column already taller than the disc's number, where it can never clear vertically, and a few rises later the game ends under it. The question is whether that disc is a cause the search cannot see, or a symptom of a board that is already lost.
The intuition
A column in Drop7 is packed by gravity, so the vertical run through every disc
in it is simply the column's height. A 4 in a column of five can never clear
downward until the column shrinks; if the row through it is also longer than
four it cannot clear at all until a neighbour goes first. Call that disc
entombed. The search's board scorer has terms for exactly this situation —
but only for 1s and 2s (dead_low_numbers, low_number_height_risk). Its
height penalties are blind to value: a 7 and a 3 at height five look the same.
And the harm of entombing a disc arrives many moves later, outside a four-move
look-ahead. So the hypothesis was that this is the missing foresight term, and
a natural trigger for an "emergency mode".
How it was tested, step by step
- Define the feature structurally from the public board: value n, column height > n, horizontal run > n; count them, weight them by height, count the gray discs trapped beneath them.
- Dump what the scorer already knows.
leafdump.cppcomputes the frozen leaf's eighteen features for every one of the 5.26 million recorded positions (seven seconds). - Ask three questions of the corpus with
analyze.py: how often the depth-1 to depth-4 behaviour policies have such a disc on the board, and at death; how many moves before death the first persistent one appears; and whether it predicts remaining lifetime beyond the eighteen leaf features, occupancy and the rise clock, on games the fit never saw. - Gate fixed in advance: present at ≥ 50% of depth-4 deaths, median lead time ≥ 10 moves, and a held-out partial correlation ≤ −0.05 with an incremental R² ≥ 0.005. All three were required.
What happened
The observation is real, and the explanation is not the one hoped for. Three quarters of the depth-4 policy's deaths (579 of 768 complete games) end with an entombed 3-or-higher on the board, and the first persistent one appears a median of 11 moves before the end — about two rises of warning. But the scorer already knows: adding the entombed features to the eighteen it has moves the held-out fit of remaining lifetime from R² 0.6952 to 0.6955, and at equal occupancy an entombed disc costs about two moves of life (35.0 versus 37.4 at 24–27 occupied cells). The disc is a marker of the last two rises, not their cause; the board is already at 31–40 occupied cells when it appears. The gate reads not supported as tested.
What this leaves open is the action question rather than the value question: when the search chose the move that entombed the disc, was there a non-entombing alternative that would have lived longer? That is a counterfactual replay from the entombing root, not a corpus statistic, and it is the experiment this one points at.
Technical recordThe record
Theory TH-20260822-entombed-disc-hazard-61faa529, experiment
EX-20260822-entombed-disc-corpus-analysis-38be404e (frozen, CHECK,
diagnostic, no seed opened), run RUN-20260822T051517Z-eecf1098, result in
research/results/ (valid, fail, not-supported-as-tested, mechanics-only).
Corpus runs/RUN-A51D-corpus/all.states, 4,863,627 non-explored positions,
whole-origin split of afterstate-net/dataset.py. Depth-4: 19.1% of states
carry an entombed ≥ 3 disc, 7.6% more than 40 moves before death, 69.8%
within 5 moves of it; 75.4% of deaths; lead-time quartiles 5.5 / 11 / 15
moves, 57% ≥ 10, 8% ≥ 20. Held-out R² for log1p(moves to death): leaf scalar +
occupancy 0.6593; 18 features + occupancy + rise clock 0.6952; plus entombed
0.6955; entombed + occupancy alone 0.5588. Held-out partial correlation of the
entombed count −0.023. Depth-3 (4,096 games) agrees on every quantity. All
numbers are in runs/RUN-20260822T051517Z-eecf1098/analysis.json.
Sources
leafdump.cpp— frozen fast-leaf features for every corpus recordanalyze.py: the entombed features, prevalence, lead time, occupancy matching and the whole-origin incremental fit
RecordsTheories, experiments and results that reference this directory
Claim: A numbered disc of value n whose column already holds more than n discs and whose horizontal run already exceeds n (an 'entombed' disc; for n >= 3 unpriced by the frozen fair leaf, which has such terms only for 1s and 2s) is an early predictor of death for the fair depth-4 policy: it is present at most deaths, it typically appears well outside the four-ply horizon (more than two rises before death), and it carries lifetime information beyond the eighteen leaf features and occupancy.
This theory is currently not-supported-as-tested at the mechanics-only (checks only, no games played) level.
It compares entombed-disc-features against fair-d4 at the CHECK (mechanics checks only, no games played) level, using previously-evaluated-development data.
valid run outcome: fail The run was valid and the outcome was fail (mechanics-only (checks only, no games played)). Read the result.
The run was valid; the outcome was fail, at the mechanics-only (checks only, no games played) level. Of 4 preregistered checks, 3 passed and 1 failed.
Corpus analysis of entombed numbered discs (value n with column height > n and horizontal run > n) over 4,863,627 non-explored positions. Prevalence: an entombed disc of value >= 3 is on the board in 19.1% of depth-4 behaviour states overall, rising from 7.6% more than 40 moves before death to 69.8% within 5 moves of it. At death: 579 of 768 complete depth-4 games (75.4%) end with one on the board (criterion 1 holds). Lead time from first persistent appearance to death: median 11 moves, quartiles 5.5-15, 57% at least 10 moves, 8% at least 20 (criterion 2 holds, narrowly). Incremental signal: held-out R^2 for log1p(moves to death) is 0.6952 with the 18 frozen leaf features + occupancy + rise clock and 0.6955 with the entombed features added (+0.0003); the held-out partial correlation of the entombed count is -0.023 (threshold -0.05). Criterion 3 fails. Occupancy-matched, an entombed >= 3 disc shortens mean remaining life by about two moves (e.g. 35.0 vs 37.4 at 24-27 occupied cells; 24.6 vs 26.3 at 28-31). Reading: the disc is a reliable marker of the policy's last two rises, but the leaf's value-blind height and cover terms already carry almost all of its lifetime information; as a static foresight term it is not what the search is missing. Gate: FAIL (not-supported-as-tested).
Technical recordLimitations recorded with the result
- Offline, teacher-labelled diagnostic on already-played behaviour games; says nothing about whether avoiding the entombing move would have extended life (a counterfactual replay is the natural follow-up).
- Linear incremental test: a nonlinear interaction with height could still carry signal a linear leaf cannot use; the NNUE leaf sees cell/pair features and could learn it.
- The structural definition ignores release readiness (whether a neighbouring clear could free the disc); dead_low_numbers discounts by readiness and this feature does not.
- Depth-4 behaviour games are 768 of the corpus's 86,784 games; depth-3 (4,096 games) agrees on every quantity.
- The corpus seeds are training-role data; the numbers are development diagnostics and not strength evidence.
Agent contextSource files, operational notes and how to reproduce
Directory: approaches/lifetime-objective/entombed-discs