ground-game/reports/260805-clay-borg-difficulty.md

id	type	title	domain	repo	status	owner	topic_slug	created	extends
GROUND-RPT-0002	report	clay-borg difficulty measurement, 2026-08-05 — and a retraction of what we nearly sent instead	consumer	ground-game	informational	bernd	whynot	2026-08-05	GROUND-WP-0005

clay-borg difficulty report — 2026-08-05

GROUND-WP-0005 (difficulty tiers and the Pressure dial) has both tasks in wait, blocked on a measured baseline. This is that baseline, with its limits stated.

Generated by make difficulty (games/ground/examples/difficulty.rs), governed by clay-borg/specs/RetrospectiveAnalysis.md §4, under CB-WP-0025 T06.

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0. First, what we nearly sent you and did not

Earlier today this report was going to say: "a greedy bot wins 200 of 200 games at five and six seats — the game is too easy there."

It would have invited you to move thresholds. It was wrong, and an adversarial review caught it before it left our repo.

A FirstLegal policy — take the first legal command, no heuristic whatsoever — scores 0% at five and six seats on the identical deals where GreedyPolicy scores 100%. At two seats it beats greedy (76.7% vs 60.0%).

Two unsophisticated agents span the entire range. A single policy's win rate is therefore a statement about the policy, not about GROUND, and we have written that into our spec as a prohibition rather than a preference.

This is the fifth claim we would have sent you on a wrong premise. It is the second stopped before sending.

1. The measurement

make difficulty, 60 seeds per cell:

seats	winnable	greedy	random	first-legal	spread	undecided
2	60%	60.0%	5.0%	76.7%	71.7	0
3	93%	88.3%	6.7%	25.0%	81.7	2
4	100%	93.3%	6.7%	30.0%	86.7	4
5	100%	100.0%	3.3%	0.0%	100.0	0
6	100%	100.0%	3.3%	0.0%	100.0	0

winnable is the column that is not about a bot. It is the fraction of deals in which an exhaustive search finds a winning line in the final round. The other three columns are what named policies actually achieve, and spread is the range between them.

2. How to read it, including what it is not

Read spread first. It ranges from 71.7 to 100.0 percentage points. Wherever it is large — everywhere — no single policy's rate tells you anything about the game. That is the finding behind §0.

winnable is conditioned on greedy's play up to the final round. It is "winnable from where greedy got to", not a property of the deal alone. A genuinely policy-free figure would search from round 1, which we measured as unaffordable: our search exceeded 2×10⁶ nodes at two seats over two rounds. We are telling you this rather than presenting the number as cleaner than it is.

It is a lower bound. A one-round search cannot see a line that needed an earlier round, so the true winnable fraction is at least these figures.

undecided deals are excluded, not counted as losses. Those are deals whose search hit the node budget. Folding "we stopped looking" into "not winnable" is the collapse our spec forbids.

3. What we think this supports, offered as reading not as ruling

The rules are yours. This is what the numbers appear to say.

• Two seats is the tight configuration. 60% winnable in the final round, and every policy struggles. If any seat count is under-tuned for difficulty, the evidence does not point here.
• Four seats and up: every deal we sampled was still winnable in the final round. 100% at 4, 5 and 6 seats. That is compatible with "too generous at high seat counts" — but it is not the claim we withdrew in §0, because it is a statement about deal winnability rather than about a bot's success.
• The 5–6 seat rows deserve the most suspicion. first-legal scores 0% there while greedy scores 100%, which is the widest spread in the table. Something about those configurations makes play matter more, not less — the opposite of "too easy" — and we do not yet understand it.

We are not proposing threshold changes. The measurement's confound (§2) is large enough that we would rather you saw it than acted on it.

4. What would make this a better instrument

• Search from round 1 rather than the last round, which removes the greedy confound entirely. Needs transposition or move-ordering; we have neither.
• A resolution figure — the smallest threshold change the measurement can distinguish, with its N. Our spec requires it and we cannot yet supply it.
• Your Pressure dial, if it lands, gives a second axis to measure against and would make the table two-dimensional.

5. Reproduction

Per GROUND-WP-0004 T02, arithmetic findings cite their reproduction by path:

clay-borg$ make difficulty              # the table above
clay-borg$ make self-tests              # includes the difficulty controls

Controls, so the figure can fail rather than merely print: a witness must replay to a win; an unwinnable position must be reported as searched out rather than as a budget cut; a budget of one node must not claim exhaustion; and the policy panel must actually disagree, or reporting three policies would be ceremony.