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

---
id: GROUND-RPT-0002
type: report
title: "clay-borg difficulty measurement, 2026-08-05 — and a retraction of what we nearly sent instead"
domain: consumer
repo: ground-game
status: informational
owner: bernd
topic_slug: whynot
created: "2026-08-05"
extends: 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](../../clay-borg/workplans/CB-WP-0025-could-we-have-won.md) T06.

---

## 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.