Guess Two-Thirds of the Average: A Living Experiment

One choice, before the history

Choose any number from 0 through 100.

Each visitor is assigned one of two views. Blind sees only these rules. Feedback also sees the current crowd before choosing. Closest to two-thirds of the final average would win, but this crowd never closes, so the page reports only a current target and provisional leaders, and only once ten contributions exist.

Assigning a view.

Your number

Seen this game or its usual result before?

Stored fields only: view assignment, guess in hundredths, and this exposure answer. No name, email, free text, or demographics. The service applies per-address rate limits; this page cannot verify one person per row.

Exact payload that will leave this browser

The published aggregate gate runs before sending is enabled.

Checking the published aggregate reconstruction. The living and model displays stay closed unless it passes.

Arm A, the dead

Aggregates, not invented people.

AGGREGATE RECONSTRUCTION

Computing the published table.

session	printed means, periods 1 to 4				printed medians, periods 1 to 4				computed mean fall
session	1	2	3	4	1	2	3	4	computed mean fall

Computed unweighted means of the four printed session means, periods 1 to 4: .

Source: Nagel 1995, Table 1B, printed page 1321. The pooled first-period annotation 36.73 comes from Figure 1B, printed page 1316. Raw participant choices and exact session sizes were not in the article, no public row file or redistribution license was located, and the page does not synthesize either. Nagel's four groups had 67 people total, 15 to 18 per session.

The Financial Times count that stays split

Source: Bosch-Domenech et al. 2002, Table 1 and Figure 1(a), printed pages 1690 and 1691. The eight-entry discrepancy was not explained in the sources checked. The original contest required integers, so 13 was nearest to the unrounded target, not exactly equal to it.

Arm C, the machines

Same game, different surface.

One protocol uses the familiar two-thirds wording. The other asks for reserve, converts it to exposure, and transforms it back with x=100-reserve. Since E/150 equals two-thirds of mean exposure, the games are affine-isomorphic. A difference can reveal framing sensitivity. It cannot prove memorized training data.

Pending. The model file has not been read.

model	protocol	raw	value	refusal	unparseable	valid mean x
Pending.

Preregistered parse: the whole trimmed completion must be one JSON object with exactly choice for famous or reserve for isomorph, holding one finite JSON number from 0 through 100. No prose, extra keys, string numbers, repair, or retry. Every raw run becomes value, refusal, or unparseable. Prior work already prompted models on this game and on reframings, so the only claim here is the paired affine comparison with raw-completion accounting, and it is made only when both protocols hold valid runs in the stored file. An arm with no stored runs is reported as empty, and no model-versus-model conclusion is drawn from it.

The seal

The rules have a fingerprint.

The analysis file is fixed to this literal SHA-256:

c7b5ab89a9a2d75301712b8fcfb2d326acec49c24b7b4e298416fc21f5dbb2d5

Checking the live bytes against the printed fingerprint.

Checking 32 printed Table 1B cells and the published annotations.

The check

What this page cannot settle.

HISTORICAL LIMITNagel's participant rows were described as available on request, but no public file or redistribution license was located. Table cells and figure annotations are aggregates. They cannot support invented individual statistics.

PROTOCOL GAPThe 1995 groups were university participants, 15 to 18 at a time, paid, simultaneous, and repeated for four periods. This page is unpaid, self-selected, sequential, possibly discussed elsewhere, and one-shot.

ASSIGNMENT LIMITThe browser draws and stores one cryptographic bit. The frozen API records a caller-supplied arm, not a server-certified assignment. The contrast is therefore a randomized diagnostic for compliant visitors, not an unqualified causal estimate.

NO SCREENED STREAMThe frozen store exposes only date, arm, guess, and exposure. It cannot implement the scout's proposed token, elapsed-time, snapshot, or bot-screen fields. Every API-valid row is included. Rate limits are abuse mitigation, not identity proof.

ANYTIME, WITH ASSUMPTIONSThe confidence sequences tolerate peeking under bounded sequential assumptions. They do not cure self-selection, drift, interference, adversarial submissions, assignment spoofing, or dependence.

NO REASONING TYPESFixed half-point neighborhoods around 33.33, 22.22, 14.81, and 0 are proximity counts. A nearby choice does not reveal how many reasoning steps a person took.

NO FINAL WINNERThe target changes whenever a row arrives. A closest guess is provisional forever unless a separately announced cohort closes. This page has no payoff and no closing cohort.

KEYNES LIMITKeynes discussed a newspaper face-selection thought experiment with a different multiplier. He did not run this numerical lab experiment. The two-thirds instrument is later.

FT DISCREPANCYThe final 2002 paper prints 1,476 in Table 1 and 1,468 in Figure 1(a). The checked sources did not explain the difference, so both remain visible.

MODEL LIMITThe isomorph tests sensitivity to a changed surface. Recognition, algebra, prompting conventions, and other framing effects can all move answers. A gap is not proof of training contamination.

FREE CHOICESAlpha 0.05, a 401-point confidence grid, a 10-row threshold for arm estimates, the target, the provisional leader, and the contrast (which also needs both views nonempty), one-point histogram bins, half-point focal neighborhoods, 10% trimming, 5/95 winsorization, strict model JSON, and refusal markers were fixed in analysis.mjs.

PRIVACY BOUNDARYThe analytical row has three small integers plus a date added by the service. Address-based limits happen at the service boundary. The page does not receive or display addresses, but it cannot claim the service processes no network identifiers.

Sources and audit trail

What was checked.

Rosemarie Nagel, Unraveling in Guessing Games, American Economic Review 85(5), 1995, 1313 to 1326Full journal scan checked for design, incentives, the Figure 1B annotation, the raw-data statement, and every Table 1B cell.

Bosch-Domenech, Montalvo, Nagel, and Satorra, One, Two, (Three), Infinity, American Economic Review 92(5), 2002, 1687 to 1701Final paper checked for the Financial Times Table 1 and Figure 1(a) counts, mean, permitted integers, and focal-value discussion.

Howard, Ramdas, McAuliffe, and Sekhon, Time-uniform, nonparametric, nonasymptotic confidence sequences, Annals of Statistics 49(2), 2021Method source for the time-uniform framework. This page uses the shared site's disclosed betting implementation, not a claim that every nuisance assumption vanishes.

Siting Estee Lu, Strategic Interactions between Large Language Models-based Agents in Beauty Contests, 2024Prior model experiments, read to avoid claiming novelty for putting language models into the game.

Alekseenko, Dagaev, Paklina, and Parshakov, Strategizing with AI, 2025Prior zero-shot and reframing work, read to narrow this page's model claim to the paired affine isomorph and complete parse accounting.

The number that moves when you look