Mechanism · a prediction allowed to lose

The throw you repeat after winning

This page fixes its guess before your hand is accepted, reveals the whole bet afterward, and keeps every miss. Its only edge is a measured population tendency: after a win, people repeat the hand that won. The other directional rule in the source literature did not survive this re-analysis.

First, somebody else’s number

The machine earns the right to point at you.

Wang and colleagues released 15,600 round-by-round trials from 52 Zhejiang University students who played 300 paid rounds against a Markov-ensemble AI in 2019, knowing it was an AI. This page carries a bit-packed transcription of each human hand and each multi-AI hand from both licensed workbooks. Before the arena opens, it reconstructs every score.

checking the embedded rows
Multi-5AI, 41 playerscomputingpaper target: mean 37.39, SD 33.12
Multi-10AI, 11 playerscomputingpaper target: mean 35.64, SD 21.21
All AI outcomescomputing
Players the AI beatcomputingthe paper says more than 95%

Verifier targets from the open rows: 6,482 AI wins, 4,561 draws, 4,557 AI losses, net +0.1234 per round, 50 of 52 positive player scores, and player 20 at 198 / 55 / 47.

The source paper’s dramatic case is player 20: the AI went 198 wins, 55 draws, 47 losses. Its supplementary note flags this as an anomalously high score against a player who did not vary their input enough. The live reconstruction above checks that row too. It is an edge case, not a typical reader.

The sealed game

The digest appears before your buttons wake.

After you win, the predictor expects you to repeat your last hand and throws the counter to it. After a draw, loss, or on round one, its expectation is drawn uniformly with WebCrypto. Nothing else is hidden in the rule.

Choose a hand

SHA-256 COMMITMENT
waiting for the published anchor

input locked until the digest is visible

Nothing disappears

The misses stay dead.

Page score0
Your score0
Draws0

no predictions yet

roundstatepredictedyouguess
No rounds played.

A hit is only a correct hand prediction. The exact interval and exact two-sided binomial p-value above test that ledger against 1/3. A single streak does not become mind-reading because it has a hash in front of it.

The n-of-one instrument

Twenty rounds have almost no power.

The published pattern belongs to a group of paid Zhejiang students, playing 300 rounds against an adapting AI. You are one reader in a different setting. This visit cannot silently promote you into that population.

Your win-stay opportunities

none yet

Power is 0% before an eligible trial.

What it would take

The long game is very long.

True win-stay 0.469

At the number of eligible post-win trials you have actually supplied, the page computes the exact chance of rejecting 1/3 at one-sided α = 0.05. That live power is the bar at left.

True rate 0.450

Exact 95% power needs 191 post-win trials. If wins supply about one third of rounds, that is about 573 rounds.

True rate 0.400

Exact 95% power needs 572 post-win trials, or about 1,716 rounds under the same one-third assumption.

Those are prospective design calculations, not promises. Your rate of wins controls how fast eligible trials arrive, and this page’s strategy changes that rate.

The re-fit

One half returns. One half does not.

The 2014 conditional-response paper plotted nine fitted probabilities but did not print their numerical values or release its round-level data. This page therefore does not claim to run “the published strategy.” It re-fits the same nine categories to the open 2020 trials, taking clockwise as R→S, S→P, P→R, exactly as the 2014 supplement defines it.

Verifier targets, mean ± SEM across 52 players: win [0.248 ± 0.012, 0.469 ± 0.025, 0.284 ± 0.016], tie [0.303 ± 0.015, 0.394 ± 0.024, 0.303 ± 0.017], loss [0.305 ± 0.017, 0.375 ± 0.024, 0.320 ± 0.016], ordered clockwise, stay, counter-clockwise.

previous resultclockwisestaycounter-clockwisepooled exact 95% CIs
computing from 15,548 transitions

Win-stay returns

computing

The mean is more than five SEM above 1/3. The ordering is win-stay above tie-stay above loss-stay. This is the one regularity the arena spends.

Clockwise lose-shift dies here

computing

The two uncertainty ranges overlap. A clockwise direction was reported in 2014 and supported in a 2016 Canadian study. In this independent sample the point estimate leans the other way. That is not a verdict on the field. It is a failed replication in this dataset.

Negative control

Shuffle what “win” means.

Within each player, keep every hand transition but shuffle the 299 outcome labels. The general urge to stay survives. The extra association between a win label and staying should not.

running deterministic label shuffle

This corrects a tempting but wrong control story. Shuffling cannot drive win-stay all the way to 1/3 because these players repeated after draws and losses too. It can only destroy the outcome-specific lift.

Chance control

Give the same predictor nothing.

The exact predictor object used in the arena plays 6,000 rounds against crypto.getRandomValues. Its memory is carried through every round. Only the opponent changes. Any waiting human seal is revealed as void before the control starts, and the control’s last state becomes the next live state.

not run yet

Passing means its exact 95% interval contains 1/3. Failing stays red and visible. This is a correctness check on the code, not a new finding about people.

The sharper way out

You can compute the counter.

A fixed conditional-response rule is a stationary policy. After you win, you already know this page predicts your last hand and plays the hand that beats it. Play the hand that beats that counter. The hint beside the arena says which one. The cryptographic seal proves the page did not peek at your click. It does not make a published rule secret, or stop you exploiting it.

For a strategy that does not leak through state, use the WebCrypto button. Uniform randomness is not merely harder for this page. It makes every opposing strategy equal in expectation.

The check

What is known, chosen, and missing.

REPRODUCED LIVE FIRSTTable 5 means and sample SDs from all 52 player score totals, plus all 15,600 AI outcomes, the 50 of 52 positive scores, and player 20’s 198/55/47 record.
RE-FIT LIVENine conditional transition means and SEMs across players, pooled counts, and exact Clopper-Pearson intervals from 15,548 within-player transitions.
PINNED INPUTOriginal workbook SHA-256 values: 2a380186…9cf271 and 04fa178c…717c3. The packed two-column transcription SHA-256 is 06136b2f…b28268.
FREE CHOICESParticipant-level probabilities are averaged equally, matching the reported mean ± SEM convention. Pooled exact intervals are shown separately. α is 0.05 and prospective power is 95%.
NEGATIVE CONTROLA fixed-seed within-player shuffle preserves transitions and outcome counts but breaks their alignment. It removes the outcome-specific win lift, not general hand repetition.
POPULATION LIMIT52 undergraduate and graduate volunteers at Zhejiang University in 2019, paid, 300 rounds, told they faced an AI. One browser visitor is not a replication of that population result.
DEPENDENCEThe 2020 opponent adapted to each player. Outcomes are partly produced by that opponent, so this re-analysis establishes an association in that interaction, not a clean causal effect of winning.
PRIVACY AND REQUESTSYour hands, scores, hashes, and random draws remain in this browser. The page sends nothing and makes no third-party network request.
Primary record

What was checked against what.

Wang et al., Scientific Reports 10:13873 (2020)Methods, 52-person population, 300-round protocol, Table 5, and the claim that the AI beat more than 95% of opponents. The two publisher-hosted supplementary workbooks supply every reconstructed round. CC BY 4.0.
Wang, Xu and Zhou, Scientific Reports 4:5830 (2014)The conditional-response model, the nine categories, the R→S clockwise convention, and the original group-level plots. Its numerical fitted parameters and raw round-level data are not supplied.
Dyson et al., Scientific Reports 6:20479 (2016)31 Canadian undergraduates, 225 trials, an outcome × strategy interaction at p < 0.001 and partial η² = 0.183, with losses numerically favoring downgrade.
Forder and Dyson, Scientific Reports 6:33809 (2016)36 UK undergraduates, 450 trials. Win-stay changed with reward framing, while loss shifts were nearly symmetric: 39.13% upgrade and 39.41% downgrade.