A Reward-Earning Quaternary Random Walk on a Parity Dial
Why this work is in the frame
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Bibliographic record
Abstract
A casino offers a game which involves a symmetric quaternary random walk on a parity \ndial with twelve nodes labeled as (1, 11, 3, 9, 5, 7, 6, 8, 4, 10, 2, 0), reading clockwise. A player \nbegins at Node 0; she tosses a copper coin to decide whether to move clockwise (if heads) \nor counterclockwise (if tails); simultaneously she tosses a silver coin to decide whether she \nwill move one step (if tails) or two steps (if heads) in the direction determined by the copper \ncoin. Whenever she lands at a new node she is said to have ‘captured’ it. If a player \nintends to capture c nodes and she wishes to toss the coins k times, then her admission fee \nis (25 + 25c + k) cents (one quarter to play, one quarter per node to capture and one penny \nper toss). The game ends as soon as either c nodes (other than Node 0) are captured or k \ntosses are over, whichever event happens earlier; and the player earns as many nickels as the \nsum of the labels of the captured nodes. How should the player determine c and k? \nThe player’s optimal choices can be derived from the theory of stochastic processes. \nAlternatively, optimal choices can be anticipated through a computer simulation. Lessons \nlearned from the game empower entrepreneurs and consumers behave optimally to determine \nwhen and how to intervene to benefit from an opportunity and/or to prevent a catastrophe.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it