A Reward-Earning Quaternary Random Walk on a Parity Dial
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.028 | 0.003 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".