A Mathematical Law for Assessing Outcome Values of Games
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Bibliographic record
Abstract
Background The predominate outcomes of many computerized simulation games, particularly business games, are numeric values, for example, financial statements, as determined by the game algorithm. Numerous types of algorithms have been put forth. Attending these algorithms are issues of their validity; numerous approaches to validation also having been put forth. Aim This research presents a type of digital analysis, Benford’s Law, as a basis for assessing the validity of simulation game numeric outcome values, that is, algorithmic validity. Method To illustrate the application of Benford’s Law, it was applied to income statement items from a business game competition. The first digits and second digits, respectively, of numeric outcome values were analyzed. Results Both the first digits and the second digits conform closely to Benford’s Law. Less conforming outcomes were those of assigned values to which Benford’s Law does not apply. Conclusion Benford’s Law is conceptually and practically appropriate for assessing simulation game numeric outcome values. An example of its application demonstrates this appropriateness.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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