Recursive comparison tests for dicot and dead-ending games under misère play
Bibliographic record
Abstract
In partizan games, where players Left and Right may have different options, there is a partial order defined as preference by Left: G ⩾ H if Left wins G + X whenever she wins H + X for any game position X. In normal play, there is an easy test for comparison: G ⩾ H if and only if Left wins G−H playing second. In misère play, where the last player to move loses, the same test does not apply-for one thing, there are no additive inverses-and very few games are comparable. If we restrict the arbitrary game X to a subset of games u, then we may have G ⩾ H “modulo U”; but without the easy test from normal play, we must give a general argument about the outcomes of G + X and H + X for all X ∈ U. In this paper, we use the novel theory of absolute combinatorial games to develop recursive comparison tests for the well-studied universes of dicots and dead-ending games. This is the first constructive test for comparison of dead-ending games under misère play using a new family of end-games called perfect murders.
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How this classification was reachedexpand
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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".