A Probabilistic Analysis of Simplified Cluedo with Storm: The Birthday Cake Case
Bibliographic record
Abstract
We present a family of probabilistic models of a simplified version of the Cluedo game. In this version of the game, instead of a murder happening, a birthday cake has mysteriously disappeared. The aim of the game is to guess, from the clues that each player will collect while playing, what happened to the cake. The winner is the player that first guesses who has eaten the cake and the room where this has happened. We implemented several probabilistic models of the game encoding different playing strategies as Markov Decision Processes in the Prism language. We investigate these strategies by comparing their effectiveness in winning the game using the Prism and Storm probabilistic model checkers. In particular, we use Prism for statistical results and Storm for exact computation. Since the generated state space is in general huge, we limit our models to only two players resulting in almost 15 billion states to check. We believe that this benchmark could serve to further improve the current state-of-the-art probabilistic model checking.
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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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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 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".