Techniques for Computing the Probability of a Gambler’s Ruin with Applications to Playing Roulette
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Bibliographic record
Abstract
An interest in gambling has greatly increased over the last few decades with the more common use of slot machines and online gambling, especially sports betting. A concern that has been publically raised is addiction and eventual gambler’s ruin (loss of all money). In this paper we provide a solution to the Gambler’s Ruin problem in regards to roulette. We compute the probability of a gamblers ruin with applications to the various betting opportunities playing roulette by determining the W+1 roots of the relevant polynomials and from there determine the probability of a gamblers ruin. We find situations where the payoff becomes higher, the probability of ruin becomes lower. Lower goals of gain are associated with a lower probability of ruin and larger bets and larger odds payoff also increase the probability of ruin.
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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 | 0.002 | 0.002 |
| 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 | 0.002 |
| 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