Applied Quantitative Research Group publishes plain-language explanations of probability, expected value and risk in games of chance, with runnable simulations instead of claims. The site has no advertising, sells nothing, and recommends no casino, system or product. Its single affiliation is a link to a short video that tests AI betting claims.
How every page is written
- Every statistic has a named source. House-edge figures come from the Wizard of Odds rules pages; behavioural figures from Croson & Sundali (2005); quotations from the original papers with page numbers; regulatory statements from the UK Gambling Commission's published standards. Figures are checked against the original text before publication, and the access date is shown.
- Legend is labelled as legend. Where popular accounts disagree with the documentary record (the 1913 Monte Carlo betting details, the Joseph Jagger story), the page says which parts are reputed and which are documented.
- Every calculation can be re-run. The simulators and calculators run in the browser; the formulas are printed next to the results so they can be checked by hand.
- No prediction, ever. No page claims an edge, a system, or a way to beat a fair wheel. The only two historical exceptions, physical wheel bias and wheel timing, are explained as history together with why they do not apply today.
Corrections and updates
Each page shows its publication date and its last review date in the byline and in its structured data. When a figure is corrected, the page is updated in place and the review date moves. The site map lists every page with its last modification date.
The pages
- Why Hot Numbers Don't Work: The Gambler's Fallacy in Roulette. The expected-value proof, the Eudaemons history, why no betting system fixes a negative-expectation game, FAQ and references.
- Free European Roulette Simulator. 100 to 100,000 spins, a real-order wheel, the return converging on the 2.70% edge.
- Roulette House Edge by Wheel. 2.70%, 5.26%, 7.69%, the formula, an expected-loss calculator.
- Martingale Roulette Calculator. Odds of ruin, expected loss, a session simulator.
- Monte Carlo 1913: 26 Blacks in a Row. The probability and what players did.
- Joseph Jagger and the Biased Wheel. The one way hot numbers ever meant something.
Frequently asked questions
Who writes these pages?
Applied Quantitative Research Group, a small, independent publisher of probability explainers. Pages are written and checked against primary sources; the group does not accept advertising or affiliate commissions from gambling operators.
Does the site recommend casinos or betting systems?
No. It explains why no system changes the expected value of a fair game, and it links to no casino. The only outbound commercial link is to a video that tests AI betting claims.
How can I verify a figure on the site?
Every statistic carries a reference with a link or DOI, and every calculator prints its formula. Open the cited source, or re-run the calculation in the browser.