Who publishes this work
Room for Chance is the personal project of Vincenzo Lo Palo. The Science collection is published under the RoomForChance name. It was prepared with AI assistance; formulas were checked with independent exact calculations and small-space enumeration, and the reported numerical studies were executed from the published code. No external academic peer review or university endorsement is claimed.
Four kinds of evidence
| Evidence | What it supports | What it does not establish |
|---|---|---|
| Exact derivation | A result under the stated model and assumptions | That a real machine satisfies the model |
| Official operator source | Game parameters and stated rules | A forecast or a financial recommendation |
| Published research | The particular findings and scope of that study | A universal claim about every player or game |
| Executed simulation | Observed behaviour of the published synthetic model | Historical results, proof from a finite sample, or an audit of an operator |
Sources and dates
Game matrices were checked against the cited official information on 22 September 2026. A current rule page should be consulted again before relying on a game's conditions. UK Lotto calculations are explicitly per main-number round; Canada LOTTO 6/49 calculations distinguish the Classic Draw from Gold Ball mechanics. A mathematical formula can remain valid even when a named game's inputs change.
Reproducible experiments
The published run records Python 3.12.14, NumPy 2.3.5, PCG64 and a separate seed for every experiment. The downloadable program generates all eleven studies. Datasets are labelled as aggregate, binned or trial-level summaries; they are not represented as full raw-draw archives. SHA-256 checksums identify the published CSV files.
Browser simulations use Mulberry32 v1 with a public seed and rejection of duplicate labels. They illustrate the same kinds of models but do not reproduce the Python bit stream. Neither seeded demonstration generator is presented as cryptographic randomness. The game picker has a separate implementation explanation.
Figures, formulas and uncertainty
Original figures are generated with Matplotlib and supplied as SVG and PNG. Captions identify model curves, simulated observations, logarithmic axes, uncertainty bars and selected extremes. Exact integer combination counts are distinguished from rounded floating-point probabilities. A zero count in a rare category is not interpreted as impossibility.
Research references
University probability material includes Harvard Stat 110 by Joe Blitzstein and Jessica Hwang. Behavioural references include Wang and colleagues on number preferences and Miller and Sanjurjo on streak selection bias. These sources serve different arguments; a result about human performance is not treated as evidence of dependence in a fair lottery.
Corrections and reuse
To report an error, use the contact form and include the page address, disputed statement and a source or calculation. Simulation CSV files and original figures may be reused under CC BY 4.0 with attribution to RoomForChance and a link to the relevant experiment. Original downloadable code is provided under the included MIT license.
A boundary that matters
The site does not sell tickets, register entries or provide paid predictions. A number generator selects; a calculator evaluates a model; an experiment measures a simulation. None makes a specified valid line more likely to match a separate uniform draw.