Multiple Opportunities

14 pages on this site touch on this topic.

• Birthday Room — How many people need to be in a room before two of them probably share a birthday? Test your intuition against an exact calculation and a simulation.
• Coincidence Generator — Generate entirely fictional synthetic lives and search them for matches — see how widening what counts as a match multiplies apparent coincidences.
• Common red flags in coincidence claims — A quick-reference list of the recurring warning signs that a striking coincidence claim has not been through, or would not survive, careful evaluation.
• Dream Diary Test — See how often a synthetic dream diary appears to 'predict' the next day purely by chance — a methodology demo with no real dreams or diary entries involved.
• How to evaluate a coincidence claim — A twelve-step method for weighing a striking coincidence, from writing down the exact claim to stating plainly what remains unresolved.
• Independence and dependence: what tells you what — Most 'multiply the probabilities together' coincidence math secretly assumes independence that real events, sharing culture, geography, and cause, rarely have.
• Multiple Comparisons — Run many independent tests and watch how quickly the chance of at least one false positive climbs — even though no single test got any less reliable.
• Multiple opportunities and selection effects — Why running many chances at a pattern makes finding one almost guaranteed, even when every individual chance was unlikely on its own.
• Post-hoc probability: painting the target after — Choosing which pattern counts as "the match" after seeing the outcome inflates apparent improbability, in coincidence lists and in research alike.
• Probability is a model, not a verdict — Why a probability is always a statement about a chosen model and reference class, not a fact about a unique event — worked through the birthday problem.
• Selection effects: what you see isn't random — When data has already been filtered by its own outcome, conclusions drawn from it can be exactly backwards, as WWII aircraft-armor analysis shows.
• The birthday problem, explained — How a room of just 23 people crosses even odds for a shared birthday — and why that surprises almost everyone who hasn't seen the calculation.
• The law of truly large numbers: it happens to someone — Given a large enough number of opportunities, even wildly improbable events become almost certain to occur to somebody, somewhere.
• Winning the lottery twice: the New Jersey case — A clerk won two lottery jackpots four months apart in 1985–86 — reported as 1-in-17-trillion odds, until statisticians asked the right question.