The Mathematics Behind Coincidences: Understanding Their Patterns

Coincidences feel magical—running into an old classmate abroad, dreaming of a song that plays on the radio the next morning, a roulette wheel landing on black again…and again. This video shows why those “whoa!” moments are not glitches in reality but predictable outcomes of scale, probability, and human perception. We unpack the birthday paradox, the Improbability Principle, cognitive biases like apophenia and the gambler’s fallacy, and even touch the frontier idea that simple patterns occur more often than you think (algorithmic probability / Kolmogorov complexity).
Sources & Further Reading
• CDC — Lightning & Your Safety: https://www.cdc.gov/lightning/about/index.html
• CDC — Lightning Strike Data & Odds: https://www.cdc.gov/lightning/data-research/index.html
• Guinness World Records — Most lightning strikes survived (Roy C. Sullivan): https://guinnessworldrecords.com/world-records/most-lightning-strikes-survived
• Wikipedia — Roy Sullivan (context & dates): https://en.wikipedia.org/wiki/Roy_Sullivan
• BetterExplained — Understanding the Birthday Paradox: https://betterexplained.com/articles/understanding-the-birthday-paradox/
• Wikipedia — Birthday Problem (math & derivation): https://en.wikipedia.org/wiki/Birthday_problem
• Britannica — Apophenia (pattern-seeking in randomness): https://www.britannica.com/topic/apophenia
• Merriam-Webster — Apophenia (concise definition): https://www.merriam-webster.com/dictionary/apophenia
• Britannica — Gambler’s Fallacy (“maturity of chances”): https://www.britannica.com/topic/doctrine-of-the-maturity-of-the-chances
• Wikipedia — Gambler’s Fallacy (examples, independence): https://en.wikipedia.org/wiki/Gambler%27s_fallacy
• Cambridge/Plus Magazine — Ramsey Theory (order is inevitable at scale): https://plus.maths.org/content/tags/ramsey-number
• David J. Hand — The Improbability Principle (book site): https://improbability-principle.com/
• Dingle (2025) — “Curious Coincidences and Kolmogorov Complexity” (preprint): https://www.preprints.org/manuscript/202507.0968/v1
• Wikipedia — Index of Coincidence (how uneven distributions raise match rates): https://en.wikipedia.org/wiki/Index_of_coincidence