Pascal and Fermat solved the 150-year “problem of points,” how to fairly split a pot in an interrupted game, and invented expected value in the process.
Key Takeaways
Pacioli (1494) split the pot by points earned so far; Tartaglia exposed the flaw: one-flip interruptions gave the winner everything unfairly.
Fermat enumerated all possible future game continuations and awarded each player their win percentage, elegant but exponential for long games.
Pascal’s recursive backward induction reached the same result without listing futures: the first known expected-value calculation.
Both methods independently yield 81.25% for an 8-to-6 lead in a race to 10, the convergence that settled 150 years of debate.
Expected value now drives actuarial life insurance pricing, Wall Street portfolio analysis, and coastal home insurance risk assessment.
Hacker News Comment Review
Ian Hacking’s The Emergence of Probability (1975) and The Taming of Chance (1990) are flagged as foundational texts the article draws on but does not cite.
Pacioli’s historical footprint is larger than noted: he also codified double-entry accounting, making him an early pioneer across two separate quantitative disciplines.
