The “problem of points” went unsolved for 150 years until Pascal and Fermat’s correspondence produced expected value, the foundation of modern risk assessment.
Key Takeaways
Pacioli’s 1494 proportional split and Tartaglia’s lead-relative fix both broke at edge cases; neither accounted for future possibilities.
Fermat solved it by enumerating all possible future coin-flip continuations; Pascal used recursive backward induction from a tied-game baseline.
Both methods converge: score 8-6 in a race to 10 points gives the leader exactly 81.25% of the pot ($81.25 on a $100 stake).
Expected value = sum of (outcome x probability) across all futures; the same calculation actuaries, portfolio analysts, and sports bettors run today.
Pascal’s recursive method scales where Fermat’s enumeration breaks down – 20 flips remaining means 1M+ futures to list.
Hacker News Comment Review
Commenters noted Luca Pacioli’s double role: he also formalized double-entry accounting, making him an unlikely founder of both modern bookkeeping and proto-probability.
The two-comment thread is thin on technical depth; discussion is anecdotal rather than analytical.
Notable Comments
@The_Blade: Links Pacioli to double-entry accounting; notes probability “has always been way behind other maths”; cites real Polymarket/Kalshi use as modern payoff.
