A Renaissance gambling dispute spawned probability theory
2 days ago
- #mathematical puzzles
- #expected value
- #probability history
- The 'problem of points' involves fairly dividing stakes in an interrupted game of chance, like a coin-flipping contest where the first to 10 points wins $100.
- Luca Pacioli proposed splitting the pot based on current points ratio, but this fails in extreme cases (e.g., after one flip).
- Tartaglia suggested awarding a player based on their lead relative to the total game length, but this also led to unfair outcomes in close games.
- Blaise Pascal and Pierre de Fermat solved it by considering future possibilities, founding modern probability theory.
- Fermat's method lists all possible game continuations to calculate win probabilities, while Pascal used backward induction from tied scores.
- Both methods converge on the same solution, using expected value (weighted averages of outcomes), exemplified by an 8-6 score yielding $81.25 for the leading player.
- Expected value is now fundamental to risk assessment in fields like insurance and finance, providing a rigorous way to price uncertainty.