The History of Probability Theory: How Fermat and Pascal’s Problem of Points Started It All

A 370-Year-Old Theory: The Origins of Probability

This week is all about probability theory — a topic that goes back to the very beginning of this channel. One of the first episodes, pretty cringeworthy in hindsight, was about the Problem of Points. Fermat and Pascal solved it in 1654. That means probability theory is only 370 years old!

The strict mathematical community immediately pushed back on that claim. Why should probability theory be said to start with this particular problem? After all, dice appeared much earlier, and Gerolamo Cardano was already calculating odds as ratios of favorable to unfavorable outcomes back in the 1560s.

How Fermat and Pascal Shaped the History of Probability Theory

What Fermat and Pascal uniquely contributed was mathematical rigor applied to a subjective understanding of probability. The Problem of Points prompted Huygens to tackle new problems and write the first book on probability theory in 1657.

By the 1660s, the very concept of probability was in the air — not just in mathematics, but in philosophy as well. Leibniz and Hobbes were discussing probability as a tool for understanding the world. And the Problem of Points itself led Pascal to reason about what we now call mathematical expectation.

The Problem of Points: The Puzzle at the Heart of Probability History

The problem (solved by Fermat and Pascal in 1654) goes like this:

Two players with equal chances of winning each round put equal amounts into a prize pool. They agree in advance that whoever reaches 6 points first takes everything. But the game is suddenly interrupted when the score is 5:3.

The question: how should the stakes be divided fairly?

What do you think?

• 5:3
• 3:1
• 2:1
• 7:1