1. Laplace's Rule of Succession: Estimating the Odds That the Sun Will Rise Tomorrow
Laplace’s "Rule of Succession" offers a simple way to estimate odds when you know nothing else. If an event has happened $n$ times in a row, the odds that it will happen again are $n+1$ to 1 [3]. This is the most basic estimate when you have no prior information.
Laplace used the sun as his example. He assumed human history began 5,000 years ago. That equals about 1,826,213 days (using roughly 365.2 days per year). From this, he calculated that you could bet on the sun rising tomorrow at 1,826,214 to 1 [3]. The 5,000-year figure was an assumption of his time.
But look at what he wrote next. Laplace added that for anyone who understands the mechanisms of nature—the forces that support the cycle of day and night and the seasons—this probability is much greater [5]. Later critics often overlook this sentence. The rule is meant for when you know nothing. But what is probability, and where did it come from?
2. Pascal and the Problem of Splitting the Money When a Bet Is Interrupted
In 1654, a gambling expert named the Chevalier de Méré asked the mathematician Blaise Pascal a question: if a bet is interrupted, how should the money be split? This is known as the "Problem of Points" [2].
Pascal and another mathematician, Pierre de Fermat, exchanged letters to solve it. Imagine a game where the first to win 3 rounds wins. If the game stops when the score is 2 to 1, how do you divide the pot? The solution depends not on past wins, but on what *could* have happened if the game continued [2].
Fermat counted all possible future outcomes. Pascal worked backward from the end. These two different methods were developed through letters over a few weeks. This exchange is often described as the foundation of modern probability theory, though saying it was "born in 1654" is a generalization [6].
Laplace was born about 100 years later, in 1749, in Normandy, northern France [1]. He took the idea of "counting possible cases" and applied it to new questions.
3. Laplace's Definition of Probability: Why We Use It Because We Are Ignorant
Laplace defined probability as the number of favorable cases divided by the total number of possible cases. This assumes all cases are equally likely. For example, the chance of rolling an even number on a die is 3 out of 6, or 1/2 [3].
In Chapter 2 of his book, Laplace wrote about a hypothetical intelligence. If this intelligence knew all the forces moving nature and the position of every object at a single moment, nothing would be uncertain. The future would be as clear as the past [4]. This thought experiment is later called "Laplace’s Demon," but the word "demon" does not appear in his text.
For Laplace, probability is not a property of chance itself. It is a measure of human ignorance. We use counting to fill the gap of what we do not know. His famous quote, often cited, is that "probability theory is only common sense reduced to calculation" [8].
His book, *A Philosophical Essay on Probabilities*, was published in 1814. It served as an introduction to his larger work from 1812 [1]. Could this method of counting ignorance work beyond gambling, for events in the sky?
4. Laplace's Bet on the Mass of Saturn: Odds of 11,000 to 1
In Chapter 9 of his essay, Laplace discussed the mass of Saturn. Based on calculations by Bouvard, the mass of Saturn was estimated as 1/3512 of the sun’s mass. Laplace applied his probability formula to this result. He stated that the odds against the error being larger than 1% were 11,000 to 1 [7].
Here, the "1" side is that the error is *greater* than 1%. The "11,000" side is that the error is *within* 1%. An odds ratio of 11,000 to 1 translates to a probability of about 99.99% (11,000 divided by 11,001). In the same chapter, he treated Jupiter’s mass (1/1071 of the sun) with odds of 1,000,000 to 1 [7].
You cannot hold Saturn in your hand to weigh it. Yet, Laplace showed how reliable a calculated value was by expressing it as a number. He refused to leave the unknown as unknown. Later comparisons suggest his value for Saturn was only about 0.5% different from modern values, though this comparison comes from a blog post [9].
5. Trying It Yourself: Recording Your Own Probability Estimates
You can record your own probability estimates. Before checking the weather forecast, write down the probability of rain today on a scale of 1 to 10 in a notebook. Check in the evening if it rained. If you do this for a few days, you might see how accurate your estimates are.
The numbers Laplace gave for the sun and Saturn were ways to express uncertainty using probability.
If you want to read more, look for introductory books on probability in your library. If you want to read Laplace himself, the English translation of *A Philosophical Essay on Probabilities* is available online. Chapters 2 (the intelligence thought experiment), 3 (the sun example), and 9 (Saturn and Jupiter) are the most relevant to this story.