Laplace's friend Bouvard used his method to calculate the masses of Jupiter and Saturn from a wide variety of observations. Laplace was so impressed that he offered his readers a famous bet: 11,000 to 1 odds that Bouvard's results for Saturn were within 1% of the correct answer, and a million to one odds for Jupiter. Nobody seems to have taken Laplace's bet, but today's technology confirms that Laplace should have won both bets.

How were they to determine the correct answer?