Here are English translations of relevant papers of Laplace (search for “Bouvard”). Laplace appeals to the next century of data. It’s not phrased as a bet there and while I can’t address everything he wrote, older translations use “bet” where newer ones use “odds.”
Newton used (his derivation of) Kepler’s laws relate the mass to the period of satellites; I think Bouvard did the same. Newton correctly calculated the mass of Jupiter because it has easily visible satellites, but was off by 15% for Saturn. Bouvard differed by 0.5% from Newton on Jupiter, but both were 2% off (Laplace was overconfident). Bouvard’s error on Saturn was less than 0.5%. Since Laplace thought he should be less accurate on Saturn, it was probably luck. Bouvard also computed the mass of Uranus within 30% by looking at its effects on other planets. ETA: since Laplace says the mass includes the moons, it probably isn’t computed from the orbits of the moons; perhaps it is the effect on other planets.
Here are English translations of relevant papers of Laplace (search for “Bouvard”). Laplace appeals to the next century of data. It’s not phrased as a bet there and while I can’t address everything he wrote, older translations use “bet” where newer ones use “odds.”
Newton used (his derivation of) Kepler’s laws relate the mass to the period of satellites; I think Bouvard did the same. Newton correctly calculated the mass of Jupiter because it has easily visible satellites, but was off by 15% for Saturn. Bouvard differed by 0.5% from Newton on Jupiter, but both were 2% off (Laplace was overconfident). Bouvard’s error on Saturn was less than 0.5%. Since Laplace thought he should be less accurate on Saturn, it was probably luck. Bouvard also computed the mass of Uranus within 30% by looking at its effects on other planets. ETA: since Laplace says the mass includes the moons, it probably isn’t computed from the orbits of the moons; perhaps it is the effect on other planets.