Abstract: In 1718 Abraham De Moivre published his Doctrine of Chances, a work on probability theory. Many of the problems solved in the book had been given to him as challenge problems by mathematically inclined friends and patrons. After the book was published, challenge problems continued to flow in. One such problem was given to him by Sir Alexander Cuming in 1721: Two players of equal skill play 𝑛 games. At the end of these games, the player who wins the majority of these games gives a spectator a number of units of money corresponding to the difference between the number of games the player has won and 𝑛/2. What is the expected amount of money the player is to receive? Cuming also generalized the question to players of unequal skill. De Moivre’s solution to the original and generalized problem, for large 𝑛, is the normal approximation to the binomial, which he obtained in 1733. In this talk, I will give the historical background to the normal approximation to the binomial and De Moivre’s method of solution, as well as Thomas Bayes’s criticism of the result.