A Canny Gambler


In 1693, Samuel Pepys wrote to Isaac Newton with this question:

“Which is more likely, to throw at least 1 six with 6 dice, or at least 2 sixes with 12 dice, or at least 3 sixes with 18 dice?”

To Pepys’ surprise, Newton found that the first choice has the highest likelihood. The probabilities are 0.665, 0.619, and 0.597 (rounded to three places).