Permutations and Combinations

In this second chapter, we introduce permutations and combinations and selection with and without replacement. Then we examine the games of bridge, poker, cribbage, euchre, rummy, dreidels, and the Australian game two-up. We emphasize the importance of bluffing in poker and the central role of bidding in bridge. A member of the rummy family is the game mahjong, which is played today by hundreds of millions of women, men, and children throughout the world. We spend quite some time making it easy for the reader with no knowledge of Chinese to understand the game. American mahjong, known as mah jongg, is introduced, and its role in modern American culture is referred to. Voltaire discovers a serious flaw in French lotto and becomes a millionaire. We mention the famous Dead Man’s Poker Hand of Wild Bill Hickok; the £1,000 challenge to all takers in the game of Whist of the Earl of Yarborough in the 1800s (equivalent today to more than US$100,000); the seventeenth century Dice Problem of Samuel Pepys answered by his Royal Society colleague Sir Isaac Newton; the well-known, but surprising, birthday paradox; and even combination locks, lotto, powerball, bingo, and ChatGPT summarizing the rules of cribbage.