A Program for Keno

Abstract

Karl J. Smith has been an instructor at Santa Rosa Junior College since 1968. He is concerned with the use of computers in mathematics courses at all levels and has also written a textbook for liberal arts students, The Nature of Modern Mathematics. In the game of Keno, a player tries to guess in advance which numbers will be selected from a pot containing eighty numbers. Twenty numbers are selected at random. The player may choose from one to fifteen spots and is paid according to the amounts shown in Table 1. Keno originated as an updated version of a Chinese lottery sport. The origins of the Chinese lotteries are unknown, but references to lotteries are found in literature centuries old. The Chinese lottery is still popular today, and the lottery ticket is made up of eighty Chinese characters taken from an ancient poem. Actually, the game of Keno is also a lottery; the payoffs referred to in this paper are maximum payoffs. That is, the total aggregate of all winners is $ 25,000 so that the expectations computed here assume that the aggregate amount won does not exceed $ 25,000. I have often wondered, is there a best bet in Keno. First, I wanted to know if it was a fair game (a game is fair if the mathematical expectation is the same as the amount paid to play the game). We will compute the expectation for a 1-spot ticket. For the privilege of playing this game you must pay $ 0.60, and if your number is one of the twenty chosen you are paid $ 1.80. First, we compute the probability of picking a winning number: