What are my chances? Using probability and number sense to educate teens about the mathematical risks of gambling

The last 20 years have seen gambling explode; it now pervades our society. Andersen (1994) recounted that before 1978, the year casino gambling came to Atlantic City, "Nevada was the only place in America where one could legally go to a casino, and there were just fourteen state lotteries" (p. 45). Furthermore, "as recently as 1990, there were just three states with casinos, not counting those on Indian reservations; now there are nine. Lotteries have spread to 37 states. Indiana and five Mississippi River states have talked themselves into allowing gambling on riverboats" (p. 45). Although Nevada and Atlantic City are considered the centers of the gambling world, casinos can be found throughout the United States, in large part because of the Indian Gaming Regulatory Act of 1988 (IGRA). Hellman (1994) identified 179 Native American casinos in 27 states; the number of casinos is now larger and continues to grow. In fact, the number of casinos in each of three states-Minnesota, Wisconsin, and Arizona-is greater than the number of casinos in Atlantic City (Hellman, 1994; Sowers, 1995). According to Fujii (1994), only Hawaii and Utah have resisted gambling's lure by "banning all forms of commercialized gambling, including lotteries" (p. 83). Gambling is also big business. According to Hellman (1994), legalized gambling's total "handle" (the total amount of money wagered) in 1992 was $329 billion, which was greater than the gross national product of Australia and Argentina combined; the total revenue from legal gambling was $30 billion. Hellman also gave an example of the various states' interest in casino gambling when he described the arrangement between the Mashantucket tribe and the state of Connecticut. In return for being allowed to install slot machines in its casinos, the tribe annually pays the state "25 percent of the slot-machine gross, or $100 million, whichever is bigger. The tribal ante is expected to hit $113 million in fiscal 1994" (p. 84). Under the IGRA, states and tribes must negotiate such agreements. Andersen (1994) reported, "The state of Nevada now derives half its public funds from gaming-related revenues. Nevadans pay no state income or inheritance tax" (p. 45). Because gambling is so prevalent, America's teens need to be educated about its associated risks. They need to know why this activity is called "gambling." Teens, who will later be adults, must become "informed consumers." Then, if ever faced with the decision to gamble or not, they can be strengthened by full knowledge of their chances of winning. They will know that the odds are against the gambler- That in the long run, the gambler loses money. To help achieve this goal, school curricula must expose students to mathematics that include discussions of probability and number sense. Many professional groups (National Council of Teachers of Mathematics, 1989, 1991; National Research Council, 1989; Mathematical Sciences Educational Board, 1990; National Council of Supervisors of Mathematics, 1989; Mathematical Association of America, 1991) support the inclusion of these two topics in the mathematics curriculum. While gambling is not the sole, or even primary, reason for studying probability and number sense, gambling does give a specific context within which an examination of these two topics may take place, creating the foundation for sensible gambling. This chapter examines how incorporating a discussion of various games of chance into a classroom unit on probability can build students' number sense while increasing their knowledge of the likelihood of random events. Specifically, this chapter will look at the mathematics of some of the most popular and easily analyzed games: lotteries, keno, roulette, and craps. Some of the fallacies and misconceptions associated with gaming will also be presented. Finally, some suggestions on how to incorporate these ideas into the classroom will be discussed.