Question: If you gamble, you care about how often you will win. The probability of winning tells you what proportion of a large number of bets will be winners. You care even more about how much you will win, because winning a lot is better than winning a little.
There are a lot of ways to gamble. You can play games, like some of the multistate lotteries, that have enormous jackpots but very small probabilities of winning. You can play games like roulette for which the probability of winning is much larger than for a multistate lottery, but with smaller jackpots. Which is the better gamble: an enormous jackpot with extremely small odds or a modest jackpot with more reasonable odds?
In this chapter you will learn about expected values. Expected values provide one way to compare games of chance that have huge jackpots but small chances of winning with games with more modest jackpots but more reasonable chances of winning. By the end of this chapter you will be able to determine whether buying a multistate lottery ticket or simply playing red in roulette is a better bet.