Recreational Math

Mathematical Games

Why is it difficult to win a lottery?

According to one state lottery site, a lottery “is a plan that provides for the distribution of money, property, or other reward or benefit to persons selected by chance from among participants some or all of whom have given a consideration for the chance of being selected.” In other words, a person buys a chance at winning a certain sum of money. But in reality—as with many games of chance—the odds are not in the participants’ favor. With most lotteries, such as a “lotto-type” lottery, a person has a better chance of being in a car or plane accident, or being hit by lightning, than winning. But that doesn’t stop many people. Every year, billions of dollars are spent on state lotteries in the United States alone.

The reason for this “dream of winning” is simple: It’s how this game of chance is perceived. Many people believe that if they just keep playing the same number(s), eventually that number or numbers will be chosen. What they often don’t realize when playing a lottery is the idea of replacement. For example, choose a 52-card deck to represent the lottery, with the queen of hearts as the winning card. Say the first picked card from the deck is the king of diamonds and it’s not reshuffled back into the deck. From there, we continue to pick cards. After each choice, if the cards are not put back into the deck, eventually, our chances of picking the queen of hearts gets better and better. After all, the choices of cards in the deck become less. If it is not picked yet, the last card will at some point be the queen of hearts.

But a regular lottery does not reshuffle the numbers. Instead, lotteries choose from the same group of numbers each week, which makes it even more difficult to win. There may be repetitions in winning numbers, but the odds of winning are the same each time the lottery is played.


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