The temptation to buy lottery tickets and dream of an unthinkable jackpot prize is far too alluring for many people. Instinctively most people know the odds of winning are not exactly in the dreamer’s favor. But are the mathematical odds clearly understood? Harvard mathematician Jeffrey S. Rosenthal breaks down for the average non-mathematician how long the odds truly are. The following is excerpted from his insightful book Struck By Lightning: The Curios World of Probabilities (Harper-Collins).
“Billions of dollars are spent on lottery tickets worldwide, by optimistic souls hoping to win a huge jackpot and live happily ever after. Is this a wise decision? Leaving aside the question of whether winning a lottery jackpot truly leads to happiness (it often has the opposite effect), what is the probability that you will win?
“A typical commercial lottery might involve, say, selecting six different numbers between 1 and 49. If your six numbers match the six numbers later selected by the lottery company, you win (or share) the big jackpot. For such a lottery, the probability of winning the jackpot is one chance in the total number of ways of choosing six different numbers out of 49 choices, which is about one chance in 14 million. The calculation is similar to the case of matching all the balls in a game of keno.
“This is an extremely small probability. To put it in context, you are over 1,000 times more likely to die in a car crash within the year. In fact, you are more likely to die in a car crash on your way to the store to buy your lottery ticket than you are to win the lottery jackpot. Indeed, if you bought one ticket a week, on average you would win the jackpot less than once every 250,000 years. Furthermore, as the number of choices increases, the probability goes down even further; when picking seven numbers between 1 and 47, the probability of matching is one chance in 63 million. It may be true that someone is going to win the lottery jackpot this week, but let me assure you: that someone will not be you.
“From a practical point of view, this means that when you are deciding whether or not to buy a lottery ticket, the possibility of winning the jackpot should not be a factor in your decision. Go ahead and buy lottery tickets if you find the experience entertaining or interesting or uplifting or fun. But you simply should not buy them with hopes of a jackpot victory. I have never purchased a commercial lottery ticket. I know the odds too well.
“On occasion, lottery jackpots will grow to enormous size, perhaps hundreds of millions of dollars. It is tempting to buy a ticket then, because even though the probability of winning is so small, the payoff is so large. However, the larger the number of people who buy tickets, the greater the probability that you will have to share the jackpot even if you do win it. In such circumstances, it is better to choose unusual lottery numbers (best is a random choice; worst is 1-2-3-4-5-6 or your child’s birthday), to reduce the risk of sharing. But the jackpot probabilities are so unimaginably small that, as a computer said about nuclear war in the Matthew Broderick movie War Games, the only way to win is not to play.”
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