You have a 10 times greater chance of being struck by lightning than you do of winning a million dollars in the District's new lottery.
The odds of lightning striking you are one in a million, according to the National Severe Storms Laboratory. The odds of winning the lottery's grand prize are one in 10 million, according to statistics and probability expert Robert L. Hershey.
"On the average, you'll lose about 48 cents of every dollar you put into the lottery," calculates Hershey, an engineer who is vice president of Science Management Corp. "Better than one ticket in nine will win a prize, on the average, but that may be a $2 prize after you've already spent $9."
The odds of winning the biggest "instant" prize of $10,000 are about one in 100,000. And even if you buy dozens of tickets, the odds that you'll win money stay the same.
"If you spend $100 on tickets," he says, "you'll probably get a few that you can cash in. But on the average you'll lose 48 dollars."
By definition, Hershey says, "a lottery is a losing game -- which is why governments do it as a profit-making venture. It is a game of chance, in which there is no way to increase the odds of your winning. It is set up so that, in the long run, the house has to win and you have to lose."
Many people ignore these mathematical facts because they have trouble thinking with numbers, contends Hershey, who seeks to counter this trend toward arithmetic ignorance in How to Think With Numbers (William Kaufman, Inc., 133 pages, $7.95).
For those with math anxiety, calculator-phobia and other 20th-century terrors, Hershey outlines these three bacis math principles governing lotteries:
* Probability -- The percentage of the time that an event occurs in the long run. For example, in coin flipping, the probability of getting "heads" is 50 percent.
* Independence of Events -- Each ticket purchased in a lottery is independent of all others purchased; you have an equal chance of winning or losing with each. Just as you have an equal chance of getting "heads" on every flip of a coin -- regardless of how many times you've already flipped it -- buying dozens of lottery tickets will not increase the odds in favor of your winning.
* Mathematical Expectation of Gain -- The calculation of how you can expect to fare in a game, arrived at by subtracting the probability of losing times the amount to be lost from the probability of winning times the payoff for winning. In a "coin-flipping" game where you win $1 for "heads" and pay $1 for "tails," the mathematical expectation of gain equals zero. All commercial gambling games have negative mathematical expectations of gain for the players and positive expectations of gain for the house.
"For someone who knows how to calculate," says Hershey, "the only justification for playing a lottery is the entertainment value. If you get a dollar's worth of thrill for your dollar ticket, that's fine. Just don't count on making money."