What Are the Odds of Winning the Lottery?

By Jeremy Cato, eHow Contributor 

Many countries allow their citizens to participate in national or state lotteries. These lotteries reward huge monetary jackpots to individuals who are able to guess a specific combination of numbers. Only a one or, at most, a few people out of several million will actually win the jackpot, so the odds (likelihood) of winning is low. There are several factors that make up your odds of winning the lottery

More on Lotteries

• Lottery systems around the world are fundamentally the same: a person must correctly choose a set of numbers from a range in order to win. For example, a person must choose six numbers from 1 to 49. In a lottery, each number occurs only once, and the order of the numbers is usually not important (although for some games, order is important).

Lottery Math - Probability

• Lotteries work based on the mathematical principle of probability. With any set of numbers, there is a finite number of possible combinations within those numbers. For example, the numbers 1, 2, 3 have six possible combinations: (123, 132, 213, 231, 312, 321). A person has a one-in-six chance (one-in-six odds) of guessing the right combination if asked to guess one. In a lottery, a person must guess the right number from 1 to 49 not once, but six times, with no number repeating. So, the odds of picking the first number are one-in-49; the odds of picking the second are one-in-48 (since only 48 numbers remain) and so on. The odds equal one-in-49 times 48 times 47 times 46 times 45 time 44 or one-in-10,068,347,520. However, to account for random order, the number is divided by 720 (720 possible six-number combinations). The final odds of winning the lottery equal one-in-13,983,816.
• United States and Other Lottery Systems

• The odds of winning in the United States or any other country are similar to the illustration in the previous section, but are often much worse, closer to one-in-100,000,000. This is because national and state lottery systems do other things that decrease your odds of winning. For example, some countries increase the range of numbers to choose from; instead of 1 through 49, it may be 1 through 69. More numbers equals worse odds of winning. Also, in the United States, there is the Megaball or Powerball, which uses a completely different set of numbers from the first five, making the odds of winning much lower.

Other Factors Affecting Odds

• The number of selections required affects the odds. Lottery games that require a person to only pick three or four single-digit numbers have somewhat better odds (and therefore lower payouts). Lottery officials make these games more difficult by requiring that the numbers appear in a certain order. The number of people playing the lottery, however, does not affect your chances. The odds are still high, even if only one person plays, but the amount of the jackpot increases if more people play, because more people are putting their money into the jackpot.

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