The chances of winning a lottery jackpot are determined by several factors, including: the count of possible numbers, the count of winning numbers drawn, whether or not order is significant and whether drawn numbers are returned for the possibility of further drawing.In a typical 6 from 49 lotto, 6 numbers are drawn from 49 and if the 6 numbers on a ticket match the numbers drawn, the ticket holder is a jackpot winner - this is true regardless of the order in which the numbers are drawn. The odds of being a jackpot winner are approximately 1 in 14 million (13,983,816 to be exact). The derivation of this result (and other winning scores) is shown in the Lottery mathematics article. To put these odds in context, suppose one buys one lottery ticket per week. 13,983,816 weeks is roughly 269,000 years; In the quarter-million years of play, one would expect to win the jackpot only once, or if one person bought a ticket every second of every day for one year, one would win the jackpot on average about 2.25 times.
The odds of winning any actual lottery can vary widely depending on the lottery design of financial engineers[clarification needed]. Mega Millions is a very popular multi-state lottery in the United States which is known for jackpots that grow very large from time to time. This attractive feature is made possible simply by designing the game to be extremely difficult to win: 1 chance in 175,711,536. That's over twelve times higher than the example above. Mega Millions players also pick six numbers, but two different "bags" are used. The first five numbers come from one bag that contains numbers from 1 to 56. The sixth number -- the "Mega Ball number" -- comes from the second bag, which contains numbers from 1 to 46. To win a Mega Millions jackpot, a player's five regular numbers must match the five regular numbers drawn and the Mega Ball number must match the Mega Ball number drawn. In other words, it is not good enough to pick 10, 18, 25, 33, 42 / 7 when the drawing is 7, 10, 25, 33, 42 / 18. Even though the player picked all the right numbers, the Mega Ball number at the end of the ticket doesn't match the one drawn, so the ticket would be credited with matching only four numbers (10, 25, 33, 42).
The SuperEnalotto of Italy is supposedly the most difficult, as players try to match 6 numbers out of 90. The odds in making the jackpot: 1 in 622,614,630.
Most lotteries give lesser prizes for matching just some of the winning numbers. The Mega Millions game is an extreme case, giving a very small payout (US$2) even if a player matches only the final Mega Ball number on the ticket. Matching more numbers, the payout goes up. Although none of these additional prizes affect the chances of winning the jackpot, they do improve the odds of winning something and therefore add a little to the value of the ticket. In most lotteries, if a large amount of smaller prizes are awarded, the jackpot will be reduced, in a similar manner that the jackpot is divided if multiple players have tickets with all the winning numbers.
In the UK National Lottery the smallest prize is £10 for matching three balls. There exists a Wheeling Challenge to create the smallest set of tickets to cover enough combinations to ensure that any 6 numbers drawn will match against at least 3 numbers on at least one of the tickets. The current record is 163 tickets.
The expected value of lottery bets is often notably low. In the United States, an expected value of 50% of the purchase price is common. For instance, when the player buys a lottery ticket for, say, $10 he obtains a financial asset with an expected value of only $5. Hence, buying a lottery ticket reduces the buyer's expected net worth. This is in contrast with financial securities like stocks and bonds whose prices are theoretically based on their expected real values, as expected by the markets at any given point in time.
In a famous occurrence, a Polish-Irish businessman named Stefan Klincewicz bought up almost all of the 1,947,792 combinations available on the Irish lottery. He and his associates paid less than one million Irish pounds while the jackpot stood at £1.7 million. There were three winning tickets, but with the "Match 4" and "Match 5" prizes, Klincewicz made a small profit overall.
