Lottery odds vary widely depending on the lottery design, and 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 6/49 lottery game in which a player chooses six numbers from 1 to 49 the odds of being a jackpot winner is 1 in 13,983,816 (note that most lotteries have much worse odds).
To put these odds in perspective, suppose a person buys one lottery ticket per week. In a quarter-million years of play, the person would be expected to win the jackpot only once (13,983,816 weeks is roughly 269,000 years). Or if one bought a ticket every other second for one year, he would probably win the jackpot just once.
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 groups of numbers are used. The first five numbers come from one group that contains numbers from 1 to 56. The sixth number - the "Mega Ball number" - comes from the second group, which contains numbers from 1 to 46.
To win a Mega Millions jackpot, a player's first five numbers must match the first five numbers drawn and the Mega Ball number chosen 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 possibly the most difficult, as players try to match 6 numbers out of 90. The odds in making the jackpot are 1 in 622,614,630, while the odds of matching 5 numbers are 1 in 1,235,346.
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.
The lottery odds may be against us. But lady luck may smile at us and give us the big jackpot!
