Probability of winning at lottery
The
chances of winning a lottery jackpot can 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-from-49 lotto, a player chooses six numbers from 1 to 49 (no duplicates are allowed). If all six numbers on the player's ticket match those produced in the official drawing, then the player is a jackpot winner. This is true regardless of the order in which the numbers are drawn. For such a lottery, the chance of being a jackpot winner is 1 in 13,983,816 (note that most lotteries have much worse odds). The derivation of this result (and other winning odds) is shown in the Lottery mathematics article. 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 [4]
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 weekly 6/49 lottery operated by the ILLF offers a two-ball cash prize to make the odds of winning some prize only 1 in 6.63. 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. On the other hand, multiple smaller prizes usually mean smaller jackpots. It is very common for the jackpot to be split evenly if multiple players have tickets with all the winning numbers.
In the UK National Lottery the smallest prize is £10 for matching three balls.
The expected value of lottery bets is often notably low. In the United States, an expected value of 50% of the purchase price is available only in the small-payout, non-jackpot games. For example, when a player buys a "pick-4" lottery ticket for $1.00, he might be getting a ticket with an expected value of only $0.50. Hence, buying a lottery ticket reduces the buyer's expected net worth. This is in sharp contrast with financial securities like stocks and bonds whose prices are theoretically based on their economic value, as judged by the markets at any given point in time.
Lotteries are sometimes described as a regressive tax, albeit a voluntary one, since those most likely to buy tickets, and to spend a larger proportion of their money on them, are typically less affluent people. The astronomically high odds against winning the larger prizes have also led to the epithets of a "tax on stupidity" and a "math tax". Although the use of the word "tax" is not strictly correct, these descriptions are intended to suggest that lotteries are government-sanctioned operations which will attract only those people who fail to understand that buying a lottery ticket is a poor economic decision. Indeed, after taking into account the present value of a given lottery prize as a single lump sum cash payment, the impact of any taxes that might apply, and the likelihood of having to share the prize with other winners, it is not uncommon to find that a ticket for a major lottery is worth less than one third of its purchase price. In other words, if a lottery ticket costs US$1 to purchase, its true economic worth may be only US$0.33 or so at the time of purchase. Of course, this is just a hypothetical example, and the actual value will depend on the details of each lottery. Some lotteries may offer tickets that are worth less than 20% of their price, while others may be worth over 50%. To raise money, lottery operators must offer tickets worth much less than what one pays for them, so the lottery is a bad choice for customers trying to come out ahead.
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.
The chances of winning a lottery jackpot can 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-from-49 lotto, a player chooses six numbers from 1 to 49 (no duplicates are allowed). If all six numbers on the player's ticket match those produced in the official drawing, then the player is a jackpot winner. This is true regardless of the order in which the numbers are drawn. For such a lottery, the chance of being a jackpot winner is 1 in 13,983,816 (note that most lotteries have much worse odds). The derivation of this result (and other winning odds) is shown in the Lottery mathematics article. 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 [4]
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 weekly 6/49 lottery operated by the ILLF offers a two-ball cash prize to make the odds of winning some prize only 1 in 6.63. 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. On the other hand, multiple smaller prizes usually mean smaller jackpots. It is very common for the jackpot to be split evenly if multiple players have tickets with all the winning numbers.
In the UK National Lottery the smallest prize is £10 for matching three balls.
The expected value of lottery bets is often notably low. In the United States, an expected value of 50% of the purchase price is available only in the small-payout, non-jackpot games. For example, when a player buys a "pick-4" lottery ticket for $1.00, he might be getting a ticket with an expected value of only $0.50. Hence, buying a lottery ticket reduces the buyer's expected net worth. This is in sharp contrast with financial securities like stocks and bonds whose prices are theoretically based on their economic value, as judged by the markets at any given point in time.
Lotteries are sometimes described as a regressive tax, albeit a voluntary one, since those most likely to buy tickets, and to spend a larger proportion of their money on them, are typically less affluent people. The astronomically high odds against winning the larger prizes have also led to the epithets of a "tax on stupidity" and a "math tax". Although the use of the word "tax" is not strictly correct, these descriptions are intended to suggest that lotteries are government-sanctioned operations which will attract only those people who fail to understand that buying a lottery ticket is a poor economic decision. Indeed, after taking into account the present value of a given lottery prize as a single lump sum cash payment, the impact of any taxes that might apply, and the likelihood of having to share the prize with other winners, it is not uncommon to find that a ticket for a major lottery is worth less than one third of its purchase price. In other words, if a lottery ticket costs US$1 to purchase, its true economic worth may be only US$0.33 or so at the time of purchase. Of course, this is just a hypothetical example, and the actual value will depend on the details of each lottery. Some lotteries may offer tickets that are worth less than 20% of their price, while others may be worth over 50%. To raise money, lottery operators must offer tickets worth much less than what one pays for them, so the lottery is a bad choice for customers trying to come out ahead.
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.
