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A lottery is a form of legalised government gambling that involves drawing lots for a prize. Lotteries are proscribed by some governments, while others endorse it to the point of organising a national or state lottery. It is common to find some degree of regulation of the lottery by governments; The most common regulation is the prohibition of selling to minors. Although lotteries were common in the United States and other countries during the nineteenth century, at the beginning of the twentieth century, most forms of gambling, including lotteries and sweepstakes, were illegal in the United States and most of Europe , As well as in many other countries. This remained so until well after World War II. In the 1960s casinos and lotteries began to reappear around the world as a means for governments to increase their incomes without raising taxes.

Lotteries come in many formats. For example, the prize may be a fixed amount of cash or property. In this format there is risk for the organiser if enough tickets are sold. More commonly, the prize fund will be a fixed percentage of revenue. A popular form of this is the "50-50" draw where the organisers promise that the prize will be 50% of the income.  Many recent lotteries allow buyers to select numbers on the lottery ticket, resulting in the possibility of multiple winners.

The purchase of lottery tickets can not be accounted for by decision models based on the maximisation of expected value. The reason is that lottery tickets cost more than the expected profit, as demonstrated by lottery math, so someone who maximises expected value should not buy lottery tickets. However, lottery purchases can be explained by decision models based on the maximisation of expected utility, since the curvature of the utility function can be adjusted to capture risk-seeking behaviour. More general models based on utility functions defined in things other than lottery results may also explain the purchase of the lottery. In addition to lottery prizes, the ticket can allow some buyers to experience an excitement and enjoy a fantasy of getting rich. If the entertainment value (or other non-monetary value) obtained by playing is high enough for a given individual, then buying a lottery ticket could represent a profit in total profit. In such a case, the dis-utility of a monetary loss could be offset by the expected combined profit of monetary and non-monetary gain, thus making the purchase a rational decision for that person.

Probability of winning

The chances of winning a lottery prize can vary widely depending on the design of the lottery, and are determined by several factors, including counting possible numbers, number of winning numbers drawn, if the order is significant or if the numbers drawn are Returned For the possibility of additional drawing.
In a single 6 of 49 lottery, a player chooses six numbers from 1 to 49 (no duplicates allowed). If the six player ticket numbers match those produced in the official draw (regardless of the order in which the numbers are drawn), then the player is a jackpot winner. For this lottery, the probability of being a jackpot winner is 1 at 13,983,816.

In bonus-ball lotteries where the bonus ball is mandatory, the odds are often even lower. In the Mega Millions multi-state lottery in the United States, 5 numbers are taken from a group of 75 and a number is drawn from a group of 15, and a player must match the 6 balls to win the jackpot. The probability of winning the pot is 1 in 258.890.850.
The odds of winning can also be reduced by increasing the group from which the numbers are drawn. In the Super Enalotto of Italy, players must match 6 numbers of 90. The probability of winning the jackpot is 1 in 622,614,630.

Most lotteries give smaller prizes to match just a few of the winning numbers. The game Mega Millions gives a prize (US $ 1) if a player matches only the bonus ball. The weekly 6/49 lottery operated by the ILLF  offers a two-ball cash prize, for which the odds are 1 in 6.63. In the UK National Lottery the smallest prize is £ 25 to match three balls. Recently, the organisers have changed the rules and offer GBP 2 to match 2 numbers.
By equalling more numbers, the payment goes up. Although none of these additional prizes affect the chances of winning the pot, they improve the odds of winning something