Probability of winning LOTTERY
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The chances of winning a lottery
jackpot are principally determined by several factors: 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 the 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
only expect to win the jackpot once.
The odds of winning any actual lottery can vary widely depending
on lottery design. 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 where
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 Mega
Ball number at the end of your 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 bad. 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.
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