Lottery Odds and PayoutsLottery odds and payout percentages are determined by several factors. A couple of factors are the number of people playing the lottery and the percentage of ticket sales that the lottery is required to devote to the awarding of prizes. Organizers almost must account for the possible count of the numbers, as well as the count of the winning numbers number. Finally, some lotteries stipulate that the order of these numbers must be exact in order to make a win, which is another contributing factor to lottery odds.
The true odds and exact probability of winning any lottery often can be found on the Internet. Usually the odds of winning are printed on the provincial or state lottery commission’s website. Examining the odds of playing a certain game is a way of being a “thrifty shopper” before you play the lottery.
The Odds of Winning
Still, if you are interested at all in the math and practicum of lottery odds and payout percentages, here is how they could work in a typical six number lottery. I will use the Lotto 6/49 which is popular in Canada. It has 49 numbers from which to choose. You must match all of the numbers drawn to win the jackpot. The odds of this happening are 1 in 13,983,816, or approximately 1 in 14 million.
To put these remote odds of winning the lottery jackpot in perspective, your need to pretend you have taken a sip of the elixir and were granted the wish of immortality. Let’s just say you can live forever and you buy one lottery ticket per week. In essence you would have to wait 13,983,816 weeks. That's roughly 269,000 years before you would have break-even odds to match all six numbers at once.
Keep in mind too that these statistics are based on a lottery that is accepting the numbers called in any order. If the numbers must appear in the order called your chances of winning the big jackpot are even weaker - 10,068,347,520 to 1.
The next factor, besides odds is your probability of winning. If a 49 number lottery has a 1 in 49 then the chance of predicting the number of the first ball called that means that there are 49 different ways of choosing that first number. For the second number called there is only a 1 in 48 chance of predicting the second number correctly. The third number as a 1 in 47 chance and so on.
Mathematically this means each of the 49 ways of choosing the first number creates 48 different ways of choosing the second. The formula for predicting the odds of picking just the two is calculated as: 49 x 48.
On drawing the third number there are only 47 ways of choosing the number; so the chances of correctly predicting 3 numbers drawn from 49 is calculated as: 49 x 48 x 47.
The math becomes astronomical as it continues until the sixth number has been drawn creating a final calculation: 49 x 48 x 47 x 46 x 45 x 44 which is 10,068,347,520. This means you have 1 chance in just over ten million of picking the six numbers correctly in no particular order.
However if there is a factorial in the equation, such as the stipulation that the numbers must be match the order in which they are drawn (as is typical of most 49 number lotteries that ask you to pick six numbers) they must be matched no matter what order they come out. Accordingly, given any set of 6 numbers, there are 6 x 5 x 4 x 3 x 2 x 1 = 720 ways the numbers could be drawn. Dividing 10,068,347,520 by 720 equals 13,983,816 – the usual odds of winning a 6/49 lottery.
Of course the odds of winning any specific lottery can vary widely depending on the lottery’s structure. Powerball, a multistate lottery in the United States with huge jackpots, is a six number lottery that is even harder to win than usual. The probability of winning Powerball is 1 chance in 146,107,962. This is because Powerball players pick six numbers, but from two different sets of numbers.
The first five numbers come from one set (a panel of numbers on the ticket) that contains numbers from 1 to 55. The sixth number -- the "Powerball number" -- comes a second panel of numbers on the ticket which contains numbers from 1 to 42. To win a jackpot, a player's five regular numbers must match the five regular numbers drawn and the Powerball number must match the Powerball number drawn. This makes the odds of winning a Powerball lottery ten times less likely than 6/49.
However to mitigate these horrific odds, many lotteries give out small cash prizes and additional tickets if you manage to match just some of the winning numbers. For example Powerball grants players a small payout (US$3) for matching only one number. In general, with Powerball, the more numbers that are matched, the higher the payout is.
The expected value of lottery bets is not that great. In the United States, an expected value of -50% is to the usual. This means you can be in the hole twice what you invested after spending money buying lottery tickets.
Another thing that most people don’t factor into their expected value is that winnings are not always paid out in one lump sum. In certain countries, but especially the USA, the winner gets to choose between an annuity payment and a one-time payment. The one-time payment is much smaller, indeed often only half, of the advertised lottery jackpot.
However, this is often more attractive than settling to receive the original huge sum which is doled out over the space of 40 years. Online lotteries are the worst for this, handing out payments that are as little as $25,000 over 40 years with a giant final payment (called a balloon payment) in the final year.
In some countries, lottery winnings are not subject to personal income tax. In Canada and Australia, all prizes are immediately paid out to winners as one lump tax-free sum.
Lotto Genie has a lottery odds calculator available on their site. Looks like a pretty neat interactive tool
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