The
chance of winning the UK National Lottery can be slim to none. In the national lottery
you pick 6 numbers out of 49 numbers. For example you pick 14, 19, 31, 33, 34,
and 45. The probability of getting the first number is 6/49. The probability of
getting the second number is 5/48 since the balls are not being replaced. The
probability of getting the 3rd 4th 5th and 6th
numbers are 4/47, 3/46, 2/45, and 1/44.
In
order to get the probability of drawing all six numbers you multiply 6/49 X
5/48 X 4/47 X 3/46 X 2/45 X 1/44 because they are mutually exclusive and independent.
This comes to 720/ 10068347520 which can be rewritten as 7.51 X 10-8.
This simplifies to 1/ 13983816 which comes to about 1 in 14 million chance of
drawing all 6 numbers or about 14 million combinations. So there’s about a 1 in
14 million chance of winning the UK National Lottery.
Another
way this can be looked at is what the odds of drawing no balls are. Since 6
balls have to be winners 43 are not so in the first draw 43 out of 49 do not
match. The chance of the second ball not matching would be 42/48 because the
balls are not being replaced. The 3rd 4th 5th
and 6th would be 41/47, 40/46, 39/45, and 38/44. In order to get the
probability that none of the balls match the winning 6 numbers you multiply
43/49 X 42/48 X 41/47 X 40/46 X 39/45 X 38/44. This comes to about
4,389,446,880/ 10,068,347, 520 which simplifies to about 43.59%. So there’s a
43.59% chance that none of the six numbers you pick will match the six numbers
drawn in the lottery.
While
you can calculate the probability of not matching any numbers or the chances of
winning the lottery there are other theories to the lottery. One of those
theories is the Expected Utility Hypothesis which says that a person who does
not like risk or that is risk averse will never gamble no matter how much risk
there is, not even if it’s a fair game. Although with the expected utility
hypothesis there is a paradox called the Allias (1953) paradox. An example of
the paradox would be two different lotteries and people making decisions with
them. The outcomes for both of them are cash prizes where (C1, C2, C3) =
($2,500,000; 500,000; 0). In the first lottery the people in the study are
asked to choose L1= (0, 1, 0) and L’1= (0.10, 0.89, 0.01). This means for L1
there’s a 0% chance of getting the first number, 100% chance of getting 500,000
and 0% chance of getting zero while L’1 has a 10% chance of getting $2,500,000,
89% chance of getting $500,000, and a 1% chance of winning nothing. The second
lottery involves choosing between L2= (0, 0.11, 0.89) and L’2= (0.10, 0, 0.90).
The Allias paradox says that most people choose L1 and L’2. This contradicts
the Expected Utility Hypothesis because the Expected Utility Hypothesis would
state that people should choose L’1 instead of L’2.
Another
theory would be which individuals are more likely to buy lottery tickets more
often than others. According to the studies lower income people spend a higher
percentage of their income on the lottery than do higher income people, people
with a poorer education buy more lottery tickets, and peer group influences
also plays a role.
Other than
the influences of who’s more likely to play the lottery more often is another
theory Lottomania. Lottomania has to do with rollover or what week the lottery
is being played and how many wins there are each week in a period of 4 weeks. The table
below is a example with the y-axis representing the percent per each of the
four weeks and that correlates with each year.
Years
In
conclusion buying a lottery ticket can seem like something that would be worth
investing in but really the odds are not in your favor when you have a 1 in 14
million chance of drawing 6 numbers out of 49. This can be calculated by
multiplying the probability of drawing each number up to 6. Also there are low
probabilities because there is a 43.59% chance of not drawing one ball that
matches the 6 numbers that are drawn in the national lottery. This can be
calculated by multiplying the probabilities of not drawing each number up to 6.
Other than the low probabilities of winning the lottery there are theories
behind it like the Expected Utility Hypothesis with a paradox, which
people are more likely to buy lottery tickets, and Lottomania. Lastly you are
better off not gambling a lot with the lottery when there are very negative
effects and low probabilities.
Michael
Beenstock, Yoel Haitovsky. “Lottomania and other anomalies in the market for
lotto.” Journal of Economic Psychology 22 (2001) 721-744. Web. February 27 2001.
Paul
Rogers. “The Cognitive Psychology of Lottery Gambling: A theoretical Review.” Journal of Gambling Studies Vol 14(2) 111-134. Web. Summer 1998.
Kam
Yu. “ Measuring The Output And Prices Of The Lottery Sector: An Application Of
Implicit Expected Utility Theory.” NBER
Working Paper No. 14020 1-22. Web. November 30th 2006.
James Clewett. “A 1 in 13,983,816
chance of winning the lottery.” Numberphile 11/16/2014.
I like how you brought up statistics of people who are more likely to buy a lotto ticket. It extends the topic into a different direction showing how gullible people are. The lottery is basically a tax for people who can't do math, because the odds of winning are outrageous. I also how you brought up the Allias paradox and how it contradicts the Expected Utility Hypothesis. It's interesting that when people are presented with the numbers, they are still willing to take the riskier option.
ReplyDeleteI thought it was interesting to learn that lower income people spend higher on the lottery than the higher income people. But when I think about it, I see how that would make sense because they are in strong hope of winning a lot of money. As much fun as the lottery seems, it seems that people risk their odds too much.
ReplyDeleteI'm a little confused as to why you start your paper by talking about the UK lottery and not the United States lottery. I have heard a lot about the lottery but I liked that your paper stated the actual probability of winning. I think that the lottery is okay in moderation and can be a fun little game but some people take it way to far because they don't actually realize that they have so little chance of winning.
ReplyDeleteAt first I thought it was the U.S. lottery but it wasn't it was the UK lottery. Very much like the Powerball in the U.S. with the chance of winning slim to none. It is fun to play every so often but then becomes unhealthy when you are spending a lot of money, especially if you come from a poor income family.
ReplyDeleteI enjoyed hearing the differences between the U.K. lottery apposed to the U.S. lottery. I am very unfamiliar with the rules of the U.K. lottery but after reading your post I have found it to be very similar to the U.S. lottery. Although you still have an very slim chance of winning the U.K. Lottery, you are still four times as likely to win it than the U.S. lottery, just something to think about.
ReplyDeletei can not explain how happy i was to read this post. I was very glad to see that you went through and thoroughly explained the concepts and math behind the lottery. i liked the different methods and approaches you explained. with that in mind, i will still play the lottery.
ReplyDeleteI was confused on why you started with the U.K. lottery instead of the U.S. lottery. Except the differences between the two were cool and easy to understand. The different methods really caught my eye as you explained them.
ReplyDeleteWith the idea of "luck" in mind, how small the probabilities are plays a lesser role with many of the lottery players. Anyway, everything but the Expected Utility Hypothesis was well clear and understood. The way I understood it was that it was concerned with people who generally don't take risks and so should not be applied to anyone who gambles; that's why it's contradiction with the other paradox sort of lost me
ReplyDeleteLike I said in the other blog about the lottery, I am one of those people that will still go out a buy a ticket even after hearing these stats. If there is even a small chance, there s part of me that believes I will win at some point. I think it is pretty obvious that the lower income people would spend more money on lottery tickets because they are more desperate. I almost think its worth it to buy a lottery ticket so you can imagine about all the stuff you could get with that kind of money. Obviously you could do that without buying a ticket, but if you buy a ticket you have a little hope, so the imagination is a little more justified.
ReplyDeleteAlmost similar and relatable to one of the blogs below, but also interesting. How small the chance is to get all 6 out of 49 numbers to win the UK lottery. Crazy how people spend money believing these very small percentages of winning. Almost the same outcomes as the Powerball
ReplyDeleteI thought it was very fascinating that you talked about the probability of none of your numbers being picked. I've never thought to think about it and looking at the 43.59% chance of none of your balls being picked is very discouraging. I think I'll pass on the lottery.
ReplyDeleteIt was nice to learn about another country's national lottery like the U.K. I think it's crazy how you have less than a 50% of one of your balls getting picked. I think you did a good job at explaining this country's lottery.
ReplyDeleteThe math behind the probability of winning the national lottery is somewhat depressing. Although it is depressing, the idea of making a contest that has such a high probability for the lack of success of entries is also somewhat interesting. I think the truly amazing accomplishment is making the odds seem better than they really are, because if you think about the lottery logically, it does not make sense that you would win. This was a really good blog post.
ReplyDelete