THOUGHTS ON THE LOTTERY
Editor's Note: Lucy M. ('17) uses mathematical reasoning to question whether it's really worthwhile to play the lottery.
Diagram 1: The numbers on the right start with the first payment of 300,000 compounded with the 1.05% increase, and shown over the course of 29 years. The final amount has the 300,000 added back in to get $19,931,654.08. The column on the right is the same numbers but with the added federal tax of 0.75%.
To the average citizen, the lottery is a glorious enigma, promising an admittedly tiny but none-the-less real chance at being a millionaire. This prospect appeals to people across economic boundaries, untimely enticing to almost every human. But the lottery is more complicated than its surface, and there are many factors that can go into making the decision to play. I will examine the Mega Millions lottery, and attempt to determine whether buying a ticket is a worthwhile pursuit.
Mega Millions is actually one of the cheapest lotteries, in terms of how big the ticket is compared to the Jackpot. The average jackpot payout for 2013 by month was about $123 million, compared with the $1 dollar necessary to play. There are of course many scratch-to-win lotteries and such that are just as cheap to buy, but none with a jackpot nearly as high as Mega Millions. Mega Millions is a national lottery, offering play in all states but Nevada, Utah Mississippi, Alabama, Hawaii and Alaska. In New York, we would be playing through the New York Lottery, which functions within Mega Millions but offers a conduit for counting and has some slight variation on rules. Mega Millions actually boasts the largest jackpot to date in the United States, with a three-way ticket in 2012 winning $656 million. Of course this actually reduced the winnings for the individual; the largest single winner was $326 million in 2014. Mega Millions is a reputable and fiscally robust lottery service, as they go.
Skipping ahead to the winnings- the current jackpot, with a draw happening on Tuesday March 31, stands at $20 million. If you were to win, getting all numbers correct, 20 million is what is promised to you, but you can receive your money in one of two ways. The first thing you can do is get a lump sum, meaning you are paid in full all at once right after you win. This can work for someone who wants the money to invest right away- that much money can make a lot of money right away. The risk is that your investment ends up losing money, whether due to a poor choice or a bad market. Also some people are more inclined to spend the money irrationally if they get it all at once. The other option for your $20 million is an annuity payment plan, meaning you get an initial payment-in this case $300,000- and are paid the rest of the money over the course of 29 years. The amount you get increases by %5 each year in order to cover increased cost of living, a change Mega Millions made recently, but you still end up getting $20 million from the lottery, just a lot more spread out (this is shown on the left hand column of diagram 1). This type of payment allows for more financial security, since you are guaranteed continuous income for 30 years.
Mega Millions is actually one of the cheapest lotteries, in terms of how big the ticket is compared to the Jackpot. The average jackpot payout for 2013 by month was about $123 million, compared with the $1 dollar necessary to play. There are of course many scratch-to-win lotteries and such that are just as cheap to buy, but none with a jackpot nearly as high as Mega Millions. Mega Millions is a national lottery, offering play in all states but Nevada, Utah Mississippi, Alabama, Hawaii and Alaska. In New York, we would be playing through the New York Lottery, which functions within Mega Millions but offers a conduit for counting and has some slight variation on rules. Mega Millions actually boasts the largest jackpot to date in the United States, with a three-way ticket in 2012 winning $656 million. Of course this actually reduced the winnings for the individual; the largest single winner was $326 million in 2014. Mega Millions is a reputable and fiscally robust lottery service, as they go.
Skipping ahead to the winnings- the current jackpot, with a draw happening on Tuesday March 31, stands at $20 million. If you were to win, getting all numbers correct, 20 million is what is promised to you, but you can receive your money in one of two ways. The first thing you can do is get a lump sum, meaning you are paid in full all at once right after you win. This can work for someone who wants the money to invest right away- that much money can make a lot of money right away. The risk is that your investment ends up losing money, whether due to a poor choice or a bad market. Also some people are more inclined to spend the money irrationally if they get it all at once. The other option for your $20 million is an annuity payment plan, meaning you get an initial payment-in this case $300,000- and are paid the rest of the money over the course of 29 years. The amount you get increases by %5 each year in order to cover increased cost of living, a change Mega Millions made recently, but you still end up getting $20 million from the lottery, just a lot more spread out (this is shown on the left hand column of diagram 1). This type of payment allows for more financial security, since you are guaranteed continuous income for 30 years.
Diagram 2
However, the jackpot isn’t the only way to play. There are 8 other winning options in Mega Millions. The way the draw works is that there are five numbers between 1 and 75, and one number between 1 and 15, known as the “easy pick”. Matching all six numbers gets you the jackpot, but you can win other prizes from matching some of the other numbers (diagram 2) and receive up to $1 million. But if someone doesn’t win the jackpot at the weekly drawing, it continues to grow until someone finally hits it. The numbers are picked under high security by a random number generator, created by Mega Millions, though not used exclusively by them. The computer generates “pseudo-random” numbers, which means it picks numbers within the designated fields without bias. This gives no advantage to plays, who can choose any number and have the same chance at winning.
These prizes that are offered by Mega Millions are not actually what you will be collecting as a potential winner. Taxation changes the ending amount of money made overall, and can have an impact on the decision of payment type. The federal government requires that when someone wins a lottery over $600, they file a separate form to the IRS during tax season, and that money is deducted %25. This actually has the same affect on both the lump sum and the annuity payments, reducing them to an overall payment of %15 million dollars, the annuity being taxed with every year (the right hand column of diagram 1). There is another issue in regards to state taxation, however. States treat the lottery as another source of income, and so add it to your total income. This may actually change your progressive income tax, if the addition bumps you up a tax bracket. This will only affect you for one tax season if you take the lump sum, then your state income could be changed for the 30 years you receive payments.
Diagram 3
Even with the damper of taxation, the amount of money possible from the current Mega Millions draw is substantial and potentially life changing. Unfortunately, the chances of winning it are not very good. The odds that you win the jackpot can be calculated using combinitorics; you multiply the number of chances for each slot for the amount of numbers possible. So for the jackpot, it would be 75x75x75x75x75x15, since there are 75 number options for the first 5 slots and 15 for the final pick. So if you buy 1 ticket, you have a 1 in 35,595,703,125 chance of winning $15 million dollars (the calculations for the rest of the prizes can be found in diagram 3). Buying more tickets increases your odds of winning, but it also decreases your prize should you win and increases the amount of money you lose if you lose- making the entire process more of a gamble. There is also always a chance of multiple winners. This possibility doesn’t actually lower your own odds, but it does lesson your prize, especially if there are more than two winners.
The expected or average value of one ticket for a $20 million dollar jackpot would be about $1.20. This number gives monetary value to an uncertain commodity like a lottery ticket. $1.20 is pretty good, considering the ticket only costs $1 to buy. Buying the ticket would not be a terrible investment, since you are buying under what it worth, although your chances of winning are still the same infinitesimal amount. It would actually be better if the jackpot was larger, as the value of the ticket would go up, and your odds would stay the same. Many people desperate to win the lottery would consider somehow cheating to win. This has in fact been done; several MIT students figured out how to dupe the Cash WinFall lottery. They figured out that since the Cash Winfall lottery was a “roll down” lottery, meaning that if the jackpot wasn’t claimed in a certain amount of time some of the money went to the easier prizes, and that if they combined bought $1,000 in tickets, the odds were in their favor to come back with over $2,000 dollars in winnings, plus added benefits. They waited until the money was in the right place, bought exactly the right amount of tickets in high volume, and eventually ended up with millions of dollars in winnings. This is not exactly cheating since it follows the rules of the game (players can play as many times as they want). It does break the system, though, since there are suddenly so many tickets going to the same person, making the odds a little unbalanced. However, this would not work with Mega Millions, because its jackpot does not “roll off”, and it would not be a worthwhile investment to try for the smaller prizes with too many tickets.
Diagram 4
There is a lot of mixed research around the affects of winning a high-stakes lottery on the human psyche. The most frequently cited phycology study has found that people have a generally fixed level of happiness. There are things, such as winning the lottery, that would cause a spike in emotions, but after a time there would be a return to normal levels- meaning that no life-altering everlasting happiness can be achieved. In fact, people who win the lottery sometimes end up worse than where they were in the first place. Jack Whittaker, for example, won $315 million dollars in West Virginia in 2002. After giving some to charity and to his extended family, he was robbed repeatedly, has blackmailed, arrested, and his granddaughter was killed under suspicious circumstances. He ended up with very little of his money left by 2007. There are other cases, such as Alex Toth and Evelyn Baseshore, of people who lost most of their money to family or tragedy or mismanagement. Now of course not everyone who wins the lottery goes down this path, but the sudden influx of enormous wealth makes the situation much more difficult. A study in Britain concluded that almost all winners spend 44% of their wealth in the first 5 years of having it. There are people who are generally more likely to play the lottery, simply based on ongoing trends from the past several years. It has been found that gender, location, age and race are all factors in high traffic players; black males from the Northeast of the boomer era seem to be the most popular (diagram 4). But there are steps you can take to make sure you are still financially stable after you win. Getting a economic consultant to help would be the first step; someone to advise you on investment choices, moderate your immediate spending, and protect your money. Mega Millions actually points you in the direction of several services should you win.
In conclusion- should you play Mega Millions, with the current jackpot of $20 million? My answer would be no. Your chances are astronomically small, the prize is drastically reduced by taxes, it is nearly impossible to cheat this kind of lottery, and the future becomes more disrupted and uncertain. However, it is best not to underestimate the power of human hope, since millions play every day trying to win. If you were to play Mega Millions, I would wait until there was a bigger pot (more money, same odds) buy a few tickets (not too much more than the expected value so as to not overdo your investment) and take the annuity payment option if you were to win. This will minimize the risk, especially of a large jackpot, and will ensure a stable income for years to come, despite the possible hike in personal income taxes. The two main things to consider are- is it worth the money in the first place to play, and is it worth the fiscal responsibility later on? If the answer is yes, then good luck!
In conclusion- should you play Mega Millions, with the current jackpot of $20 million? My answer would be no. Your chances are astronomically small, the prize is drastically reduced by taxes, it is nearly impossible to cheat this kind of lottery, and the future becomes more disrupted and uncertain. However, it is best not to underestimate the power of human hope, since millions play every day trying to win. If you were to play Mega Millions, I would wait until there was a bigger pot (more money, same odds) buy a few tickets (not too much more than the expected value so as to not overdo your investment) and take the annuity payment option if you were to win. This will minimize the risk, especially of a large jackpot, and will ensure a stable income for years to come, despite the possible hike in personal income taxes. The two main things to consider are- is it worth the money in the first place to play, and is it worth the fiscal responsibility later on? If the answer is yes, then good luck!
http://www.businessinsider.com/lottery-winners-who-lost-everything-2013-12
http://www.gfkmri.com/Portals/6/assets/CIImages/Product_Apr2012_Lottery.jpg
http://www.irs.gov/instructions/iw2g/ar02.html#d0e443
http://www.megamillions.com/
“How not to be Wrong; The Power of Mathematical Thinking”, by Jordan Ellenberg.
http://www.forbes.com/sites/susanadams/2012/11/28/why-winning-powerball-wont-make-you-happy/
http://www.gfkmri.com/Portals/6/assets/CIImages/Product_Apr2012_Lottery.jpg
http://www.irs.gov/instructions/iw2g/ar02.html#d0e443
http://www.megamillions.com/
“How not to be Wrong; The Power of Mathematical Thinking”, by Jordan Ellenberg.
http://www.forbes.com/sites/susanadams/2012/11/28/why-winning-powerball-wont-make-you-happy/
