A football field covered with M&M’s says don’t waste your money playing the lottery
I’m sure you’ve seen the photos of many of those many delighted lottery winners! Yes, they do exist.
As we all know, though, winning the Powerball requires a lot of luck. For every smiling winner there are millions of people with nothing to show for their money.
How much luck does it take to win the lottery? According to this Powerball site, the odds of picking all six two-digit numbers correctly is one chance in 146,107,962. This is bleak, but how bleak? Some state lotteries show you how to do the mathematics, but I doubt that this complicated math can counteract the heavy advertising done by the lotteries–advertising that takes advantage of widespread innumeracy. How can the small chance of winning the lottery be conveyed in a visual and understandable way?
I decided to use plain M&M’s (not peanut) and a football field for my thought experiment. I didn’t really do this demonstration, but you could. If you’d like to do it, just go out and buy 146,107,962 M&M’s. Instead of actually buying the M&M’s, I used mathematics.
I decided to allow all six lottery numbers to serve as the coordinates for ONE M&M in a big pile of M&M’s. I started by wondering whether 146,107,962 M&M’s might cover a football field (the field between the goal lines, not including the end zones). A football field, between the goal lines measure 300 ft long x 160 feet wide = 48,000 square feet. That equals 6,912,000 square inches. Based on my experiments with M&M’s at home, I found that 17 M&M’s will cover about 3 square inches. 146,107,962 M&M’s would thus completely cover three football fields, from goal line to goal line.
So . . . here’s the proposition. Assume that ONE M&M was painted silver and mixed into the M&M’s that covered 3 adjacent football fields that had been completely covered with M&M’s. Then assume that a lottery company allowed you to pay $1 to walk out into those 3 huge fields blindfolded to pick up only one M&M with a tweezer–the silver one. Would you do it, or would you rather keep your dollar? Or how about this option: would you scoop up one liter of M&M’s (enough to fill about one quart, which you could do by scooping up a bit more than a square foot) for $549?
BTW, I refered to this site to determine how many M&M’s there are in a specific volume. It turns out that one liter (which is a little more than a quart) of M&M’s is about 1098 M&M’s.
This thought experiment helped me to understand the low odds of winning the lottery, but I’m curious. Would this visual have the power to cure anyone else of the urge to spend their hard-earned money on the lottery? Could this serve as an “anti-lottery ad”?
If none of this cures you of the urge to play the lottery, consider this: coming into large sums of money will only temporarily change your happiness level.
also, to save the interest calculations, im talking about the cash value of the jackpot.
Given, the $48 million current jackpot ($23.3 million cash value), each ticket is only worth 36 cents (which means every dollar spent is 64 cents going to the lottery gods)
At a cash value of $117,307,870 - buying a ticket is worth $1.
Both of these calculations assume a single winner.
I made a quick jpeg image that is 12474×11713 = 146107962 pixels large, 1.64MB. It is completely white, except for one pixel which is black. (honestly I think there are a few grey pixels surrounding it due to jpeg compression). This pixel represents your odds of winning the powerball jackpot, though I’d still like to see it done in m&m’s. I reccomend hunting with a 1:1 zoom ratio or better, otherwise the pixel may not be visible!
http://www.megaupload.com/?d=ZH3UNRWM
Happy hunting, and just so you know you’re not on a wild goose chase, the location of the pixel is written below, in rot13 encoding:
fvk gjb bar svir cvkryf evtug
svir rvtug sbhe sbhe cvkryf qbja
Conversely there is a 100% chance that the money will be given away. It is not a win=lose game but a who wins game. There is a social-cultural flaw in your logic. Let’s say I am not real bright and I know that. I did not go to college and have few skills, because I am not skilled, I am not good looking and I am not socially connected. My chance of becoming a doctor? zero My chance of becoming president? zero My chance of making money in real estate or the stock market?zero My chance of making 50 grand a year? zero My chance of winning the lottery? 1 in a 150 million. Guess which choice I am going to make? the one with the better odds of course. Now I am a doctor and see these people daily. It is not a stupid choice for them. A slim chance is infinitely better than no chance at all.
Just before the UK National lottery started I heard an interview with a representative of a bookmakers. He was asked to put the odds of winning into perspective for the general public. He said:
The odds of winning the Lottery are about 14 million to one. To give you some idea of another bet that would get you similar odds, we would offer you odds of 14 million to one on Elvis Presley landing a UFO on the back of the Loch Ness Monster.
That quote put me off playing the lottery, and I regret that, for a reason that has already been mentioned and which I will come back to.
Charlie said that you would have a marginally improved chance of winning if you played the same numbers every draw, all your life. This appeals to the vague idea that most people have that “in the long run” each number must come up equally often. If the numbers are being drawn truly at random, then “eventually” each number gets picked the same number of times.
I did some experiments on how long the “long run” is in a number of situations. I measured the ratio of actual occurrences of each number against the expectation that they should all come up equally often. By this measure the “score” for each number should approach 1.
In dice rolling I found that after a hundred rolls, there had been 21 threes but only 12 fours; which is clearly not even. After 1000 rolls of the dice both three and six were well ahead while one was a long way back. After 1,000,000 rolls of the dice there was a difference of 650 between first and last place, but that was only 0.5% of the expected occurrences for each number, so we are starting to approach equality, but we are not there yet.
After 5,000,000 rolls of the dice the difference between the number that had come up the most often and the least was only 0.209% of the expected occurrences. Which means that in dice rolling “the long run” is approximately 5 million rolls of the dice.
So the “long run” for rolling a dice once a week is approximately 96,000 years.
Since the National Lottery involves more numbers than a dice, it will take longer for each number to come up equally often. Statisticians have ways of working out things like this. If P is the probability of winning, then the average wait to win is 1/p, which for the National Lottery works out at 268,919 years.
Which means that for Charlie to be right about his hope that playing the same numbers will even marginally improve his chances of winning, he would have to play the lottery every week for 268,919 years before winning. At a dollar a week he would have to spend almost $14 million dollars, and eat an awful lot of birthday cake.
But despite this, and despite such visual models as Erich’s field of M&M’s, there are good reasons for paying the so-called “idiot tax”.
Playing the lottery is not about winning. It is not about how much that money will change your life, or how many cars or condo’s you can buy. It isn’t about giving up your job and settling back to a life of endless golfing holidays. It’s about what Tim called the “fantasy”.
There have been many studies that show that money does not buy us happiness, and my guess is that this is because happiness is not an absolute concept but a relative one; you are happy today relative to how you felt a week ago. So once you have become accustomed to having $5 million in the bank and being able to go on holiday every five minutes, you start to look for something else to make you happier than you were last week.
I don’t know how it works in the US, but over here a small percentage of the stake money is given to good causes. So when folks ask me why I waste my money on something I cannot hope to win, I tell them that this is my way of giving to charity. Sometimes I think about how lucky I am in my life, and I think about the people I may have helped in some small way through playing the lottery.
But the truth is, its the fantasy that does it for me. I sit on the train on a Friday coming home from work and as I watch the green fields and the river slide past the window I dream about what it would mean if I won the lottery this weekend. The sheer unadulterated pleasure I get from being able to have that dream every week is worth much more to me than the pound I pay to play, and I often wonder if it isn’t the best pound I ever spent.
How about this.. if you have $146,107,962 and the jack pot is around 200,000,000 (which has happened in my state, then just buy all the numbers and you make $53,892038. Easy.
Dave: Clever thinking. I hope that on the week you pony up for that sure win that you don’t have to split the prize with any co-winners (especially with a person who bought a single computer-generated randomly chosen ticket).
Well, Dave & Erich - technically if you waited until the jackpot was already $200,000,000 and dropped 150M on tickets, the jackpot would likely grow significantly (depending on the amount of the ticket cost that goes to the pot)… so the “profit” would likely be considerably larger with only one winner.
Except… you buy tickets with your after-tax $150M. Even were you to be the sole winner of a $200M jackpot and had a great tax guy who somehow got you down to 25% tax range… you’d come out even at best.
So.. there’s still only one winner. Uncle Sam and his 50 children, and numerous fiefdoms spread all over the world.
I have spent about $20 in my lifetime on lottery tickets. I bought my last ticket in 1998 when I won $10,000 and haven’t bought one since. I am one of the few who have actually MADE money off of the lottery.
I am a lottey player. I don’t spend much money on it and it has payed out for me. If I choose to spend my money on lottery tickets that is on me. I don’t see anything about smokers, they literally burn up there money, and most likely will get canceer later on for it. there are worse things money can go to.
All y’all are wrong. The lotto/powerball odds are 50/50; either you win, or you don’t. Simple as that.
I do win the lottery - the profits pay for my college.
So by all means, the rest of you please keep playing, and I’ll reap the benefits.
Here’s the thing:
Yes: It is basically pointless to buy a lottery ticket.
But that’s not really what you’re paying for. Think about it.
When you buy a lottery ticket, you’re paying for a fantasy. Between the time of buying the ticket and checking the numbers (and finding out you’ve lost) you get to fantasize about what you’d do with the money if you’d won, where you’d travel, what you’d invest in, who you’d help out, etc.
All you have to do is pay a dollar and you get a few days to feel hopeful and fantasize. Then you lose and you pay another dollar and get to keep doing what you were doing before.
Cheap hope is pretty hard to come by, after all. It might ultimately be naïve to buy lottery tickets of any form, but you could do worse. You could be spending your money on crack or PCP, for instance.
And anyways, it’s only a dollar. I’d pay a buck for hope–even the cheap, far-fetched kind.
Kevin: I largely agree with you. Playing the lottery can be a “cheap hope.” I probably buy a lottery ticket once per year. I don’t expect to win, but it is fun to bring it home and let the kids scratch it off. Truly, I can’t think of any significant problem with this approach. It’s morally no different than blowing a bit of money on any other form of entertainment.
There are some people out there for whom hope is not so cheap, however, because they buy LOTS of lottery tickets when they can’t really afford any.
There is another statistic to consider:
The odds of winning are 0% if you don’t buy a ticket
** Brother can you spare a buck?
The probability of winning the jackpot isn’t enough to declare every lottery game irrational. You need to consider the probability of winning multiplied by the “real” payout — in other words the expected value of the real payout.
Sure it’s rational to play: when the expected value of the real payout = $1. I assume that the player is risk neutral.
Now assuming that you want “the real” payout to be a lump sum cash-in-hand less taxes, the nominal jackpot must grow to cover discounted cash flows (present value) and those pesky government tax predations.
Once the *nominal payout* becomes very large, people flock to buy tickets. Thereby moving towards rational behavior in a game usually for dupes only.
A state lottery board could use dynamic pricing — when the expected value of the *nominal payout* falls below $1, lower the price of each ticket so that it continues (more) rational to play. But, of course, the state bets on irrational behavior and usually wins.
anti-supernaturalist
My boyfriend bought a scratch-off ticket a couple of days ago for one dollar. We scratched off three dog paws in a row, won ten dollars, and ordered crab cakes with dinner. My initial inclination when he’d asked for a dollar to buy the ticket was to yammer off the one about the statistical likelihood of being struck by lightening versus that of actually winning something in the lottery. I was glad I kept my mouth shut because, hey: ten dollars.