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.
> One of my cow-orkers would pick numbers like 1 2 3 4 5 6
> his rationale was that if that did win, he probably would not be sharing the prize with anyone else.
Unfortunately, that particular combination is the most widely played combination, so he WOULD have to share the prize with a lot of people. He'd probably only get a few thousand dollars out of it at most. But it sounds like he only does it so he can sass other people anyway.
The argument of buying a fantasy on the cheap is an interesting one, because each dollar (or stack of them) increases your chance of acquiring buyers remorse at some point in your life — it could range from slight disappointment to deep regret — but hey, what are the odds of that!
So you think to yourself I'm a proud carpe diam kinda guy — I don't bother with regrets. Fine, then live without regretting whatever the trajectory of your net worth is _without_ a ridiculously unlikely win-fall.
Now, you'll excuse me while I go check my numbers.
> Gasp Says:
> You’ve had too much crack, Dave.
> Sure. Lotteries were set up by the strong to prey on the weak.
You reckon not, Gasp? The weak-minded can't see that the house (in many cases a government controlled body) always wins, and the house is happy to focus their attention on the magnificent silver M&M. If you don't think the house is strong, then just try setting up your own lottery – you might find it will suddenly flex its muscles at you or worse. A greedy feasting predator fiercely defends its prey against other predators.
We all know the statistics… So what?
The people who won also knew the statistics.
And I am sure they are happy to have played while ignoring people begging them not to play…
I am not stupid.
I am not bad at maths; I know the chances are close to none.
But I also know many people won.
Remember one thing: By putting someone down, you automaticaly think of yourself as superior (more intelligent, did not get aught into this "scam", etc…).
never "wasted" my money on lottery yet …
so i guess i dont under stand the point here …
hehe …
I wonder how the odds of winning the lottery compare with the odds of one's hard drive failing.
I mention this because I so often see situations in which people dismiss relatively high-probability threats (failing to back up hard drive, failing to purchase flood insurance, failing to wear seat belts, failing to wear a motorcycle helmet, smoking tobacco, etc.) but embrace low-probability benefits (winning the lottery).
That said, when the jackpot reaches outlandishly high levels, I buy a ticket. One ticket. It's worth it to me for the entertainment value. It costs about the same as a candy bar from the vending machine, but the potential benefits are much greater.
> One of my cow-orkers would pick numbers like 1 2 3 4 5 6
> his rationale was that if that did win, he probably would not be sharing the prize with anyone else.
Actually the best way to increase your odds of not having to share the prize is to use quick picks (lottery computer picks numbers). Because most people do a poor job picking random numbers. They use birthdays (limiting some numbers to 12 and 31) or other non-random selections. If a good number of people pick amongst the same non-random subset of numbers, they are more likely to have to share.
Jaems said:
Why not skip the trip to the store, and spend the commute time daydreaming what you'd do with a MacArthur genius grant? Then put the money you would have spent in a jar, and at the end of the month you and the wife can go out for dinner and a movie.
That said, why do we so often fall back on the dimensions of a football field to supply an idea of scale? I myself find it compelling, yet I can count on the fingers of one hand the times I have actually been in a football stadium.
The odds of winning the lottery are 1 in 146,107,962. The lottery is called the stupid tax.
The idea of marriage is that, out of all the people in the world, you have found the *one* person who is right for you.
According the U. S. Census Bureau's website, as of 09-21-07, the population of the world is estimated at 6,619,726,434. A spouse is the silver M&M with odds of 1 in over 6 billion.
People get married every day, but you will seldom hear anyone tell them they are stupid for doing so.
That really puts things in perspective for me.
I used to be angry at the way the lottery rips people off. But the nice thing is that (in the US at least) proceedings from the lottery go into the school systems.
So the lottery taxes people who are bad at math, and uses the money to teach math to their children. Good deal.
A friend noticed that a certain subset of number get drawn more often than others in the powerball drawings. I was curious, so I downloaded a list of the winning numbers from the last 3 years, and started analysing the frequencies of individual number picks.
It turned out that a subset of numbers get drawn more often than the others, 3 of the powerball numbers get drawn more frequently that the others and 1 multiplier gets drawn much more often than the others.
This is probably an unintended effect caused by manufacturing inconsistencies in the ping-pong balls used in the drawings, or perhaps even due to variation is aerodynamics of weight distribution caused by the ink used to print the numbers on the balls.
So, can this knowledge be used to enhance you chances of winning…. Yes and no. I wrote a small program to compare combinations of the more frequent numbers against the know winning combinations and found that using the more frequenly picked numbers could increase the probability of winning one of the small prizes. Assuming you pick the same 5 sets of numbers, with the most drawn powerball numbers and a multiplier of 5, the average payback is $20 for every $200 spent. (Notice that this is still a net loss.)
This actually works in favor of the lottery. Suppose someone notices this, tracks the numbers and builds lists of thee numbers. Twice a week, he buys 5 chances with the powerplay option for a total of $10 per drawing. Within about two months he will probably win one lesser prize and the multiplier will bump the prize up to more that the $10 paid for the ticket.
This convinces the player that the "system" works (which it does, since it has inceased the odds in his favor, just not enough to be profitable) and encourages the player to continue. It is however, like pouring water in and out of a bucket with a hole in the bottom.
Niklaus: Good anaysis. So even the relative winners are big losers.
I found a site that had some great stats about the return expected by playing the lottery versus investing:
A person who spends $100 per month on the lottery—slightly less than the average resident of Rhode Island spends on the lottery over a forty-year period would be $144,000 richer if he instead invested that money. A lottery player who spends $50 per month—slightly less than the average resident of Massachusetts—would have an additional $72,201 if he instead invested his money, and the average New Yorker, who spends about $25 a month on the lottery, could be over $36,000 richer by retirement age if he instead invested in the stock market.
For the highest-spending lottery players, the difference is even more dramatic. A person who spends $300 a month on the lottery could instead earn nearly half a million dollars in the stock market—$433,208 more than he would win playing the lottery. According to the National Gambling Impact Study Commission, in 1998 the top 5 percent of players spent $3,870 or more annually, and the top 10 percent spent $2,593 or more3. There are five states where per capita annual lottery spending exceeds $500 (Rhode island, South Dakota, Delaware, West Virginia and Massachusetts), and in the majority of lottery states, per capita spending is over $100.
See http://www.taxfoundation.org/news/show/1302.html
That would be another simple way of looking at the transaction. Then again, those occasional photos of those happy winners of big prizes make the long-term averages difficult to register in the human mind.
You're fighting the power of emotions and the power of "just in case". $1 gives you the feeling of excitement that you -theoretically- might win, even though your chances are close to nil. Is it a worse waste of money than going to the movies? Or to a football game? You exchange money for a feeling. And then there is the power of "just in case". Just in case you might win. That's one of the basis of religion. Believe in god just in case it actually exists…
Conclusion: you're wasting your time. People will continue to play the lottery. And the more broke and hopeless the people, the more they will play, since then only a miracle (which is what winning the lottery really is) can take them out of their misery.
In its most simple probabilistic terms (assuming the jackpot is the only prize, that only one person wins it, and that there are not opportunities for investment [all bad assumptions]), then it would be worth it to buy a ticket when the prize was equal to $146,107,961.
At this payout, high probability of a $1 loss and the low probability of a $146,107,961 gain come out equal.
This becomes more complicated if you add in the possibilities of winning "some" money from getting half or more of the numbers, if you know how many people are buying tickets (to calculate the probability that two or more people will win), and if the real world exists (ie, there are interest paying savings accounts, treasury bonds, and stock markets for investing). It becomes incredibly more complicated if you know that certain number combinations are selected more often than others.
Give a 1/146,107,961 probability of winning – that means if that many or more tickets are bought in each drawing, there is high probability that SOMEONE will win each time. You must not discount the power of general thinking that there is a possibility it will be you.
Problem is, I can calculate how "rational" it is to play… and I can show at what point it becomes rational… but I can't show that people have even considered these calculations when they play… because they haven't. Most people play without any idea of how "rational" they are being (or not).
In Florida, the odds equate to picking the correct 1 inch out of 362 miles!
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. 🙂