Why are people so poor at math/finances? (Gambling)

Great Debates
1

The Powerball lottery this past week was up to some $250 million or so. I was listening to a news report about it on the radio and I heard one person say that he was buying $500 worth of tickets, hoping to win. :eek: He said “It’s a good investment” :eek: :eek: :rolleyes:

Now I’m not out to begrudge anyone the enjoyment of taking a buck and plunking it down on the lottery. I do so myself from time to time. But I don’t consider it an investment. I understand that, for all intents and purposes, I’m throwing that dollar away. [sup]*[/sup]

Basic math will tell you that playing the lottery as an serious investment is pretty much sheer lunacy. You’d be better off getting shares in a uranium field in Asbury Park, or trying to invent no-cal pizza. But to view $500 on the lottery as a serious investment?

Of course, this is really just an extension of people’s (maybe mainly Americans) poor finance skills. People will shop all over looking to save a few bucks on an item, then put it on their credit card at 18%. There are litterally billions of dollars sitting around in checking accounts that earn no interest.

Why are people so ignorant of basic math/finance skills? Logic should tell you that you’re better off taking $1000 out of savings and paying off an 18% credit card bill, than leaving it in savings to earn 3% (if you’re lucky). Yet, many of us leave the money in savings and allow the credit card interest to grow faster than the savings interest. There are plenty of people who do not invest in their company’s 401(k) plan (if they have one, of course) despite the obvious benefits of doing so.

This isn’t meant to be a rant, for two reasons. First of all (aside from the plunking mega-money on the lottery, and the not contrubuting to the 401(k)), the above person was me. I had credit card debt that I got into without giving much thought to the matter. Secondly, I want to get to the root causes. Why do people think and act this way? In my case, it was largely a matter of not being taught this at school. Basic finances were not taught, and I did not learn it from my parents either. The only finances education I had in school was in third grade, when the teacher gave us all “checking accounts,” gave us “paychecks” and “bills” and taught us to balance a checkbook. However, by the time I needed to put this skill to actual use, it was long forgotten. Through the rest of my elementary and high-school education, I received no financial education at all, and not having any real money at home, I took no interest in it. Eventually (as most people do, I guess) I did take an interest and began learning about these matters.

I’m not here to lay blame on anyone for my personal delay in learning about these matters. I could have educated myself on the subject in college, but chose not to. But my wonderment is this… the high school I went to was clearly sub-standard when it came to secular education. So, I expect that in my case, I was given no instruction. What about everyone else, however? Are the vast majority of people as ignorant as I was about basic matters of credit card debt, savings and viewing the lottery as an “investment?” I don’t know if the person on the radio was spending rent money on the lottery or if it was simply “mad money” that he had, but we all probably know of people (and I’m not talking about people who have a serious gambling addiction) who do spend serious money on the lottery (or other forms of gambling) that they do need for rent, food and the other neccesities of life and view it as an investment. Why? Why are we so ignorant of these matters?

[sup]*[/sup]The reason I play anyway is best illustrated in this story:

The story is told of old Hershel, who lived seventy nine years in righteous piety. Finally a few weeks before his eightieth birthday, he offers a prayer to God.

“Dear God, I’ve never asked you for anything before. I’ve lived my life according to Your will and did everything You asked of me. Now I’d like that, before I turn eighty years old, I’d like to win the lottery. I’d like for my wife, who has struggled in poverty all these years, to have a comfortable end to her days.”

One week passes, and Hershel doesn’t win the lottery. Another week, still no winner. A third week. A fourth. Hershel is getting frustrated. After a fifth week passes, and his eightith birthday quickly approaching, he finally loses his patience.

“Lord! Is this so much to ask. I’ve lived my life by Your teachings. Everything I’ve done, I’ve done for Your sake! Why can’t I have this one thing for myself?!”

The heavens open up and a voice booms down:

“Hershel, do me a favor and help me out a little bit… buy a ticket!”

So, I play on the off-hand chance that God has decided to grant me the favor and fortune of winning the lottery. I don’t want to make it any harder on Him than it has to be. :slight_smile:

Zev Steinhardt

2

zev, concentrating on the Lotto issue, several questions come to mind:

  1. In terms of gambling, is the axiom that if the rate of return on the bet is higher than the odds against winning, it is a good bet, a correct axiom?

  2. If yes, is the axiom inapplicable at extremely high odds? IOW, many people would agree that a bet paying 3-1 that you have a 50% chance of winning is a good bet. Does the same apply when the bet pays 1 billion - 1, and the odds of winning are 1 in a million?

  3. Specifically, does any of the above apply to the Lotto, where you cannot be certain of the amount of your winnings, as there may be co-winners?

  4. Stepping away from the Lotto example, and going toward ‘investment,’ is a high-risk, high-yield investment ever an intelligent investment stratagy? Does it ever make sense to make an investment with potentially huge returns, but where the likely result is that you will lose most or all of your investment?

Sua

3

**

I’d have to honestly state that I don’t know. I was never much of a gambler. It sounds right to me, but I can’t state for sure. But, in any event, considering the astronomical odds against winning the lottery, is it ever really a “good bet?”

**

Those are all very questions, which I don’t have the answers to.

Sometimes it is a good idea. If one is very young, and can afford to lose the money, AND if one is well-educated about the investment and willing to take the risks, then sometimes it may make sense to do so. But one cannot ‘educate’ himself about the lottery since, in the end, his chance is exactly the same as someone who just allows the computer to pick random numbers (assuming an equal number of plays, of course).

In the end, as I said, I’m not railing against the lottery. I play it too (but never more than a buck at a time!). What I’m railing at is people * can’t afford to lose the money* doing so anyway. And the same would apply to legitimate investments as well too (except that it’s far more common for people to blow money on the lottery than on bad investments).

Zev Steinhardt

4

Drawing on Modern Portfolio Theory, I would say that yes, under certain circumstances, it pays to make an extremely risky investment with a potentially huge return, IF AND ONLY IF the following conditions apply.

1.) You can afford to lose.
2.) You can make the investment as part of a portfolio of investments whose performance is not correlated or negatively correlated with one another.

Some would also add a third condition: that you have also taken into account the risk-free rate of return, or that which you can get by buying a Treasury that matures at the date you need the money. This is because all investments have an “opportunity cost” equal to the risk-free rate of return.

With regard to the Lotto, the odds are lousy by design. If the odds ever favored the ticketholders, the Lotto would cease to have utility as a fundraising tool, and would quickly cease to exist. In the meantime, the odds will always favor the house.

5

I think that, in the case of people risking money they can’t afford to lose by playing the Lottery, the state is at least partially to blame. The states need Lottery revenue to fund programs (ironically, many of these are programs that pay welfare money to people who are spending money they can’t afford. . .in the words of Andy Rooney: “This is robbing Peter to pay Peter”). The states all produce ads for the Lottery which imply there’s no smarter thing you can do with your money than “invest” in lottery tickets!

On an interesting note, I had an uncle who bought about $40.00 worth of various lottery tickets per month. He did this from the time he retired til the time he died. He could well afford to lose the money. But the interesting thing is, in the average year, he “won” about as much as he spent. Of course, one could argue that the money would have been better spent in investments, but then he wouldn’t have had nearly as much fun. He got a little “boost” every time he won. It was money he was more than willing to spend on what he considered entertainment.

BTW, I was taught to balance a check book in high school, but the rest of my financial education has been “self-taught”.

6

You can’t study the lottery without invoking utility theory. Utility theory explains things like why poor people play the lotto more than rich people, and why poor people tend to be under-insured and rich people tend to be over-insured.

Basically, even though the mathematical expectation of a lottery ticket may be negative, the utility of it may be positive if the ‘utility’ of $1 is less than the combined utility of a 1/10,000,000 chance of winning $5,000,000, PLUS the utility of having hope of someday getting out of your financial circumstances, PLUS the utility of the entertainment of the lotto itself.

Take insurance. In terms of mathematical expectation, insurance is a ‘bad bet’. If an insurance company is willing to pay you $100,000 if you die, they will charge you premiums such that on average people will pay more in premiums than they recover in death benefits. That’s how they make their profit. Insurance is gambling, and the insurance company is the ‘house’, and takes a percentage.

But rich people insure because the risk of losing everything to them is greater than the cost of the premiums. Poor people under-insure because they have less to lose, and the premium payments have greater utility. So even though the math is the same for rich and poor, their behaviour is very different. Utility theory explains the difference.

As for the failure of people to invest, I think that has more to do with a young person’s inability to really understand the passage of time. When I was 20, thinking about retirement seemed to be not very important, because retirement seemed impossibly far away. Even ten years seemed incredibly distant. So it’s easy to say, “I’ll worry about that later.” Now that I’m 40, I really feel the press of time. If I want to retire at 55, the clock is really ticking. Suddenly, saving for retirement becomes incredibly important - maybe one of of the most important factors in my financial thinking. Every time I want to buy something expensive, the thought creeps into my head, “But if you invest that money, think about how much more you’ll have in 20 years.” I NEVER used to think that way.

7

Bets with positive expected values are not necessarily “good bets” for any given individual. You have to take into account marginal utility theory. For example, take coin flip bet where you pay 50k if you lose but receive 60k if you win. The bet has a positive expected value but it’s not really a good bet for someone whose entire net worth is 50k, while a multi-millionaire would be an idiot not to take this bet.
There are also cases where it could be considered a rational bet even if there is a negative expected value. Take the lottery. The utility of the huge win may well be worth the relatively low sum for entry even if the bet does have a negative expected value. $500 is probably out of most people’s utility for the poor odds on the lottery and if it isn’t, then the marginal utility of the winnings isn’t worth the bet (Bill Gates doesn’t won’t signifantly benefit from an extra couple hundred mil)!

My mind boggles at people’s poor understanding of the concepts of applied mathematics like finance and gambling odds, particularly “bernoulli trial” bets where the previous outcomes don’t effect future outcomes (Like roulette). It’s amazing how many people think that just because black has come up 5 times in a row that red is now “due.” I always get a kick when I after I explain the idea to someone very clearly I still get a “Yea but, you know.”

8

Re the 100 mil awards vs. the 1-7,000,000 odds:

It depends on how many tickets you buy. Step the numbers down a little. If a $1, 1 in 2 bet pays off more than $1, then buying lots of tickets is a good idea, because in the long run, your more than $1 will pay off the $1 losses.
Now imagine a $1, 1-10, $20 payoff. Now, if you win, that will pay off enough to cover your losses up to that point, statistically speaking. But, if you stop playing before you hit that 1 in 10 shot, you lose money.

Scale that up to the lottery. A $1, 1-7,000,000, $100,000,000 payoff is only a good investment if you can buy 7,000,000 tickets.
Note!: this is assuming that the odds are not recalculated for each ticket. If you buy 7,000,000 random tickets, rather than buy every possible ticket, then you haven’t improved your odds enough to move into the investment category.

But I am curious why people can’t either predict that they will lose money, or notice that they are, and stop.

9

Boy, so many ways to respond.

First the direct op, why are we lousy at probability? We are wired to be lousy at it. At least at probability as defined by mathamaticians. We are wired to count recent and more visible events as more salient, more heavily weighted, than accumulated past performances. We are wired to discount payoffs that are percieved as farther off in the future. We are wired to compare payoffs to what we already got, rather than strictly logically. It is more about psychology than math. These examples from Inevitable Illusions:

A few choices:

You are given $300 providing you choose
A. To get $100 more for sure or
B. To toss a coin and get $200 more if you win the toss.

Most choose A.

You are given $500 providing that you choose between
A. Giving back $100
B. Coin toss - lose and you pay $200.

[spoiler]Most choose B.

Why do we decide like this when all the choices are probablistically equivilent?[/spoiler]

Utility theory is a way of putting it I guess, but the real point is that we take intellectual shortcuts, that were selected because in most conditions that were critical to our survival, they were accurate. But now they result in the cognitive equivalent of optical illusions. And if we are not careful our shortcuts can lead us in devstatingly wrong directions.

10

Another factor - humans are wired to look for causation. It’s wired into us in a very powerful way, because it’s such a strong survival trait. It’s how we learn. Touch something hot, it’ll burn you. Hear a growl, and soon a carnivore will appear. That sort of thing.

This makes us uniquely unsuited to making sense of things that do not have causes, such as random trials. This is why there is so much superstition in the world. Baseball players put on a new hat, and hit a triple. The next time, they don’t wear the hat, and strike out. The brain then starts screaming, “It’s the HAT!”.

I know people who swear that if they tap the ‘pull’ button with the back of their hand, they win more than if they press it with a finger. Or people have ‘lucky’ machines, or lucky shoes or hats. All of these beliefs are the brain’s attempt to assign causation to what it’s seeing. And once people buy into the causation, they no longer believe in the odds, because they have a ‘secret’.

‘Common sense’ does not apply to random events.

11

It get’s even worse than Dseid’s examples. I can’t find the studies that were done though they can be found in this book (a great read if your really interested):
http://www.amazon.com/exec/obidos/tg/detail/-/0070504776/ref=pd_sim_books_2/103-3161427-0678233?v=glance&s=books

The upshot is that people prefer a certain gain to an uncertain gain with a higher positive expected value and an uncertain loss over a certain loss with a lower negative expected value. This is why the average person is a horrible investor - they take their profits too soon but let their losses ride.

Ill make up some examples to explain but they are only to illustrate, not from any study:

Given these two choices:

a. Get 50 dollars
b. Flip a coin and get $110 if you win but nothing if you lose

Most people choose A even though B has a greater positive expected value.

Given these two choices:

a. Give me 50 dollars
b. Flip a coin and give me $110 if you lose but nothing if you win.

People will against choose B even though it has a lower expected value.

12

I don’t know why I typed against. It shouldn’t be “again” either.

13

I remember something on TV about a couple in CA(?) who, having spent $150,000 (thats one hunded and fifty thousand dollars!!!) finally hit two jackpots in the same day, to the tune of several millions of dollars. The good news is: that’s kind of funny, in the buggering common sense aspect. The bad news: a great number of people without neither the wit nor the finance are going to be encouraged to injure themselves irreversibly.

I like to gamble a bit, its fun. I also have a guilty pleasure in watching a good prize fight, that is, something outside the grasp of the pustule Don King. But in both cases, if pressed, I must admit that the human cost far outweighs my petty pleasures.

Abolish them both.

14

I’m not looking to abolish the lottery, elucidator. Am I’m not out to get gambling either. I don’t see a problem with someone taking some “mad money” (that they can afford to lose) and going to Vegas and taking their chances. If that’s their amusement and they can afford it, fine and well.

I just want to know why people make foolish financial decisions, when simple mathematics shows that better decisions can be made. The lottery is just one example of this, but the others I cited (people earning 3% in the bank while paying 18% in credit card debt) are equally valid.

Zev Steinhardt

15

Sometimes decisions aren’t made just on the numbers. For example, I have at times been the person paying 18% on my credit card while earning 3% on the money in the bank. I knew perfectly well that this was costing me money. I also knew that if I took the money from the bank to pay off the credit card, I would probably not put the money I saved on credit card payments into the bank.

16

Hmm, 250 Million you say? Quite some time back, me and a friend calculated up how many combinations of numbers were in the powerball. It came to like ~42 Million.

See, If you had 42 million, that[/ would be a good investment.

17

“See, If you had 42 million, that[/ would be a good investment.”

If someone else also played your numbers you’d get less.

"I do so myself from time to time. But I don’t consider it an investment. I understand that, for all intents and purposes, I’m throwing that dollar away. "

Still a person who buys 500 tickets has better odds of winning than someone who only bought one ticket, right?

To me a lottery is just another tax on poor people, because the rich don’t need to play it.

18

The reason why so many people are terrible at probability is that so many people don’t understand probability. I often make the joke that everything has a 50% chance of occurring. Either it will, or it won’t. It wouldn’t surprise me in the least if many people took this at face value because they don’t understand the concept of probability.
It’s why the house can win. They give you 7 to 1 odds on a hard eight in craps and all people can think is “wow. For $1, I can earn $7.” But if they took the time to calculate it out, they’d see that the correct odds are 8 to 1. So by lowering the payout, the house earns money over the long run by offering up what people think is a good deal.

The odds of winning the jackpot at Powerball are 1 in 123,396,455 but even that number is misleading. You have to factor in odds that will help you (lesser prizes) and odds that someone else will win the pot too (unknown, but estimatable) as well as taxes on the final prize.

suasponte, you are correct in your analysis but there’s one thing that’s different for large prizes than for smaller ones. We’re not talking about a mathematical hypothetical where you have an infinite number of trials and in the long run you’ll find positive expectation. The person buying lottery tickets has a finite amount of time in which to buy them and almost no amount of spending will equal the amount they’ll win if they win the jackpot. This changes things for two reasons.

  1. Any jackpot they win, from $1 million up to last night’s $215 million will make people come out ahead no matter how much money they put into it.
  2. Using this line of reasoning, people spend a lot more money than they probably should.

The odds don’t change. You still have a 1 in 123 million chance of winning whatever the pot is.

Last night got the better of me and my friends and we put $30 into a pool to share the jackpot. We won $10 total which is much better than I ever expected us to do and statistically better than average.

19

Need??? You’ve got to be kidding.

20

In my opinion, the most outrageous feature of state lotteries in the U.S. is that the winnings are taxed, at least at the federal level. When you couple this with the fact that most state lotteries typically have about a 50% payout ($5.00 paid out if prizes for every $10.00 of tickets purchased) you’ve got about the worst “investment” imaginable.

Not all lotteries, however, are quite this bad. UK Premium bonds aka, the perpetual lottery ticket, actually have a positive expected return, about 3.5% – plus, your initial capital is never lost.

Premium Bonds

The truly hilarious thing is that Premium Bonds are, apparently, illegal in the United States!