Friday, January 7, 2011

What are the Odds?

As is often the case, the news media fills their slow news days with the ever popular coverage of people lined up to purchase lottery tickets. Apparently the Republican “takeover” of the House is now old news and eyes are glazing over regarding the pending repeal of ObamaCare.

Oddly, when a lottery like the Mega-Millions has accumulated a huge jackpot, people mistakenly begin to believe that the odds are tipping in their favor… somewhat like the belief that a slot machine that hasn’t paid out is a while is just straining to burst from pent up... odds, I guess?

As a result, thinking their dream of untold riches is close at hand, they line up to purchase lottery tickets… or as I like to term it; to pay their “Stupidity Tax”. Sadly, the demographics reveal that those in society who have the least amount of disposable income tend to purchase lottery tickets. The subtle disclosure on the Oregon Lottery ads even states: “For entertainment only, not for investment purposes”.

The truth is that most people have no sense of actually how astronomical their chances of winning the mega-jackpot are. A brief comparative look at the odds of various potential events is in order:

Being killed in a car crash: .......... 1 in 5,000
Being killed by poisoning: ............ 1 in 86,000
Being killed by a dog: ................ 1 in 700,000
Dying while in the bath tub: .......... 1 in 1,000,000
Being killed by freezing: ............. 1 in 3,000,000
Being killed by lightening: ........... 1 in 2,000,000
Being killed in a tornado: ............ 1 in 2,000,000
Being killed by falling out of bed: ... 1 in 2,000,000
Being killed in a plane crash: ........ 1 in 25,000,000
Winning the Mega-Millions Lottery: .... 1 in 176,000,000
Being killed by space debris: ......... 1 in 5,000,000,000

Some would argue that the odds are zero if you don’t buy a lottery ticket at all. And they would be correct. But once you decide to part with that cash; really, how strong is your potential return on that “investment”?

Some critics of government lotteries state that it exploits those who can least afford it. Yet the Stupidity Tax is also a voluntary one. I personally am not a strong anti-tax adversary, but I do freely exercise my choice to not pay this particular tax.

Still occasionally there are winners. Two ticket purchasers recently won $380 million. Hopefully the winners won’t be killed in a car crash on their way to the bank. Frankly, the odds aren't very good.


Gorilla Bananas said...

It's obviously a bad investment in a statistical sense, but I wouldn't go so far as to call people who buy lottery tickets irrational. If the cost of the ticket has a negligable effect on your lifestyle, a tiny probability of a huge increase in wealth may be be a good deal for you. Don't forget than insurance is also a "bad investment" in a statistical sense.

DJan said...

I have bought a few lottery tickets in the past, and I know the odds. Sometimes it has been to help support the environment or whatever. It never occurred to me that I might actually win. Good post, Robert.

Octopus said...

Why are 'chances' always called 'odds' when the probability of picking any number divisible by two are 'even' ? And why is a 'lottery' called a 'lottery' when the return on investment is very 'little' ?

Infidel753 said...

GB has a point. I've occasionally bought lottery tickets, but only when I had enough disposable money that I could blow a few bucks on them and not miss it.

Unfortunately, as you say, most lottery tickets are bought by those who can least afford them. Most likely because the same people are least capable of accurately assessing probability.

The fiendish part is that, every time, someone eventually wins. And the innumerates who didn't buy tickets think, "If I'd bought one, it could have been me!" (Yes -- it could have.) And those who bought tickets think that, in some sense, they came close.

billy pilgrim said...

i get awfully tired of receiving emails at work encouraging people to join the lottery group. it makes me feel anti-social for not joining not to mention all the time wasted by the lottery addicts.

Jon said...

Realistically, the odds are essentially the same whether you buy a ticket or not. That said, it is still fun to buy a dream for a buck.

Robert the Skeptic said...

Bananas Oh I would strongly disagree; purchasing lottery tickets is the epitome of "irrational"; emotional considerations buoying hope of winning shows a profound lack of understanding of how great the odds are against winning.

The problem lies in our inability to truly "visualize" the scope of the problem. Take for example your computer screen: say your monitor is set for a resolution of 1024 x 768. If the screen is all white except for a single red pixel, your chance of randomly hitting that pixel with a pin is only 1 in 786,432. In comparison to the equivalent lottery odds, you now must randomly pinpoint that red pixel on a screen 14 x 14 feet in size. Forget random - I'm not confident you could find that single pixel even if you looked for it.

Insurance is not based on straight randomness but on "calculated" probabilities. Car accidents occur more than house fires, so car insurance costs more than hazard insurance. From an actuary: "Gambling creates risk; insurance protects you from risk. Insurance responds to risk you already face. You own a building, so you want to be sure it's there tomorrow. The next day the building is either there, or it's not. Insurance, unlike gambling, does not create risk.

DJan Well we like to justify our choices to diminish that we have ignored the overwhelming odds not in our favor. Most lottery funds go into general "economic development", whatever that means. Would it not be more direct to contribute directly to a cause we support... and in doing so, also get their monthly periodical?

Robert the Skeptic said...

Octopus The terms "odds" and "even" are mutually exclusive... "even" generally meaning 50/50. So the odds that a coin toss will come up heads or tails are "even odds".

Lottery from the phrase "casting lots".

Infidel There is not a winner following "every" lottery draw, hence the increase in the sizes of the pot after each run. What people get caught up in is that they think that the larger the pot, the more "likely" there is to be a winner. This is irrational.

We do this when we think we came "close" to winning. In a single-digit lottery we think that if we picked 43 and the winning number was 42, we were "close". Randomness is not sequential, we either selected the winning number or we did not - 43 was equally as off as 176,397,243. We think of numbers as sequential, that's just an emotional position we impose on our thinking when dealing with random numbers.

Robert the Skeptic said...

Billy Well pooling resources does increase your odds; but then your winnings would be proportionally divided. But yes, those e-mails are indeed annoying.

Jon Well actually the odds are not the same. Your odds of winning if do not purchase a ticket are 0 in 176,000,000. Thanks for visiting and commenting.

Kay Dennison said...

I'm not a gambler. I am too frugal for that. That said, I don't play the lottery. I do buy an instant ticket now and again and usually get a winner now and then. Right now I'm ahead for the year by about $20.00. That won't last but at 2 bucks a ticket, it's a harmless pastime.

Rain said...

For so many who have won it, it hasn't exactly brought joy. I keep thinking I will buy a ticket just for the fun but always forget. If I did, I'd buy one as if fate wants me to have it, one would be enough... Yes, a rather fatalistic view.

Robert the Skeptic said...

Kay I confess I have bought a lottery ticket or two as a lark. But like you I don't gamble as I know the odds are against me. In Las Vegas I used to play the quarter slots just to see how many games I could play before I got tapped out. But when gambling becomes an addiction, then the problems start.

Rain I think what you buy when you purchase a ticket is the fleeting momentary thrill that must "maybe..." And for most, that momentary fun feeling is all we need.

MartyrMom said...

Yep, Robert, each year I purchase 20 to 25 dollars worth to give to dear old dad for Christmas. I help feed his only addiction. I know, I :(

The Mother said...

Unfortunately, the system is stacked against even the winners. There are loads of tear jerking tales about the lucky ones being exploited by anyone and everyone out to make a buck.

They don't hand out money handling smarts with the payout.

secret agent woman said...

I don't play the lottery but I've often thought that the jackpot should be divided up into one million dollar winnings for however many people - say 380 winners for a 380 million jackpot. There's hardly anyone who wouldn't significantly benefit from that sort of cash influx, and many more people could win. And NO ONE needs 380 million dollars. It would still be crazy odds, but a little more reasonable to buy a ticket once in a while.

Robert the Skeptic said...

MartyrMom Well, it you are doing it for those stated "entertainment purposes", have fun with that! The ones who are hoping for it to be a retirement plan are in big trouble.

Dr. Mom Yes, there have been many tragic stories about the fates of lottery winners including even some who have been murdered.

Secret Agent They would have to "manipulate" the winning numbers to have the jackpots come out with the right number of winners for each million. That takes the legitimacy out of the random process.

Nance said...

In SC, where we have a larger than average per capita burden of stupidity, the lottery profits are used to fund education. The irony leaves a metallic taste in my mouth.

I really like your new blog "digs"!

Robert the Skeptic said...

The irony is not lost on me. In Oregon they made a big deal out of emphasizing that lottery funds were to be used for economic development, NOT to fund education. At some point, though, one has to admit that money is money... wherever you can get it from.

Thought I would change the look of the blog as I've changed a bunch of other stuff in my life.. including our actual "digs".

Gorilla Bananas said...

You've missed my point, Robert. Insurance contracts may be based on probabilities, but like lotteries they pay out less, on average, than the cost of purchasing them. The rationality of choice depends on utilities as well as probabilities, and utilities are inherently subjective.

Robert the Skeptic said...

Bananas Insurance is a bad investment in a purely statistical sense. The term "investment" implies that one will gain some compensation in return for taking the risk.

In a rational sense, insurance is not an investment but a "risk management". And unlike lottery odds which have no factors which can be applied which change the odds, the risks covered by insurance contain a myriad of mitigating factors which can alter the odds. Fire can be caused by electricity, gas, candles, appliances, lightening, stupid neighbors... and that is only risk by fire. Winds, storms, earthquakes; the list of very objective factors continually alter the probabilities. Lottery odds again are not altered; and the point of my article was that people believe they are altered by the size of the jackpot. NOT Rational.

Or in the case of insurance versus lottery; regarding insurance, I truly hope I DON'T win!

KleinsteMotte said...

Still waiting for our house fire insurance. The odds against us is that the fire marshall cannot locate the culprit. And we continue to pay insurance while we wait. Of course there's the lawsuit that might make it to court in the next 10 years or so. We are not a priority in the backed up court cases because ???
By the way I find it interesting that we put facts on death by car and airplane. Why are we spending so much on air security when the odds are in our favour??
We're more likely to die driving to the airport.
Lotteries are a way of life. Call in to win, join now and maybe win...That happens all daylong. Even on line things pop up. Win is a word that suggest profit.
Take a chance or ?? Dream.
You are right though. I love the image of a red pixel. So real.

secret agent woman said...

Not if they drew/generated the right number of winning numbers.

Robert the Skeptic said...

KleinsteMotte When there are vested interests on the odds, such as in an insurance payout, there are potntially corrupting influences which effect the payout.

SecretAgent You are correct, such ad in a "door prize" where one or more winners are selected from the pool of purchased tickets. But then that dramatically lowers the odds in favor of the ticket purchasers. For the lottery to be financially lucrative (and it is) the winning number(s) need to be outside of, and independent from, the pool of selected numbers, that is, tickets sold. This is why often nobody has the winning number. It has to be this way for the lottery to be accepted as legitimately random.

Entre Nous said...

I actually bought a ticket thinking, what the ----. Won 150.00. Not going to do it again for a few years. Thats about all the luck I have :}

Robert the Skeptic said...

Entre Nous Matching a smaller set of numbers yields better odds for the ticket purchaser, hence the higher number of winner and, likewise, the smaller jackpot.

Megamillions said...

People used to live with hopes. What are the odds to find a big love of your life? Heh...
However, nowadays, lottery companies funds many good projects like environmental ones. So some money are returning to players, this or another way.
To improve your odds, please play in group or setup an lottery syndicate. It helps for regular players.