Lotto Is a Place Where Nothing Ever Happens

The Powerball lottery jackpot, which now stands at $20 million, is tough to win — and sometimes, nobody wins it.

It’s incredibly hard to match all six numbers drawn for the game. To get an idea of just how long the odds are, software engineer Andrew Arrow built a clever little program that randomly generates six lottery numbers (including, naturally, a powerball), and then spits out an infinite set of random guesses, counting how many matches the computer finds.

In the time it took us to write this post, the applet made 5,467 guesses and never matched more than two winning numbers on the same ticket.

Of course, the trick of playing the lottery is that the belief you might win the jackpot can be neurobiologically as satisfying as actually winning. In which case the lottery isn’t a tax on people who are bad at math; it’s cheap entertainment.

(HT: Jennifer Godwin)


"It's incredibly hard to match all six numbers drawn for the game."

there is no "skill" involved so it is not "hard" or "easy"

"'s cheap entertainment."

and that basically sums up everything in a neat package.

thanks for the posting and the links in the blog though, they were an entertaining read and it cost me nothing!
(except some time...)


Saying you have to match 6 numbers is technically true, but could be misleading. Most people would assume you have a 1-in-10 chance of matching each number, when really it is a 1-in-99 chance. I don't know exactly how the drawings work, but don't they have 99 balls circulating in 6 tanks. So in each position you have a 1-in-99 chance of getting the correct number? By making each ball a double-digit number they effectively reduce your odds by 90%(for just one ball) while in people's minds the odds are much better ("I just have to match 6 numbers!", when they really have to match all 12 numerals and in the correct order!).


I highly doubt that I will feel just as satisfied if I win the lottery or just knowing I might win. But, I have never played the lottery and wouldn't know that for sure.
Playing "the lottery isn't a tax on people who are bad at math; it's cheap entertainment." That's funny.
I just wonder if the sensation of satisfaction is greater when the lottery player has lower income than average or higher. My guess is that the lottery player with higher income than average feels less satisfaction playing because they don't worry so much of financial matters as much as lower income players do. So the fantasy of winning for someone with less income player is more satisfying than the higher income player.

Joe Hass

The program you link to is flawed. In order to win any Pick 6 or Pick 5+1 game in the United States, you merely need to match the numbers. That program only counts a match if it matches the number in the exact position. That makes the odds harder (in the hundreds of billions instead of hundreds of millions).


that program is flawed since it does not count a number correct if it is in a different order. For example if the 4th number in the first guess is 8, and the random number generator picks 8 as the 2nd number at some point, that is not considered a correct pick.


If you play the lotto/tax , you should always play at least one number above 31 so you have better odds of not splitting the pot.

I did a sociological science project in school where I polled lotto players about how they chose their numbers. They gave various reasons -- and some choose randomly, i.e., having no specific reason -- but one common way is to use one or more important dates (birthday, anniversary, etc.). Certainly not everyone uses dates, and some dates could have numbers above 31 if the year is included.

But enough people do use dates, that it makes sense to always pick at least one number outside the month-day ranges. Doing so doesn't improve your chance of winning the lotto, but it does improve your chance of not splitting the pot if you do win. This also rules out using a randomly generated "quick pick" unless you are allowed to choose a set with a number greater than 31.



It is a tax for people who are bad at math. Weather the feeling of buying ten $1 lottery tickets outweighs a $10 movie ticket for any individual may define it as cheap entertainment or not.

The expected outcome from playing the lottery is something like 30 or 40 cents on the dollar (including consideration for taxes, multiple winners, but not including the marginal value of a dollar to a multimillionaire vs. the marginal value of the dollar at risk). In contrast a hand of Blackjack correctly played has an expected outcome of something like 97 cents on the dollar.


Steve (#5) is correct. The program you link to matches only on exact permutations, not on combinations. The odds of matching six numbers in _any_ order is far higher than what that app indicates. (Though it's still not wonderful.)


The odds of getting 5 + powerball are one in (59 choose 5) * 39, or one in 195,249,054. That's two thirds of the population of the US. If anything it should be a surprise that the jackpot gets hit as often as it does.


You can be 100% sure you won't have to "split the pot" (don't throw me in that briar patch!!) by not purchasing a ticket, too, but it doesn't improve your chances of winning anything.


The odds of any six numbers winning are the same as any other six numbers. Other than worrying about splitting with others who pick dates (which definitely affects your expected value), there's no reason not to just play these numbers: 1-2-3-4-5-6. Easy to remember, but you just *know* those numbers will never come up. Neither will the numbers you play instead.


the jackpot is at 20 million? that means someone just did the impossible, in your eyes,, and won!!


The drawing works like this:

1. They pick 5 balls out of 59 circulating in a tank.
2. They pick 1 ball out of 39 in a separate tank.

They say the odds of winning it all are 1 in 195,249,054 and the odds of winning $200k are 1 in 5,138,133. You win $200k if you get all 5 of the first draw but not the 1 of the second draw.


Somebody always wins. It may take months, but the jackpot keeps rolling over, and eventually somebody wins it. Believing you can win is the same as believing that if you go in the ocean you'll be attacked by a shark. It is a belief in destiny.

But pretending that playing the lottery is a complete waste of time and money is like saying humans aren't the natural prey of the shark. When we're in the water, we are.


Isn't there someone in a lawsuit against a lottery about the lottery not publishing the amount of losing tickets versus winning tickets? That showing the odds is not really true against the actual amount of tickets sold?

My question is if the multistate lotteries are some how biased against southeastern states or is it just that more people spend more money in mid-west states etc which generates more winners in those locations?


how about a lottery bailout?- just have the government put up $350 billion for a prize, and see how many people buy tix- not much different or unethical than giving it to bank of america so they can buy more banks and become even too-bigger-to-fail


Check out the googleads next to the number generator.

Eric M. Jones

I read once that you are 5000 times more likely to be killed by an asteroid THIS YEAR than that you will win the Powerball Lotto with one ticket.

People throw money into this gaping hole anyway...a tax on people who are bad at math. And they say, "somebody's gotta' win." But I know that I won't win...correct to nine decimal places.

But I have an over-riding reason not to play even the smallest Lotto or raffle: My brain greedily slobbers on the fantasy of what I will do with the winnings that I will never ever get. So --book it on down the road Jack--my brain's got better things to do.


@dave #2

Not quite sure what you're trying to say, but you're really tripping over the math and making a number of wild assumptions. I'm pretty sure that people recognize that their chances of any given number are roughly one in ten (that is, 5 balls are chosen from a pool of 59, and the power ball is 1 out of 39), and cannot figure it out any further, and thus erroneously assume that their odds of winning may be higher. Anonymous #9 shows the true actual odds.

@anonymous #9

Not surprising at all, because you're only showing the odds of one play. I don't think I know anyone who plays only once per ticket per drawing. I'd say 5-10 picks is more typical.


I had a stats teacher in high school who pulled out all the old tricks about things that are more likely than winning the lottery (struck by lightning 5 times, getting into a car accident with your long-lost time while simultaneously getting bit by a shark and having a vending machine fall on top of you, yada yada...)

But at the end of it, he said, "But I do still occasionally play the lottery. Because as bad as the odds are of you winning are, do you know what the odds of you winning if you DON'T play are?"