# Very Long Odds in the Israeli Lottery

A funny thing happened in Israel last week. The winning state lottery numbers were the same as the numbers drawn three weeks earlier. Lottery officials denied allegations of rigging: “We are in the business of luck, and when it comes to chances and probabilities anything is possible, even the rare and infrequent, like in this case,” said Dr. **Chaim Melamed**, the statistics expert for the national lottery company. An examination of the machines and lottery balls revealed no irregularities. **Yitzhak Melechson**, a statistics professor at the University of Tel Aviv, said that “the incident of six numbers repeating themselves within a month is an event of once in 10,000 years.” [%comments]

## The Wizard of Odds.

Even long odds have their day.

## LB

"The incident of six numbers repeating themselves within a month is an event of once in 10,000 years." Probably true... but the likelihood that 6 numbers will repeat within a month in some lottery somewhere in the world is probably considerably higher. There are probably 200+ lotteries in the world. If they all have the same odds of having a six number repeat within a month, this could be expected to happen somewhere once every 50 years.

## The Wizard of Evens.

If there are 1000 lotteries world-wide, would you then expect this to happen once in ten years?

Somewhere.

## Eric M. Jones

And each winner won 666 thousand pounds.

A sign of the End Times to be sure.

## David S

But the point is that it did happen.

What does this mean for other areas where we rely on the 'impossibility' of very unlikely events - especially the criminal justice system?

"Your Honor, the likelihood of such a close DNA match is such that it could only happen once every 1000 years!"

## Ian Kemmish

It seems incredible (and disappointing) that anyone who claims to be engaged in one of the numerical sciences should write such a headline - or even consent to have an innumerate editor write it for him. It may not be as amusing a demonstration of the independence of trials as that in "Rosencrantz and Guildenstern Are Dead", but this set of six numbers is of course no more and no less likely than any other set of six.

Maybe you should research and publish a histogram of how often, and how far apart in time, lottery draws around the world produce repeated results?

## Nosybear

The professor is right if you are looking at any one lottery, for example, if you're betting that the Israeli lottery will come up with the same set of numbers a few weeks apart, good luck, the probability is the product of the individual probabilities. Now consider the number of lotteries going on at any one time in the world. The chance that any one of them comes up with the same set of numbers in a couple weeks is the sum of the probabilities of all the individual lotteries coming up with the combination, still a rather small number but not impossible. Wizard got the analysis right. Similarly, take a really big Powerball drawing here in the States. The odds of your one ticket winning it are about 130,000,000 to 1. If all the possible combinations are played, though, the odds of someone winning it are 1:1.

## Chad Wafer

What would be more interesting is to know how many winners there were.

## Stephan Schubert

Well, the Jews are living in the year 5771 - so "It's about time" then ;)

## Mani

I always thought that winning the lottery were the same odds as the same numbers appearing two days in a row. Please correct me if I'm wrong.

## Greg

This is not right. While the calculation in the above quote may be correct, it is not answering the right question. See the below link for a good explanation.

http://theoryclass.wordpress.com/2010/10/21/what-is-the-right-question-nobody-cares/#more-1066

## kevin

reminds me of that scene in Casino where Robert DeNiro finally fires the slot machine manager.

## MariaCMS

I believe the calculation of the statistician that this event of repeating numbers will happen only once in in 10,000 years. But that doesn't mean that it is completely impossible for this event to occur three weeks later. If you've studied statistics you would know that nothing is impossible, or in other words, nothing has a probability of 0%. So, anything can happen. I do believe that if something like this happens once more, then there is something going on behind the curtain. But, I believe no one should panic for this yet.

## Greg

I play plenty of poker. I have learned one thing if it can happen then it will eventually. It would be news if something could happen and it never ever did.

When I play poker and the flop in Texas Hold'em is Ace, Ace, Ace people go wow. But in reality it is the same as any other flop. All cards have equal chance of coming out.

Most people are ignorant about statistics.

## JoaquinCMS

I agree with the comments stated before about statistics, there is no such thing as a 0% chance of something happening, as there is no such thing as a 100% chances of happening, with the exception of death. Hence, even if the statistician said it happens once every 10,000 years, it is just an average, since the probabilities of it happening again this year is 0.0001%, which really is not much, but it means it could happen, hence we shall not assume that it cant happen tomorrow or the day after, it is just really unlikely to happen.

We've had questions about the acronym CMS before, and I just wanted to clarify that we all belong to a Catholic school in the middle of Oregon, where we are all live in extreme levels of poverty, we pay for our education by working in one of the factories near the campus. I work in the steroid labs, and I'm a test subject in which the steroids are tested. (Hence the acronym, Catholics Making Steroids).

## Danilo Balu

Last night, here in Brazil, 4 numbers (out of 6) were repeated in our most important lottery after just 4 days of the last drawn (Saturday)! You?d have won USD15millions on Saturday and just USD100 yesterday.

## Greg

14. Greg,

While it is true for a flop of three particular cards is as likely as any other, a flop with a particular value, like three aces, is a lot less likely than a rainbow flow. There are four possible three-card combos that are three aces, and a really large number of bad flops. So while AS, AC, AH is as likely as 2C, 5D, 7S, there are a lot more flops like the latter than the former.

## Chris

Here's a question- how does something cross the line from being "expected" to a "freak happening" or even "evidence of fraud?"

For instance, if no lottery in the world had *ever* had the same six numbers come up in the same months, that in itself would be statistically odd enough to seem noteworthy. On the other hand, if the same numbers came up *three* times in the same month for a given lottery anywhere, that would seem unlikely to the point of suspicion.

How do you draw the line between "truly remarkable" and "bound to happen eventually?"

## DB

The odds of the same numbers repeating them selfs so quickly is outragous but everything is bound to happend atleast once. It has probly happend before and maybe the same winning numbers in one place have been the same in another place at that time. odds might be against it happening but everything is bound to happend once.

## Gerald

This event is possible. I agree that nothing has a 0% of happening. Even if the human race could take in account everything on this planet and cover every minute detail, there is always that chance that something out of the ordinary can occur.

Also, do you ever notice how if a random sequence occurs, say a number with six different digits (Ex. 197530) it doesn't seem random. Yet if a number with similar digits appears ( Ex. 777777) it seems like something "fishy' is going on. I think as humans when we tend to leave something to luck, we hope for something random yet still expectant to occur. When an outcome that seems extremely bizarre comes around, we freak out.

"Expect the unexpected."