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Odds are, stunning coincidences can be expected

Insider BuzzInsider Buzz: Odds are, stunning coincidences can be expected
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Lotteries show that through sheer numbers, the uncanny happens; in Bulgaria, the same combination won twice in one week

History isn't supposed to repeat itself in the lottery. But earlier this month, a 1-in-5.2 million shot came through in Bulgaria, as the same six winning numbers turned up in two consecutive drawings. And 18 Bulgarians profited by betting on recent history: They chose the winning combination of numbers from the drawing four days earlier — which hadn't been selected by anyone the first time around — and split the pot.

The coincidence drew international news coverage and sparked a probe by a government-appointed commission. Bulgarian officials ultimately chalked it up to coincidence.

That might seem dubious upon first glance. But with millions of people choosing numbers in hundreds of lotteries around the world each week, coincidences are bound to happen. And they have, many times, including repeat winners and repeated numbers in other lotteries that didn't receive the international attention of Bulgaria's déjà vu drawing.

With so many numbers colliding each week, the lottery might be the ideal proving ground for something that statisticians have long recognized: Given enough opportunities, the seemingly impossible becomes plausible. "Coincidences aren't really surprising," says David M. Smith, a statistician who wrote a blog post about the Bulgaria lottery. "Unusual things happen all the time, but only some of them are remarkable."

The general principle guiding Mr. Smith and other mathematicians and statisticians in their blasé reactions to the reappearance of the Bulgarian lottery's winning 4, 15, 23, 24, 35 and 42 is that this would have happened eventually. There are lotteries in dozens of countries, and multiple ones within countries — scores in the U.S. alone. Many of these lotteries have had multiple drawings each week for decades. If there have been, say, a million lottery drawings, then a coincidence as unlikely as this one becomes more of a 1-in-5 yawn. That still means that any one player's chances of winning the lottery are close to zero.

The probability of Bulgaria's repeated winning numbers became a subject of some disagreement. A Bulgarian mathematician estimated the probability at 1 in 4.2 million, a figure that was widely reported. Clio Cresswell, a mathematician at the University of Sydney in Australia, came up with 1 in 14 million. Many others arrived at 1 in 5.2 million.

One explanation for the wide range is that Bulgaria has multiple lotteries. Dr. Cresswell's calculations relied on a different Bulgarian lottery with numbers ranging from 1 to 49. Mr. Smith and others made their calculations assuming the possible numbers went up to 42, the correct range for this particular lottery. As for the 1-in-4.2 million estimate, the Bulgarian mathematician didn't respond to requests for comment.

Other lottery coincidences in the past have been deemed more remarkable. In 1986, Evelyn Marie Adams won the New Jersey lottery for the second time in four months, an outcome called a "1 in 17 trillion" long shot in a New York Times article that attributed the figure to state lottery officials. That calculation overstated things quite a bit, by answering the question, "What was the probability that those two particular tickets would win?" rather than, "What was the probability that somewhere in the U.S. in 1986 someone would win the lottery for the second time." The odds of that happening were closer to 1 and 10, according to a pair of Purdue University statisticians who reframed the question in a published letter to the editor.

Lottery coincidences abound. The Columbian newspaper of Vancouver, Wash., got a visit from an Oregon detective in 2000 after it published the next day's winning numbers for the Pick 4 Oregon Lottery, 6-8-5-5. It turns out that a deadline rush to fill in the prior day's winning digits led to a mistaken retrieval of Virginia's numbers rather than Oregon's. Those winning Virginia picks coincidentally ended up being the same as those that won in Oregon's lottery the following day.

Sometimes numbers repeat in the same state. Last month, 4-1-9 came up on the same day, at midday and in the evening, on two consecutive drawings of the Michigan Lottery's Daily 3. And earlier this month, 3-7-5 won on two consecutive drawings in a New York game.

Satori Publishing, a Michigan City, Ind., company that maintains a database of winning lottery numbers, dug through more than 750,000 prior lottery drawings in search of repeat winners at the request of The Wall Street Journal. It didn't find any consecutive victories for the same set of numbers in pick-five or pick-six games, but did find four instances in which a set of five numbers won more than once, though not consecutively, in the same lottery: once in Poland and three times in Pennsylvania.

Bulgaria stands apart because the drawings were consecutive and featured six numbers, making the coincidence even more unlikely. But the attention it drew is consistent with a widely held misconception that there is a system or order that makes sense of random processes. Some lottery players believe that winning lottery combinations can be reasoned out, or that a recent set of winning numbers is less likely to win again than any other combination.

That 18 Bulgarians correctly guessed the numbers on Sept. 10, after none had on Sept. 6, added to the suspicion of wrongdoing. But this could merely reflect one of the common betting strategies for lottery players seeking a system.

Don Ylvisaker, professor emeritus of statistics at the University of California, Los Angeles, tabulated 19.9 million sets of six numbers entered into California's Super Lotto on April 7, 2004. The second most popular set of six numbers entered was the winning combination from the prior drawing. Also in the Top 10 were 1 2 3 4 5 6 and two combinations listed on the back of tickets as sample numbers in directions for entering the lottery.

Other studies of lottery entries show that numbers 31 and lower are chosen more frequently than higher numbers, possibly because bettors incorporate birthdays into their selections. So a smart entrant would choose higher numbers, and skip other combinations likely to be popular so as not to have to split the pot. While betting the last drawing's numbers paid off for 18 Bulgarians, it wasn't a strong strategy because they had to share with each other. Of course, now that 4, 15, 23, 24, 35 and 42 have come up twice in a row, they may seem particularly meaningful to future bettors seeking order in randomness.

UCLA's Mr. Ylvisaker is precluded by contract from betting in the California lottery and by geography from entering Bulgaria's, but he did place one gamble: "I wager this combination will be played in the Bulgarian lottery for a very long time."

News story photo(Click to display full-size in gallery)

News story photo(Click to display full-size in gallery)

Wall Street Journal

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20 comments. Last comment 5 years ago by savagegoose.
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time*treat's avatar - radar

United States
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March 30, 2005
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Posted: September 29, 2009, 9:49 am - IP Logged

Those that for years were saying a truly random game would sometimes have a dozen or more people split the jackpot may finally be satisfied...

... but I doubt it. Skeptical

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

    HaveABall's avatar - rocket

    United States
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    Posted: September 29, 2009, 11:11 am - IP Logged

    WOW, thank you for posting a very enjoyable article.Naughty

    Having millions of dollars in my financial accounts means more, consistent fun for me.Lovies

      Todd's avatar - Cylon 2.gif
      Chief Bottle Washer
      New Jersey
      United States
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      Posted: September 29, 2009, 11:31 am - IP Logged

      WOW, thank you for posting a very enjoyable article.Naughty

      Gladly — Don't forget to rate the story!  Also, use a service like Digg if you want to share with others.  (Digg and others are in the "Share" button.)

       

      Check the State Lottery Report Card
      What grade did your lottery earn?

       

      Sign the Petition for True Lottery Drawings
      Help eliminate computerized drawings!

        Avatar

        Honduras
        Member #20982
        August 29, 2005
        4715 Posts
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        Posted: September 29, 2009, 11:52 am - IP Logged

        Actually i believe it can happen if they use a ball drawing machine it has to do with the path the machine took tose particular days...If it had been RNG then that will had been something [i am talking Pick5 & above], however you have to admit, the reality that it happened is kind of shocking, but it can happened in a ball drawing machine...Now if there is 2 different ball drawings machine it can also happened but the thing is with less frequency and remember we are talking about something that rarely happens...

        what would had really caught my attention and i would had really laugh would had been had the winner been the same and she/he always chose quick picks....That would had been something....

        Another reason why i like the lottery is because i sort of believe something like "Astrology" but a little bit different involving numbers, i feel that you could hear the voice of God in random lottery games if you look carefully...

        This remind me of something i said some years ago that i believe...I said that if you could listen to everybody in the world talking and you pay close attention randomly the voice of X person in X location of the world connected with the voice of Y person connected in Y location in the world could be the voice of God...well something like that i believe in the lottery...

        The Forex trades: 1.6 Trillion dollars EVERY day, that´s more than the GDP of the Carribbean Central America, COMBINED. Enough to feed every crook out there for centuries...To all Geniuses & Powers Countries of the World the Planet needs breakthroughs in all Medicine, Veterinary, Biology related fields, Psychology, Population Psychology/Sociology..They need to genetically ingeneer new plants species/types to give more variety of plants and thus have more resources for combating diseases¨


         


         


         

         


          maringoman's avatar - kobold
          Massachusetts
          United States
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          Posted: September 29, 2009, 2:50 pm - IP Logged

          Weird things happen alot. I remember the story

          where 110 people hit 5 of 6 powerball numbers in 2005.

          Google "2005 wonton foods powerball numbers" and read

          the New York Times story. 110 people, can you believe that?

           

            Todd's avatar - Cylon 2.gif
            Chief Bottle Washer
            New Jersey
            United States
            Member #1
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            Posted: September 29, 2009, 2:55 pm - IP Logged

            Weird things happen alot. I remember the story

            where 110 people hit 5 of 6 powerball numbers in 2005.

            Google "2005 wonton foods powerball numbers" and read

            the New York Times story. 110 people, can you believe that?

             

            Um, why bother sending people to Google?  The story is right here: http://www.lotterypost.com/news/112702

             

            Check the State Lottery Report Card
            What grade did your lottery earn?

             

            Sign the Petition for True Lottery Drawings
            Help eliminate computerized drawings!

              maringoman's avatar - kobold
              Massachusetts
              United States
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              Posted: September 29, 2009, 3:13 pm - IP Logged

              Um, why bother sending people to Google?  The story is right here: http://www.lotterypost.com/news/112702

              Nice, next time I'll check here first. The story is like something out of HollyWood.

                Toney725's avatar - speedykat
                Stone Mountain, GA
                United States
                Member #3189
                January 1, 2004
                22701 Posts
                Online
                Posted: September 29, 2009, 4:58 pm - IP Logged

                4 numbers match Hurley's numbers from Lost: 4, 8, 15,16, 23 & 42.  Hmm....

                  ThatScaryChick's avatar - 61A4sr9 jpg?1
                  Idaho
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                  Posted: September 29, 2009, 5:21 pm - IP Logged

                  Great article. I wonder if there will be a lot of people, who will continue to play that line hoping it will come out again.

                  "No one remembers the person who almost climbed the mountain, only the person who eventually gets to the top."

                    barbos's avatar - gold bar-and-cash1.jpg
                    California
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                    Posted: September 30, 2009, 1:09 am - IP Logged

                      Well, top picks chart for powerball is no surprise - those who pick their own numbers are using birthdays and the kids ages for that purpose. Just look at a significant drop after 30.

                      Avatar
                      NY
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                      Posted: September 30, 2009, 1:15 am - IP Logged

                      Those that for years were saying a truly random game would sometimes have a dozen or more people split the jackpot may finally be satisfied...

                      ... but I doubt it. Skeptical

                      While it's obviously possible (and perhaps even probable if lotteries exist long enough), anyone who thinks a random game has any real chance of producing a dozen jackpot winners doesn't understand how random probability works. If the entire game was completely random, the probability of a dozen winners would probably make the odds for PB look like a sure thing. The thing is, only one side of the game is random, and that's the numbers that are drawn as the winning numbers. As the article says (and as many have pointed out for a very long time), the numbers that players choose aren't random. On the extremely rare occasions that there are an unusually large number of winners, it's because of the non-random part of the game.

                        WIN  D's avatar - q05Q0
                        Stone Mountain*Georgia
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                        Posted: September 30, 2009, 6:30 am - IP Logged

                         Gee..... you write so beautifully KY Floyd.   I enjoy reading your post very much, and they always seem to have such original and interesting perspectives. You have a talent expressing and creating vivid mental images.

                         Ever consider writing a book?

                         

                         

                        The only real failure .....is the failure to try.                               

                                                      Luck is a very rare thing....... Odds not so much. 

                                                      Odds never change .....but probability does. 

                                                                                                               Win d    

                          savagegoose's avatar - ProfilePho
                          adelaide sa
                          Australia
                          Member #37136
                          April 11, 2006
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                          Posted: September 30, 2009, 11:06 am - IP Logged

                          i love how something as basic as the laws of math, can produce such disparate results from supposed highly educated people. no wonder finance is in a mess. statistics and probablity isnt meant ot be an error pron feild, numbers is numbers. yet 3 statiticians all report diifferent odds?

                           

                          maybe they where 3 unemployed statiticians.

                          2014 winnings S= spent W= won

                          JAN S 119/ W71 ; FEB S90 /W 13 ; MAR S93/ W75 ; APR S146/ W50 ; MAY S94/ W32 : JUN S98 /W 13 JUL S110 /W21 ; AUG S185 / W56 ; SEP S 140/W 13 ; OCT S 130 / W 66 ; NOV S104 / W47

                          S $1313W $461Tot -$851

                           

                           

                            rdgrnr's avatar - walt
                            Way back up in them dadgum hills, son!
                            United States
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                            April 28, 2009
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                            Posted: September 30, 2009, 3:46 pm - IP Logged

                            Odds are odds are odds. The expert statisticians can hardly agree on what the odds are on any given probability or possibility. The one thing they seem to agree on however, is that your odds on a 6 number game are virtually zero.

                            So who bets money on a proposition where you have virtually NO chance of success? Us, because no matter what the odds are we know that at some point in time SOMEONE is going to beat those odds and it just might be one of us. The only odds that matter to us are that the odds of winning are only truly zero if you are among those who are too wise to bet against impossible odds.

                            So our dollar in the pot gives us VIRTUALLY no chance while a dollar saved gives us ABSOLUTELY no chance.

                            Our dollar in the kitty gives us the same odds as everyone else with a dollar in the kitty and one of those dollars invested IS going to make someone very wealthy.

                            There are a lot of multi-millionaires out there who may take exception to the refrain that the lottery is a tax on stupid people.

                            I can guarantee one thing. Every drawing there are a certain number of people that buy tickets. One or more of those people is going to win millions. It is JUST as likely to be one of us as it is anybody. That's good enough odds for me to kick in a buck.


                                                                         
                                                 
                                                                     

                             

                             

                             

                             

                                                                                                                               

                            "The only thing necessary for evil to triumph is for good men to do nothing"

                                                                                                                        --Edmund Burke