Why the Exact Same Lottery Numbers Came Up Twice in One Week

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In 2009, the Bulgarian lottery turned the same number sequence twice within five days. Naturally, this made people a tad suspicious. After all, the odds of the same number sequence appearing twice in a row are millions to one against. But actually, it wasn't that suspicious at all.

Top image: California Lottery "Snowfall" Commercial.

On September 6, 2009, some Bulgarian was probably made very happy when the winning lottery numbers - 4, 15, 23, 24, 35, 43 - were announced. On September 10th of that same year, the same lottery numbers were announced, making quite a few Bulgarians unhappy. Rumors started going around, and people began insisting that the lottery was fixed.


They weren't alone. Around the world there are a lot of lotteries going, and every time one draws the same numbers within a certain amount of time, the same claims are made. The lottery is fixed. Someone's making sure that certain people win, that certain people don't win, or that nobody wins. It makes sense, considering the massive odds against that sequence of numbers being picked again.


What's not accounted for by the conspiracy theorists, is that there's a difference between a particular number sequence being repeated and any number sequence being repeated. The Bulgarian lottery had possible numbers ranging from 1 to 49. If they were trying to get the September 6th sequence - 4, 15, 23, 24, 35, and 43 - drawn again, the odds would be 13,983,816 to one. No one would, or should, believe those odds. But if you're trying to match any number sequence with any other number sequence, the odds are a bit different.

On September 7th, a new set of lottery numbers was picked. Anyone trying to match the September 6th sequence had one additional chance to match it. Anyone trying to match any number sequence also had one additional chance to match numbers. On September 8th, another set of numbers was drawn. Anyone trying to match the September 6th sequence had one additional chance to match. Anyone trying to match any number sequence had two chances to match numbers - one for the September 6th sequence, and one for the September 7th sequence. One new number, two new chances. The next day, three new chances. A thousand days later, a thousand new chances with each new number. The odds add up fast. In fact, comparing in a thousand picks of 6 numbers with a range from 1 to 49 would get you 499,500 chances at a match. Half a million chances at fourteen million total outcomes isn't that improbable.


That being said, five draws isn't a thousand, and the Bulgarian lottery was an amazing coincidence. Still, with so many local, state, and national lotteries running all year round, all around the world, a few amazing coincidences are going to happen.

(If, however, someone knows that another "coincidence" is going to happen on their watch, and they can get in contact with me, I'd be happy to cash in, split the money with them, and write a post on what an innocent coincidence it all is.)


[Via The Improbability Principle.]