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Basic Counting Rules

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Lucky Streak

Credit: Robert Couse-Baker
Source: http://www.flickr.com/photos/29233640@N07/4283923344/
License: CC BY-NC 3.0

Do you know anyone who plays the lottery? Some people play the same numbers every week. Other people study past winning combinations. They hope they can find a pattern and predict the next winning numbers. But do approaches like that really work?

Counting Out All the Possibilities

People who develop systems to play the lottery don't understand probability. With the lottery, every week is a new event. Each ball has an equal chance of being drawn each week. If you look at each drawing as an independent event, it's clear that you cannot predict what will happen based on past events. But what about the notion of "streaks"? If a number hasn't come up in several weeks, shouldn't it be time for it to appear soon?

Not exactly. If you look at results over the long term, probability tells you that there's no such thing as a lucky streak. Consider a simpler problem. Imagine that you're going to flip a coin 10 times. How likely is it that you'll get tails every time? If you count out all the possibilities, you'll find that you're as likely to get tails all 10 times as you are to get heads the first time and tails the next nine times—or as you are to get an alternating sequence of HTHTHTHTHT. Each sequence of flips is just as probable as all the others. 

Credit: Jase Curtis
Source: http://www.flickr.com/photos/25722571@N08/5670402267
License: CC BY-NC 3.0

So, if you think back to the lottery, it's just as likely that 52 won't come up for 10 weeks in a row as it is for there to be 9 weeks without 52 followed by one week with 52. What does that say about the people who sell "strategies" to beat the lottery? The odds are good that they're making their living by deluding their customers.

See for yourself: http://www.youtube.com/watch?v=FcWuq_Nrcko

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Image Attributions

  1. [1]^ Credit: Robert Couse-Baker; Source: http://www.flickr.com/photos/29233640@N07/4283923344/; License: CC BY-NC 3.0
  2. [2]^ Credit: Jase Curtis; Source: http://www.flickr.com/photos/25722571@N08/5670402267; License: CC BY-NC 3.0

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