<story><title>South Africa&apos;s lottery probed as 5, 6, 7, 8, 9 and 10 drawn</title><url>https://www.bbc.co.uk/news/world-africa-55154525</url></story><parent_chain><item><author>FemmeAndroid</author><text>So there are a few people mentioning that the chances of this happening are equal to the chance of any other set of 6 numbers coming up, but something I like to think about is how to estimate the size of the set of winning combinations that would trigger this kind of reaction, and what the chances of one member of that set being the winning numbers would be.&lt;p&gt;So let say, a set of:&lt;p&gt;- sequential numbers.&lt;p&gt;- sequential primes.&lt;p&gt;- sequential even or odd.&lt;p&gt;- a commonly memorized multiplication table 3,6,9,12...&lt;p&gt;- squares 2,4,8,16,32...&lt;p&gt;- other famous sequences - eg fibonacci&lt;p&gt;- famous numbers - eg 4,8,15,16,23,42&lt;p&gt;- the same numbers being picked multiple days in a row&lt;p&gt;As a bonus, I like to think of the number of lotteries important enough to warrant making the news.  Then you can calculate how frequently you can expect to see a &amp;#x27;crazy lottery winning combination&amp;#x27; story.</text></item></parent_chain><comment><author>wolfgang42</author><text>If you take OEIS as a database of “interesting sequences” (some of them are only interesting to mathematicians), and pull out all of the running groups of 6 (in the sequence as provided, which of course doesn’t include the full version of very long or infinite sequences) that could be a powerball number, you get 1,097,698; or about a 2.6% chance; just the first 6 digits of each sequence gives a mere 32,110; or about 0.076%. Of course most of these aren’t actually very interesting, after all; but it does provide a rough approximation.&lt;p&gt;(Code here: &amp;lt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;gist.github.com&amp;#x2F;wolfgang42&amp;#x2F;2df001b05065488620700f0fdfa58a08&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;gist.github.com&amp;#x2F;wolfgang42&amp;#x2F;2df001b05065488620700f0fd...&lt;/a&gt;&amp;gt;)</text></comment>
<story><title>South Africa&apos;s lottery probed as 5, 6, 7, 8, 9 and 10 drawn</title><url>https://www.bbc.co.uk/news/world-africa-55154525</url></story><parent_chain><item><author>FemmeAndroid</author><text>So there are a few people mentioning that the chances of this happening are equal to the chance of any other set of 6 numbers coming up, but something I like to think about is how to estimate the size of the set of winning combinations that would trigger this kind of reaction, and what the chances of one member of that set being the winning numbers would be.&lt;p&gt;So let say, a set of:&lt;p&gt;- sequential numbers.&lt;p&gt;- sequential primes.&lt;p&gt;- sequential even or odd.&lt;p&gt;- a commonly memorized multiplication table 3,6,9,12...&lt;p&gt;- squares 2,4,8,16,32...&lt;p&gt;- other famous sequences - eg fibonacci&lt;p&gt;- famous numbers - eg 4,8,15,16,23,42&lt;p&gt;- the same numbers being picked multiple days in a row&lt;p&gt;As a bonus, I like to think of the number of lotteries important enough to warrant making the news.  Then you can calculate how frequently you can expect to see a &amp;#x27;crazy lottery winning combination&amp;#x27; story.</text></item></parent_chain><comment><author>idolaspecus</author><text>I think this is an important point. I think someone asked &amp;quot;what&amp;#x27;s the probability this number is chosen?&amp;quot; and many people respond with 1 in 42 million or something like that. But in fact this is only true &lt;i&gt;under the assumption the lottery is implemented perfectly&lt;/i&gt;. But this assumption is what is under scrutiny here. Because the lottery is not some ideal process in the mathematical universe, it&amp;#x27;s a process in the physical universe implemented by humans. Because it&amp;#x27;s a real process implemented by humans, there&amp;#x27;s all sorts of ways we can imagine the results could be skewed by the implementation details, and we can imagine all sorts of outputs that might be more likely given the most likely flaws in the implementation.</text></comment>