<story><title>St. Petersburg paradox</title><url>https://en.wikipedia.org/wiki/St._Petersburg_paradox</url></story><parent_chain><item><author>mikeash</author><text>Infinity can be difficult to grasp.&lt;p&gt;Fortunately, there is a huge difference between &amp;quot;infinite&amp;quot; and &amp;quot;really large,&amp;quot; which is often key. So applying these results to the real world often doesn&amp;#x27;t work out.&lt;p&gt;As the Wikipedia article points out, although the expected value of the game is infinite if the casino has infinite money, it&amp;#x27;s not only finite but quite small if the casino has finite money. Even if the casino were backed by the entire world GDP, the expected value of the game is only around $50.&lt;p&gt;This to me is a satisfying resolution to the problem presented.</text></item></parent_chain><comment><author>femto113</author><text>These analyses mostly ignore the obvious fact that the value of infinite money isn&amp;#x27;t, in fact, infinite, because eventually you&amp;#x27;d run out of things to buy.  Using the aggregate wealth of the entire world (which is probably in the neighborhood of $250 trillion[1]) as a bankroll yields a expected value of about $50.&lt;p&gt;[1] &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;blogs.reuters.com&amp;#x2F;felix-salmon&amp;#x2F;2014&amp;#x2F;04&amp;#x2F;04&amp;#x2F;stop-adding-up-the-wealth-of-the-poor&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;blogs.reuters.com&amp;#x2F;felix-salmon&amp;#x2F;2014&amp;#x2F;04&amp;#x2F;04&amp;#x2F;stop-adding...&lt;/a&gt;</text></comment>
<story><title>St. Petersburg paradox</title><url>https://en.wikipedia.org/wiki/St._Petersburg_paradox</url></story><parent_chain><item><author>mikeash</author><text>Infinity can be difficult to grasp.&lt;p&gt;Fortunately, there is a huge difference between &amp;quot;infinite&amp;quot; and &amp;quot;really large,&amp;quot; which is often key. So applying these results to the real world often doesn&amp;#x27;t work out.&lt;p&gt;As the Wikipedia article points out, although the expected value of the game is infinite if the casino has infinite money, it&amp;#x27;s not only finite but quite small if the casino has finite money. Even if the casino were backed by the entire world GDP, the expected value of the game is only around $50.&lt;p&gt;This to me is a satisfying resolution to the problem presented.</text></item></parent_chain><comment><author>nostromo</author><text>Not only that, but the most common outcome is $2.  The median is $3.  The chance of winning $1024 is less than 1&amp;#x2F;10th of a percent.&lt;p&gt;Even if the house had unlimited resources, it&amp;#x27;d be hard to convince me to pay a large amount of money to play -- assuming I could only pay once.</text></comment>