Two envelopes problem
The game looks like this in tree form:<p><pre><code>             -&gt; Keep    -&gt; 2A
          2A -&gt; Switch  -&gt; A
    0.5 -&gt;
          A  -&gt; Keep    -&gt; A
             -&gt; Switch  -&gt; 2A

</code></pre>
Switch and keep both have an expectation of 3A&#x2F;2 because (1&#x2F;2)<i>2A + (1&#x2F;2)A. In the equation in the article they use  (1&#x2F;2)</i>2A + (1&#x2F;2)*A&#x2F;2. They count A&#x2F;2 as half of what the actual outcome should be. The mistake was abusing the A to have different meanings.<p>They created two trees one with 2A.<p><pre><code>             -&gt; Keep    -&gt; 2A
          2A -&gt; Switch  -&gt; A
    0.5 -&gt;
          A  -&gt; Keep    -&gt; A
             -&gt; Switch  -&gt; 2A
</code></pre>
And another with 1&#x2F;2A<p><pre><code>                -&gt; Keep    -&gt; A
          A     -&gt; Switch  -&gt; 1&#x2F;2A
    0.5 -&gt;
          1&#x2F;2A  -&gt; Keep    -&gt; 1&#x2F;2A
                -&gt; Switch  -&gt; A

</code></pre>
Than they treated the chance node as selecting from these two different trees at the same time with 1&#x2F;2 probability. Which is nonsensical. You can&#x27;t be in an entirely different game with 1&#x2F;2 probability - it isn&#x27;t the same game so for analysis purposes it has 0 probability of being reached.