Counterintuitive problem: People in a room keep giving dollars to random others
&gt; <i>If on quick reflection you thought “more or less equally”, you are not alone. I asked 5 super-smart PhDs this question and they all had the same initial intuition.</i><p>Mmm ... What kind of PhD did they ask? Mathematicians have a strong bias for exact solutions, and not too much intuition for this kind of problems. Have they tried asking Physicists?<p>It&#x27;s not surprising that the distribution is not even. I expect that the spread increase in time. I guess something like<p>average + k1 * sqrt(t) * erf((n- middle) * k2)<p>where t is the number of simulation steps, and k1 and k2 are some magic constants that I&#x27;m too lazy to estimate. (&quot;Proof&quot;: Everything is a Gaussian.)<p>I was surprised that at some point the distribution was almost linear. Perhaps k2 is not a constant, and the correct guesss of the estimation is<p>average + k1 * sqrt(t) * erf((n- middle) * sqrt(t) * k2&#x27;)<p>This estimation fails when t is big. (And it&#x27;s probably incorrect anyway.)<p>After some time the person with more money apparently starts to increase the amount of money. I&#x27;d like to see a longer simulation to see if after some time the first one accumulates most of the money.