40k coin tosses yield ambiguous evidence for dynamical bias
&gt; A first comment is that it would have been better for each individual to have done both &quot;Heads up&quot;and &quot;Tails up&quot; tosses (which was part of the intended protocol, but on this aspect of the protocol there was a miscommunication)<p>That was a pretty unfortunate error in the experiment. Maybe it doesn&#x27;t matter but now we don&#x27;t know. It would also have been nice to have them swap coins halfway to expose any individual per coin biasing. It may seem like an irrelevant thing but I&#x27;ve been a lifelong magician specializing in advanced slight of hand coin magic. I carry a set of coins with me all day, every day and handle them constantly. It started out as practice but evolved into both practice and a kind of fidget toy. I have sets of coins I&#x27;ve probably handled for thousands of hours over decades.<p>Most people think of coins as immutable but they actually change quite a bit after hundreds of hours of handling. Most advanced coin magicians don&#x27;t tend to use &quot;trick&quot; coins from a magic shop because they are actually too limiting. The coins I use are completely normal circulated coins but they are very specific because there are subtle differences in how coins handle which, at the most advanced levels, can matter. I have year-matched sets of coins I&#x27;ve carefully assembled because they have the degree of surface wear (sometimes called &#x27;softness&#x27;) and edge-milling which works best for the style of slights I do. Coins also vary in shape and many aren&#x27;t quite round. I&#x27;ve actually hired a specialized machinist (aka coin-smith) to &#x27;true-up&#x27; the shape and then re-mill the edges of certain coins.<p>Based on my admittedly unusual experience in handling coins, I suspect that weight, edge and surface variations in individual coins could have a material aerodynamic impact at this statistical level (sub-half a percent). BTW, there are coin magicians who have mastered the ability to flip a normal coin and control the outcome to &gt;95%. While the coin is normal in every way, it does need to be a coin they&#x27;ve specifically trained with. Otherwise the hit rate falls considerably.