Miller and Sanjurjo (2015) suggest that many analyses of the hot hand and the gambler's fallacies are subject to a bias. The purpose of this note is to describe our understanding of their main point in terms we hope are simpler and more accessible to non-mathematicians than is the original

When asked to mentally simulate coin tosses, people generate sequences which differ systematically from those generated by fair coins. It has been rarely noted that this divergence is apparent already in the very first mental toss. Analysis of several existing data sets reveals that about 80% of...