People only play these games if they expect to get to the top of the pyramid themselves. But each iteration of this game requires 10 times as many players as the last, so only 9 iterations would require a billion players . People can be fooled by averages. So A has the higher batting average in both halves of the season. Because people tend to average averages .
People look for, and perceive, patterns in randomness.
Pattern-finding is the essence of learning, and reflects a natural human need to make sense of the environment. But we are often misled by specious patterns. Innumerate people are often victims of pseudo-science. Pseudo-science tends to rely on hypotheses which are not falsifiable . Karl Popper criticized Freudianism for its immunity to falsification .