Introduction

The roots of probability go back to prehistoric games of chance and gambling. Today's dice are descendants of knucklebones from various animals such as sheep, deer, oxen and llamas. These early dice had four sides that were often roughly tetrahedral, and on specimens unearthed from prehistoric American Indian burial mounds we see marked sides and a polish resulting from extensive use. There's also evidence of extensive gambling by the ancient Greeks and Romans. Sundry gaming tables were scratched or carved into stone corridors of the Roman Coliseum, and even into steps leading to the temple of Venus. Gambling was an amusement that was popular from soldiers in barracks to the highest strata of society. No upscale banquet was complete without games of knucklebone dice.

With the aim of winning, people must have thought about strategies. It is safe to say that people believed dice could sometimes be hot, the day lucky or the planets fortuitously aligned, and not surprisingly, there are examples of loaded dice from those far-off days. A few even tried to gain an edge by using rudimentary probability—this we know from recorded attempts by ancient Romans to understand gambling odds. But probability theory is notorious for leading even keen thinkers astray. For example …

Gerolamo Cardano (1501–1576) was a highly-regarded doctor, not to mention that he earned mathematical immortality through his contributions to solving the general cubic equation.