Gambling with Secrets: Part 3/8 (Probability Theory & Randomness)

Gerolamo Cardano developed probability space methodology for gambling by recognizing that dice unpredictability stems from unknown initial conditions like exact speed, position, and direction rather than supernatural forces.

Cardano calculated dice probabilities by applying his probability space framework to single die rolls showing one-sixth chance for any specific number, then extending the method to multiple dice revealing pair probabilities.

Mathematicians distinguish truly random sequences from human-generated imitations by analyzing frequency stability, which measures whether all subsequence patterns appear with equal likelihood across extended observations.

Humans systematically fail to generate random-appearing sequences when asked to simulate coin flips without actual randomness sources, unconsciously favoring certain patterns while avoiding others that seem less random despite equal mathematical probability.

Blaise Pascal and Pierre de Fermat refined Cardano’s probability ideas through correspondence analyzing sequences of random events like multiple coin flips, shifting focus from single outcomes to extended random processes.

Mathematicians calculate compound event sample spaces by multiplying individual outcome quantities, with three dice producing 216 total possibilities through six times six times six combinations.