Part 1/8:

The Surprising Mathematics Behind a Coin Toss Game

In the realm of probability and statistics, simple games often yield complex and counterintuitive results. One such case is presented in a simulation involving coin tossing, where players can either increase or decrease their wealth depending on the outcome of each flip. This article explores the mathematical principles governing this game and illustrates the paradoxes that arise from seemingly favorable circumstances.

The Game Setup

Imagine starting with $100 and flipping a coin multiple times. The rules are straightforward:

Heads: Increase your current amount by 80% (multiply by 1.8).
Tails: Decrease your current amount by 50% (multiply by 0.5).