Example: Add luck vs skill gambling model #321
Description
This PR proposes a new example demonstrating how short-term gambling outcomes are dominated by stochastic variation even when agents differ in skill.
In the model, agents have fixed skill levels that slightly bias their probability of winning a bet. Agents repeatedly place fixed-size bets, and outcomes remain noisy. After a short number of rounds, agents are ranked by wealth, and the average skill of the top and bottom performers is compared.
The example shows that, over short horizons, early winners are not reliably more skilled than early losers. The skill distributions of these groups overlap substantially, illustrating why short-term success is a poor indicator of true ability. This captures phenomena such as beginner’s luck, overconfidence after early wins, and misattribution of success in gambling and similar domains.
The example is intentionally simple and pedagogical. It focuses on a single mechanism with small skill advantages and avoids additional behavioral assumptions or long-term dynamics. This makes the model simple and easy to understand.