Mathematical models distinguish skill from luck in card games

Researchers and economists are using mathematical frameworks to distinguish between games of pure skill and those driven by chance. By utilizing Elo-style rating spreads, experts can measure how much a player's past performance predicts future outcomes.

Studies from the University of Heidelberg suggest that while chess is a pure skill game with a high rating spread, poker falls significantly lower. Using a benchmark called ‘50%-chess’—which involves replacing half of chess results with coin flips—researchers found poker lands at approximately ‘25%-chess,’ indicating it is predominantly a game of chance.

A 2025 framework published on arXiv using a Skill–Luck Index further supports these findings. In this model, chess receives a perfect score of +1, backgammon is considered perfectly balanced at 0, and poker scores +0.33, suggesting it is slightly skill-leaning but still heavily influenced by luck.