How the Math of Shuffling Cards Almost Brought Down an Online Poker Empire
How the Math of Shuffling Cards Almost Brought Down an Online Poker Empire
Manon Bischoff
September, 05, 2025
Summary
A standard 52-card deck can be arranged in 52! (about 8×10⁶⁷) unique ways—so vast that it’s practically impossible for two people, even across all of human history, to shuffle cards into the same order. This illustrates how quickly numbers grow and how improbable repetition becomes. The concept relates to the birthday paradox, showing that shared outcomes are rare despite large sample sizes. In the 1990s, flawed online poker algorithms revealed how difficult true randomness is to simulate. Weak random number generation made card orders predictable, prompting developers to adopt improved algorithms like the Fisher–Yates shuffle for fairer, more secure games.
Reference
Bischoff, M. (2025, September 5). How the math of shuffling cards almost brought down an online poker empire. Scientific American. https://www.scientificamerican.com/article/how-the-math-of-shuffling-cards-almost-brought-down-an-online-poker-empire/