The Math

The math behind the archive.

ShuffleArchive rests on three ideas: the space of possible decks is almost incomprehensibly large, a small number of riffle shuffles is enough to land anywhere in it, and the shuffling itself is modeled on how a real hand does it, not on a shortcut. Each is worth its own page.

01

8.07 × 10⁶⁷

52 factorial →

How many ways a 52-card deck can be arranged, what a factorial actually means, and how small the archive is against it.

02

0.334

Seven shuffles →

The Bayer–Diaconis result on how many riffle shuffles it takes to randomize a deck, and why this archive runs more than seven.

03

GSR

The GSR model →

The Gilbert–Shannon–Reeds model of a real riffle shuffle, and why it deliberately isn’t the algorithm certified poker rooms use.

Skeptical? Good.

None of this is meant to be taken on faith. The methodology page covers exactly how a shuffle is produced, what gets archived, and the results of the 2026 audit that checked every one of the archive's 12,300,339 recorded shuffles against every other one. It was the first time that comparison was ever run.

Read the methodology →