BoldPoker Shuffle Analysis
BoldPoker uses the Fisher-Yates shuffle to guarantee unbiased shuffling of the deck. Naïve shuffling implementations introduce predictable biases which gives exploitable information to players who are aware of this.
The Shuffles module in shuffles.ex contains implementations of Fisher-Yates as well as a subtly-wrong shuffle implementation.
The .csv files in distributions compare the distribution produced by both shuffle algorithms for various sample sizes (it takes a while for the biases to become visible).
Visualisations of the distributions can be found here: https://boldpoker.net/design#bold_poker_shuffle
The raw data – a list of 1mm decks shuffled with each respective algorithm – can be downloaded here: BoldPoker decks BotchedPoker decks