Definition:Modified Perfect Faro Shuffle

Definition

A modified perfect Faro shuffle is a shuffle performed on a deck of cards $D$ of size $2 n$.

Cut $D$ into $2$ piles $D_1$ (the top half) and $D_2$ (the bottom half) of exactly $n$ cards each.

The shuffled deck $D'$ is assembled by alternating the cards in $D$:

The cards in positions $2, 4, 6, \ldots, 2 n$ of $D'$ are to be occupied by the cards $1, 2, \ldots, n$ of $D_1$ in the same order

The cards in positions $1, 3, 5, \ldots, 2 n - 1$ of $D'$ are to be occupied by the cards $1, 2, \ldots, n$ of $D_2$ in the same order.

Thus a card in position $k$ in $D$ ends up in position $2 k \bmod \paren {2 n + 1}$ in $D'$.

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-3}$ Riffling