Faro Shuffle Position Tracker

Track where a card lands after any number of perfect out-faro shuffles of a 52-card deck.

How it works

A faro shuffle splits the deck exactly in half and weaves the two halves together one card at a time, so perfectly that no two cards from the same half ever end up next to each other. There are two versions. In an out-faro, the original top and bottom cards stay on top and bottom. In an in-faro, they move one position in from the outside. This tool tracks the out-faro, the version tied to the well-known "eight shuffles restore the deck" fact.

Number the 52 positions 1 to 52 from the top. On a perfect out-faro, a card at position p (counting from 0) moves to position (2p) mod 51, except the very bottom card, which never moves. Worked example: the card at position 11 (index 10) goes to (2 x 10) mod 51 = 20, so it lands at position 21 after one out-faro. Do it again and it moves to (2 x 20) mod 51 = 40, position 41. Keep going and after 8 total out-faros it returns to position 11, exactly where it started, because 2 raised to the 8th power is one more than a multiple of 51 (256 = 5 x 51 + 1). That numeric coincidence is the entire reason the classic trick works.

This matters for magic because a handful of famous tricks (the ones where a shuffled deck reveals a chosen card, or where the deck seems to "remember" its own order) rely on controlled faro shuffles instead of any sleight during the reveal. Knowing exactly where a card travels lets a performer set up a trick mathematically instead of secretly forcing or peeking at a card mid-routine.

FAQ

Is a real faro shuffle actually perfect every time?

No, and that is the hard part. A true faro needs the deck split into two exact 26-card halves and woven together with no gaps or double cards. Most magicians spend months practicing before they can do it reliably, and even experienced hands miss it under pressure. This tool models the ideal math so you can understand what a perfect faro does, not promise that any shuffle you do by hand will be perfect.

Why does position 52 (index 51) never move?

Because an out-faro is defined to keep the top and bottom cards fixed while everything else weaves together. That fixed point is part of the definition, not a special exception in the math. It is also why the position-52 row of the tool always returns the same position no matter how many shuffles you enter.

What is the difference between an out-faro and an in-faro?

Both are perfect weaves of two 26-card halves. An out-faro keeps the original top card on top and the original bottom card on bottom. An in-faro pushes both of those cards one spot in, so the top half's first card ends up second, not first. The two use different formulas and different restoration counts, and this tool only tracks the out-faro.

Do I need this for tricks that use a key card?

Not usually. Most beginner-level tricks track a single reference card through cuts and overhand shuffles, not perfect faros. This tool is for the more advanced end of the hobby, where a performer wants to understand exactly how a controlled faro moves a whole deck rather than tracking one card by eye.

If tracking cards through shuffles interests you, start with the key card, the most useful beginner card principle, then see how to control a card to the top of the deck. A deck that is easy to weave evenly also helps, so it is worth reading how to choose and care for a deck of cards.