Seven. That is the famous answer and it is correct — provided you cut the deck roughly in half before every riffle.
That condition is the part which rarely gets quoted, and it does most of the work. Cut carelessly instead, anywhere in the deck, and the answer is about fourteen. You can watch the difference below.
1 Choose how you cut
2 Riffle it
3 Or shuffle hundreds of decks at once
| Shuffles | Cut in half | Cut carelessly |
|---|
7
if you cut it in half · about 14 if you do not
A number like seven needs something to count, and the thing being counted is rising sequences.
Take a deck in order and ask how many increasing runs you would have to pull out to rebuild it. A new deck is one — it is already a single unbroken run. Cut it once and riffle, and you have two interleaved runs. Riffle again and you have about four. Each shuffle roughly doubles them.
A properly random deck of 52 cards averages about 26.5 rising sequences. So the question "how many shuffles?" becomes "how many doublings until we reach 26.5?", and the answer is around seven.
What makes seven a real answer rather than a rough one is that the approach is abrupt. The deck is not slowly getting more random; it stays noticeably ordered and then, over about two shuffles, it stops being. That sharp turn is called a cutoff, and it is the reason a single number can be quoted at all.
Bayer and Diaconis proved the seven in 1992, for a model of shuffling that makes two assumptions:
One. The cards interleave the way real hands interleave — in clumps of unpredictable size, not one at a time. This one is realistic, and it is what makes the shuffle random at all. A perfect faro, interleaving exactly one card at a time, randomizes nothing: eight of those put the deck back where it started.
Two. The deck is cut roughly in half before each riffle. This one is an assumption about you.
In June 2026, Mark Sellke, Jialu Shi and Jiamin Wang published a proof that relaxes the second condition, allowing the cut to fall anywhere. The number roughly doubles: about fourteen.
That is worth sitting with. The gap between seven and fourteen is not a disagreement about mathematics. Both numbers are right. They are answers to two different questions, and the one people repeat is the answer about a cut that most players do not actually make.
These are measured rather than quoted — 400 decks per row, shuffled under the same model the 1992 proof uses. The button above runs the same thing in your browser, so you can watch the numbers land near these rather than take them on trust.
| Shuffles | Cut in half | Cut carelessly |
|---|---|---|
| 1 | 2.0 | 2.0 |
| 3 | 8.0 | 5.9 |
| 5 | 19.6 | 12.0 |
| 7 | 24.8 | 17.5 |
| 10 | 26.4 | 23.3 |
| 14 | 26.5 | 25.8 |
| 20 | 26.5 | 26.4 |
A properly random deck measured 26.4 in the same run. So at seven shuffles a deck cut near the middle is about 94% of the way there, and a carelessly cut deck is about 66% — roughly where the careful one was after five.
The practical version: if you cut near the middle each time, seven is a fair habit. If you cut wherever your thumb lands, make it ten to fourteen. It costs a few seconds and it removes the assumption you were relying on without knowing.
Seven riffle shuffles, if you cut the deck roughly in half before each one. That is Bayer and Diaconis, 1992.
If you cut carelessly instead, cutting anywhere in the deck, it is about fourteen — proved by Sellke, Shi, and Wang in 2026.
Because of how fast the order breaks up. A new deck is one unbroken rising sequence, each riffle roughly doubles the number of them, and a random deck averages about 26.5.
Seven doublings is enough to get there. The approach is abrupt rather than gradual, which is why a single number can be quoted at all.
It depends on how you cut. Seven gets a deck cut near the middle to about 94% of the way to random. The same seven on a carelessly cut deck reach about 66%.
If you are not watching where you cut, ten to fourteen is the safer habit.
No, it does the opposite. A perfect faro interleaves the halves exactly one card at a time, so nothing is lost and nothing is random.
Eight perfect out-faros return a 52-card deck to the order it started in, which is on the faro shuffle page. Randomness comes from the sloppiness of a real riffle.
Not for randomness. Once a deck is random, more shuffling leaves it random, so extra shuffles cost nothing but time.
The rising sequences settle at about 26.5 and stay there however long you keep going.
This sits under mathematical card tricks. The shuffle that destroys nothing at all is the faro shuffle, the shuffle that cannot spoil an order is the Gilbreath principle, and the size of what a real riffle destroys is on the 52 factorial page.