Shuffling a deck of cards might seem like a simple, even thoughtless, part of any card game—but beneath that casual action lies one of the most fascinating questions in the world of mathematics, probability, and game theory: How many times do you actually need to shuffle a deck of cards to make it truly random?
The answer, surprisingly, is not just “a few times.” It’s a precise number, and it comes from deep within the world of mathematical analysis.
The Magic Number: Seven
According to mathematicians, specifically a 1992 paper by Persi Diaconis and Dave Bayer, the number of times you need to riffle shuffle a standard 52-card deck to achieve near-random order is seven. This doesn’t mean the deck becomes perfectly random after seven shuffles—true randomness is a philosophical debate as much as a statistical one—but it does mean that after seven proper riffle shuffles, the deck is statistically indistinguishable from being randomly ordered.
Shuffle it fewer than seven times, and patterns remain. Cards that were once adjacent are likely still near each other, suits may cluster, and sequences from the original order might linger. But after seven, the structure has effectively dissolved.
Not All Shuffles Are Equal
It’s important to note that this rule applies to the riffle shuffle—the technique where the deck is split into two roughly equal halves and interleaved in alternating sequence. This is distinct from the overhand shuffle (where small packets are pulled off and restacked), or the often-seen “mash” or “table shuffle” commonly used in casinos, which is less efficient from a randomness standpoint unless repeated many more times.
If the shuffle is poorly done—say, the interleaving is clumsy, or you repeatedly drop large blocks of cards together—then seven shuffles might not be enough. True randomness depends on quality as well as quantity.
What About Faros?
Interestingly, there’s a kind of perfect shuffle called the faro shuffle, where the deck is split exactly in half and interleaved perfectly, one card at a time. It doesn’t randomize the deck at all. In fact, if you perform eight perfect out-faro shuffles in a row, the deck returns to its original order. So if you're shuffling with sleight-of-hand perfection, it’s possible to give the illusion of randomizing the cards while keeping full control.
Why It Matters
In casual games, most players shuffle just a few times and get on with it. But in any setting where fairness matters—such as in professional poker, magic performances, or casino dealing—ensuring a deck is truly mixed is essential. For magicians and card mechanics, understanding the mathematics of shuffling isn't just about fairness; it’s about control. Knowing how order degrades over time is a tool just as valuable as a false cut or a second deal.
The Bottom Line
Seven good riffle shuffles. That’s the answer if you want a reasonably random deck. Any fewer, and the ghosts of order still haunt the cards. Any more, and you’re only reinforcing that randomness—probably unnecessarily, unless your audience insists.
So next time someone casually shuffles twice and deals, just remember: the math isn’t on their side.
Image: Daniel Madison
Deck used in image: Madison Sharps.
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