What a riffle shuffle actually mixes
In a riffle shuffle, a deck is split into two packets, then cards from each packet are released in alternating bursts so the packets interleave. The cards usually do not fall in a perfectly alternating pattern: several may come from one side in a row. That uneven interleaving is part of what makes the shuffle useful. It breaks up runs of cards while creating new neighboring pairs.
After another riffle, those new groupings are disrupted again. Repetition gradually weakens the clues left by the deck’s starting order—such as cards that began next to each other remaining neighbors.
Why seven is a benchmark, not a guarantee
The familiar seven-shuffle figure comes from mathematical analysis of an idealized riffle shuffle. In that model, the cut and the interleaving behave in specified ways, and “nearly random” means the resulting deck’s possible orders are close to the distribution expected from a thoroughly mixed deck. It does not mean every ordering is equally likely after exactly seven physical shuffles, or that a particular deck is guaranteed to be well mixed.
Real technique varies. A person may make similar cuts each time, release cards in large clumps, or repeatedly preserve chunks of the original order. Those habits can leave structure behind even when the shuffle count reaches seven. Conversely, a skilled, varied shuffle can mix more effectively.
The practical lesson is to treat seven as a useful rule of thumb for ordinary riffle shuffling, not a magic switch. If the deck matters, vary the cuts and interleaving; the goal is to break up surviving patterns, not merely to count to seven.
