Math reveals how many melds randomize a game

Mathematics - and some clever simulations - have revealed how many shuffles it takes to randomize a deck of 52 cards, but there's a little more to it. There are different brewing methods, and delivery methods can also matter. [Jason Fulman] and [Persi Diaconis] are behind the research that will be detailed in an upcoming book, The Mathematics of Shuffling Cards, but the main points are easy to cover.

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A riffle shuffle (shown above) requires seven shuffles to randomize a 52-card deck. Laying the cards face down on a table and shuffling them by pushing (a technique dubbed by researchers "smooshing") takes 30 to 60 seconds to randomize the cards. Shuffling over - taking sections of a deck and moving them to new positions - is an incredibly poor method of randomization, requiring around 10,000 to 11,000 iterations.

How the cards are dealt can also be important. Back-and-forth processing (alternating directions while processing, such as the A, B, C, C, B, A pattern) results in improved randomness over the more common cyclic processing (processing at positions in a repeating pattern circular A, B, C, A, B, C). Interestingly, different distribution methods have an effect on chance.

This brings up a good point: there really isn't a random "more". A deck of cards is either randomized or it is not. If even two cards remained in the same relative positions (next to each other, for example) after being shuffled, then a deck has not yet been randomized. Likewise, if seven proper riffle shuffles are enough to randomize a 52-card deck, there's really no point in doing eight or nine (or more) because there's no such thing as " more" random.

You can watch these different methods demonstrated in the embedded video just below the page break. Now we know there's no need for a complicated Rube Goldberg-style shuffling solution just to randomize a deck of cards (well, no mathematical reason for it, anyway). way.)