The Best (and Worst) Ways to Shuffle Cards - Numberphile

**Dieter** · 04-09-2015, 07:13 AM

Originally Posted by Aslan

You will see dealers who shuffle near perfectly, interlacing most every card,

A perfect riffle is a bad shuffle.

I have never seen a random shuffle, ever. I have seen some effective shuffles.

The purpose of a shuffle is not to randomize the deck. The purpose of the shuffle is to reorder the deck, ideally in an unpredictable* way.

If you paid attention to what Diaconis said, 7 riffles is not the pinnacle of randomness in reordering the deck. It is the lower threshold of reasonably unpredictable reordering of a 52 card deck, based on the top & bottom cards moving to other positions in the deck.

The summary of the video should be: "When shuffling cards, if all you can do is riffle, do it at least 7 times." They didn't touch on what happens when you add other operations into the shuffle (hint: they help a lot, when combined with riffles).

*Now if you're going to go and say that unpredictable is random, maybe - but there's a lower threshold for "I'm pretty uncertain about what the next 3 cards are" vs "enough reordering has occurred such that every possible permutation is equally likely".

**Aslan** · 04-09-2015, 08:03 AM

Originally Posted by Dieter

A perfect riffle is a bad shuffle.

I have never seen a random shuffle, ever. I have seen some effective shuffles.

The purpose of a shuffle is not to randomize the deck. The purpose of the shuffle is to reorder the deck, ideally in an unpredictable* way.

If you paid attention to what Diaconis said, 7 riffles is not the pinnacle of randomness in reordering the deck. It is the lower threshold of reasonably unpredictable reordering of a 52 card deck, based on the top & bottom cards moving to other positions in the deck.

The summary of the video should be: "When shuffling cards, if all you can do is riffle, do it at least 7 times." They didn't touch on what happens when you add other operations into the shuffle (hint: they help a lot, when combined with riffles).

*Now if you're going to go and say that unpredictable is random, maybe - but there's a lower threshold for "I'm pretty uncertain about what the next 3 cards are" vs "enough reordering has occurred such that every possible permutation is equally likely".

Yes, I understand that seven shuffles is the minimum threshold as to what might be considered a random shuffle. Also, the other procedures may or may not help in achieving randomness, for example, stripping the deck. You would think so, but I couldn't say definitively, or how much it adds. Interestingly, I believe our simulation software (Norm, correct me if I am wrong) is based on a random or at least simulated random shuffling. If in fact the hand shuffles, and ASM shuffles for that matter, are not random or even near random, then that may hint of what I have always suspected, and that is that certain configurations of cards (minimum clumpiness, for instance) may tend to persist when subjected to a normal house shuffle.

Also, even with a truly random shuffle, I do not know if there are any more likely configuration of cards that result. I know every card has an equal chance, but does every configuration, that is, the overall composition of the cards, since there is more than randomness affecting overall composition, for example, the fact that 4 ranks of cards all have the same value of ten. IF there tends to be a ten every two or three cards, that alone drives a tendency toward a certain deck composition, or am I reading too much into it? It may also lead to a tendency for more clumpiness, but a clumpiness of tens is different from a clumpiness of small cards which may be 22222, or 23456, or 66666 (to name just three), as opposed to 10, 10, 10, 10, 10 (always the same).

I realize that house shuffles do not attempt to randomize the deck, and I am not even sure that it would favor the house to do so. What I do believe is that casinos have spent more time studying the effects of random shuffles versus "reordering" shuffles, for want of a better term, than players have. The fact that casinos continue to simply reorder the cards in a fairly unpredictable manner, may indicate that their studies show no appreciable difference from a random shuffle, or maybe even that a simple reordering of the cards actually favors the house, at least under certain circumstances. It's an area I believe should be studied. Besides the reordering of the cards, I see the house taking pains to prevent shuffle tracking, ace steering and edge sorting. These measures are born of much study, I am sure, why not the number of actual riffles themselves and the deliberate failing to achieve a minimal threshold for randomness, unless they have simply discovered it doesn't make a cost effective difference (number of hands per hour/time spent shuffling vs. the expected units won per shoe)?