There are so many fun games in playing cards, for anyone at any age. Do you notice that there is a must-do operation for all of them? You need to shuffle playing cards before each round. No exception!
They are all to achieve the same outcome: Randomize the cards or disorder them to make it fair for the next round.
To shuffle playing cards is to make them random, which is about mathematics. In theory, various shuffling methods can draw different levels of outcomes.
We are here to introduce a few effective shuffling methods, including how to perform, their characteristics, and a few pros and cons. Don’t worry, no complicated formulas or mathematical theories are involved.
Here we are talking about nothing but playing card games, in the normal fashions. The methods below are not about how to shuffle playing cards to cheat or for magic performance. No tricks but some scientific ways of shuffling playing cards.
These may not sound very practical to know the detail. But, this fun fact may give you a certain idea:
- Which is the more effective way to shuffle playing cards?
- How random does this method offer?
- How much time should it take to make a reasonably good shuffle?
- Does a perfect shuffling exist at all?
- How to create a disorder effectively?
Nonetheless, it is good to know and may help avoid any possible cheats.
According to Professor Persi Diaconis from Stanford University, this is the most efficient way to shuffle playing cards. This is probably the more common style we see anywhere…
The steps are relatively simple:
- Divide a deck into two halves and cross shuffle playing cards
- Hold the cards in each hand with thumbs inward
- Then, release your thumbs and overlay the cards, alternating between the two halves
- Repeat a few times
We should have seen this method in any card games with anyone or in movies. It must be fairly good as it gets so popular. However, there is actually a drawback: Cards are somehow being bent in the process, which may cause damage. In fact, before using machines, casinos often change to a new deck frequently, to avoid anyone possibly taking advantage here.
People may argue that riffling is somewhat predictable, in theory. If the overlaying is perfectly executed (one card overlaying another one), then the card combination could come back to the original, e.g. after 8 times.
Of course, this is all theoretical, and many factors could stop the above happen, like which half starts interleaving. All the randomness is caused by inaccuracies while shuffling. For example, we cannot be sure that the cross-shuffling is perfectly and exactly one card over another.
Experts suggest that 7 times (which takes about 30 seconds) can yield a pretty good random effect.
Regardless, riffling remains reliable and handy in shuffling playing cards. To achieve better random results, you can apply other methods after a few rounds of riffling. Just to add more randomness into the mixing up the cards…
Professor Diaconis regards this as a “balanced” way of shuffling a deck of cards.
We may not often see in games with family and friends. The difficulty is that smooshing or scrambling takes up more space. At home, we often play at a dining table or coffee table with limited space. In addition, there are gambling chips, snacks, and drinks there in front of each player.
On the other hand, professional tournaments usually apply this method to guarantee randomness. This is the exact way to shuffle playing cards as that in Mahjong, Rummikub, or Scrabble.
Apart from better randomness, another advantage of smooshing is the amount of time it takes. One minute of shuffling can provide a very good result. Of course, it may take extra seconds to collect all the cards on the table back into a deck.
Yes, it may look awkward, but this is no doubt proven more unpredictable and effective. If anyone is clumsy and has problems in mastering riffling and overhand, then smooshing is probably the best way to go. Simple and easy! You do not need time to master it at all.
The verdict from Professor Persi Diaconis is “the most time-consuming”. Sounds bad, but let’s see how it fares…
These are the steps to do an overhand shuffle:
- Hold the deck on your left hand
- Right hand slide off a number of cards from the bottom
- Put them on the top of your left deck
- Right hand continues to pull another amount of cards out from the bottom of those cards and put them on the top of the left deck
- Tip: May use your left thumb to help hold the upper set of cards
- Repeat numerous times
This sounds complicated and does not seem as effective as expected. Experts said, 10,000 times of overhand method could make it perfectly random, in theory. It takes time to achieve the same degree of randomness, but it is obviously not feasible to reach that extent.
It may not be a bad idea to apply overhand as a supplement method. Just casually repeat a few times before distributing the cards to players. Does not take much time, and no harm to add extra variations…
The above are the more common methods to shuffle playing cards. There are many other more complicated ways to achieve randomnesses, such as Monge shuffle, Milk shuffle, and Faro Shuffle.
Even though we said it may not be perfectly random, there is no reason to be obsessed about how to shuffle playing cards. As Professor Persi Diaconis said, there are simply an astronomical number of combinations in a deck of cards. It is virtually impossible to memorize all the cards after regular shuffles… unless your fellow players have a superpower.
Apart from designs, fun facts and history, playing cards have so much to explore.