When I was a kid, I had a passion for card tricks. One day someone showed me a card trick based on a mathematical formula. It was astonishing. He gave me the formula for doing it, but didn’t tell me how it worked, so I set about trying to figure it out for myself. No matter how hard I tried, I just couldn’t see where the formula came from. I even asked a couple of high-powered students at CalTech (California Institute of Technology) for help. They said “Sure. Give us a couple of days and we will get back to you.” I never heard from them again.
Many years late, I did figure it out. I was extremely proud of myself, not because I had solved a very complex problem but because I had solved a very easy one. It just didn’t look easy when I first saw it, and for many years thereafter.
Card tricks still fascinate me, especially those based on mathematical formulas. I will tell you about this one a bit later in this blog. But first I would like to establish why playing cards themselves justly deserve a place on the list of what I like to call “Extraordinary Ordinary Things.”
What Are Playing Cards?
The answer is pretty much in the name. Playing cards (or simply “cards”) are made to be played with, i.e. used for a social recreation.
Playing cards come in a variety of forms depending on their history and intended use. The simplest form can be made of heavy paper, thin cardboard, cotton-paper blend, or thin plastic. The two sides of the card are marked with distinguishing motifs. The “face” of each card is marked with a motif that identifies that particular card. The “back” is often a standard motif for all the cards being used, i.e. they are identical. This means from looking at the back of a card, you have no clue what is on the other side.
Playing cards are typically palm-sized for convenient handling, and are sometimes sold together in a set (deck or pack). The cards are usually covered with an invisible finish to make them easier to handle.
Playing cards have numerous uses, the most common one being reflected in the name, i.e. for playing games. They are also used in magic tricks, cardistry (skillful card shuffling and manual manipulation), card throwing, constructing elaborate card houses (“like a house of cards”), teaching, mathematical probability modeling, and at times even as currency and for secret messages, etc.
History of Playing Cards
The origin of playing cards is not totally clear. Evidence suggests playing cards may have been invented circa 9th century C.E. China. However, rather than being made of paper (or today plastic) these prototype playing cards seem to have been made as wood blocks using early printing technology. One of the earliest known references to card games appears in a 9th-century text known as the Collection of Miscellanea at Duyang, written by Tang dynasty writer Su E. It describes how in 868 Princess Tongchang, daughter of Emperor Yizong of Tang, played what was called the “leaf game” with members of the Wei clan, the family of the princess’ husband.
Other games using playing cards also began appearing from the Tang dynasty onward. However, unlike their modern descendants, these cards did not contain suits or numbers, but rather were printed with instructions or forfeits for whoever drew them.
Exactly when and where suits began to appear is unknown. However, what is known is that almost everywhere they did appear, they followed the same general pattern. A deck consisted of 48 cards divided into four suites. Each suit contained 12 cards with the top two usually being a representation of a king and a vizier. The remaining 12 cards were composed of numbers and pips (small symbols on the face of the card that designate the card’s suit).
By the 11th century, playing cards were spreading throughout the Asia and into Egypt. Somewhere along the line, the 48-card deck evolved into a 52 card pack. Again, there were 10 numbered cards with pips and three so-called “court cards,” showing the King as the top-valued card and two other prominent male members of the court. Exactly when the Queen took the second spot is unclear, likewise with the Jack (a knave or underling) taking the third value spot.
The earliest known four-suited playing cards began appearing in Europe in around 1365. They are known to have existed in Catalonia and Switzerland in 1371 and numerous other locations, such as Florence and Paris, by 1380. These were handmade, with printed playing cards first appearing in Augsburg, Nuremberg, and Ulm starting around 1418.
During the mid-16th century, Portuguese traders introduced playing cards to Japan.
The Joker was introduced into the deck in the United States in the late 18th and early 19th. It was devised for the game called euchre, which spread from Europe to the U.S. after the American Revolution (1775–1783). In euchre, the highest value card is the Jack of designated highest value suit (“trump suit”). The Joker was introduced to outrank the Jack. The name Joker is believed to derive from juker, a variant name for euchre.
Although found fascinating by most people, cards have long had a doubtful reputation. In medieval Europe, card games were blamed for occasioning gambling, drinking, and a host of other vices antithetical to a moral society. In some places, card playing became so widespread and considered so reprehensible that authorities banned it. For example, in 1377 an ordinance banned card games in Paris on workdays, reserving it exclusively for weekends. At the same time, preachers railed against cards as “the Devil’s picture book” leading to a life of depravity. Everybody played cards: kings and dukes, clerics, friars, noblewomen, prostitutes, sailors, and prisoners.
Even though playing cards are universal across the globe, there are still regional differences, notably with regard to suits.
English suits consist of clubs, diamonds, hearts, spades. However, in other cultures, the designs can be different. For example, in a French deck the suits are clovers, hearts, pikes, tiles. In German, acorns, bells, hearts, leaves. In Italian and Spanish, clubs, coins, cups, swords. So if you go into a shop to buy a deck of playing cards, depending on the country you may be surprised as to what you get.
Although hard to document, some historians suggest the suits in a deck were meant to represent the four classes of medieval society. Cups and chalices (modern hearts) might have stood for the clergy; swords (spades) for the nobility or the military; coins (diamonds) for the merchants; and batons (clubs) for peasants. However, there are a number of counter-examples. For instance, bells are found on early German “hunting cards.” These pips would have been a more fitting symbol of German nobility than spades, because bells were often attached to the jess (leg leash) of a hawk in falconry, a sport reserved for the Rhineland’s wealthiest. By contrast, bells in French decks might have represented the upper class, reflecting the fact that the paving stones of the chancel (the area around the altar in a church) were diamond shaped. They were also used to mark the graves of aristocrats.
Perhaps not surprisingly, in 1793 in the wake of the French Revolution, French authorities banned depiction of royalty on playing cards. The King, Queens, and Jacks became liberté, egalité, and fraternité. The ban lasted for nearly 12 years until Napoleon Bonaparte was crowned Emperor of France (December 1805) and rescinded the ban as being rather silly.
In the United Kingdom, which is very fond of its monarchy, many have players adopted the so-called “British Rule.” Traditionally, the King of any suit has a higher value than the Queen. However, when the reigning monarch is a woman, which has been the case in the U.K. now for some 67 years (since 1953), the values of the King and Queen are reversed such that the Queen has a higher value than the King.
The humble playing card is such a ubiquitous object that it may be hard to imagine it has undergone significant evolution over its thousand or so year history. In particular, some of the basic features of a playing card took centuries to develop, largely due to the use of cards for gambling.
For example, for most of their history, the backs of cards were plain and undistinguishable. However, in the early 19th century it occurred to Thomas De La Rue & Company, a British company, to print lithographic designs such as dots, stars, and other simple patterns on the backs of cards. This was not simply a sales gimmick to make their products look more appealing to potential purchasers; the innovation also offered significant advantages.
Cards with plain backs easily picked up smudges, in effect “marking” them such that an astute opponent could figure out what it was. Gamblers hated this. By contrast, Thomas De La Rue’s pattern-backed cards could be used over and over again without picking up such telltale markings. Gamblers loved this.
However, this turned out to be a two-edged sword because it allows unscrupulous gamblers to connive with manufacturers to “mark the deck.” Basically, this meant producing decks of cards with subtle differences in the back pattern unnoticeable by honest players, but clearly telling dishonest players exactly what each card is. While gamblers hate marked cards, magicians love them because it allows them to do amazing tricks for the fun and entertainment of their audiences, not to empty their wallets.
Perhaps surprisingly, it was several years later that card makers added “indices.” These are numbers and symbols in the upper left corner of the card, which instantly tell the cardholder the value and the suit of any cards they are holding. Previously, players had to work out the value and suit of cards by literally counting the number of pips on them, meaning they often had to hold the cards spread out in both hands to keep track of the cards they were playing. Marking the value and suit in the upper left corner allowed cards to be discretely hold in a single hand so the player could quickly and easily glance at them to decide how good a hand they were holding and what to do with them to increase their chance of winning the game—and perhaps a big pot of money.
Although playing cards today are largely standardized, you may occasionally be surprised. I recently had an embarrassing experience when I bought a deck of cards in Belgium. It had the standard English suits of clubs, diamonds, hearts, spades, plus Jokers. But when I tried to show someone a magic trick with this new deck, something kept going wrong.
After three or four tries, and becoming increasingly frustrated and embarrassed, I finally gave up. It was only a few days later that I discovered that this deck had three Jokers instead of the standard two. I don’t know if this is how cards are made in Belgium or if it was an accident of production. However, from now on when I buy a deck of cards, in Belgium or anywhere else, I am going to check each and every card individually to make certain the deck contains what I think it does.
Playing Cards in Language
In English, the popularity of playing cards is clearly reflected in the almost endless number of idioms related to the activity. This is probably true of many other languages as well. Arguably, it is not too much to say that playing cards have become so deeply embedded in our psyche that they are literally part of our being and influence the way we think about things. Let’s look at few of these ubiquitous playing card idioms, and imagine trying to get through the day without using any of them.
Not all such idioms mention playing cards directly, but rather refer to games played with cards.
Here are some idioms that specifically mention the word “card” or “cards.”
Shuffle the cards (deck)
Literally, mix up the cards to ensure they are randomly distributed in the deck, i.e. the dealer has not arranged the cards to their or an accomplice’s advantage.
Figuratively, to change, rearrange, or reorganize something already established such as a routine, policy, organizational structure, etc.
Example: There seemed to be no way of usefully modifying the current organizational structure, so they shuffled the deck and started all over again from the statement of principles.
Play one’s cards right
Literally, make the best use of the cards one has been dealt to increase the chances of winning.
Figuratively, make the best use of the opportunities one has in a situation in order to increase the chances of getting the best result possible.
Example: If Jenny plays her cards right, she is certain to be elected.
Have a trump card; play a trump card
Literally, derived from the Latin word triumphus, which means triumph or victory, to have or play a trump card is to make a maneuver likely to win the game. The term trump is most commonly used in bridge, whist, and a few other games where the suit of a card being played is of significant importance.
Figuratively, to have a winning advantage, usually unknown to your opponent until you play it.
Example: Tomorrow, when the prosecution questions the final witness, I expect them to play a trump card that will completely change the direction of the trial.
House of cards
Literally, to build a model structure (house) using only playing cards delicately balanced one atop another.
Figuratively, a plan or an organization with a very unstable structure such that it can be easily destroyed.
Example: The investors were unaware the company they were building was house of cards that could come crashing down if the slightest thing went wrong.
Have a card up one’s sleeve; have an ace up one’s sleeve
Literally, to cheat by concealing a card up your sleeve, which you surreptitiously introduce into the game to your advantage.
Figuratively, to have a secret stratagem or plan to be used if and when needed.
Have the cards stacked against someone
Literally, to arrange the cards in a deck so the dealer has a better chance of winning the game. To avoid any possibility stacking, the deck is usually cut and shuffled before the cards are dealt out to the players.
Figuratively, to have things arranged unfairly against someone to put them at an unfair disadvantage.
Example: Because the other candidate was the boss’s nephew, the cards were stacked against me when I went for the job interview.
Lay one’s cards on the table
Literally, to show the cards one has in their hands by laying them on the table for everyone to see.
Figuratively, to be honest and open about one’s intentions or resources.
Example: Come on, let’s all lay our cards on the table. What does each of us really want from these negotiations?
Wild card
Literally, a card that can represent and take on the value of any card the player chooses.
Figuratively, an unpredictable person or event. If something is a wild card, you shouldn’t count on it,
Example: Watch out for Mandy. She’s a wild card.
A few cards short of a deck
Simple-minded, stupid, crazy.
Example: Kevin often does some very strange things. I think he is a few cards short of a deck.
The following are idioms related to cards or card games.
Hold all the aces
Literally, since in many games (notably poker) the ace has the highest value, if you are holding all of the aces, you are almost certain to have an unbeatable hand.
Figuratively, to have an almost unbeatable advantage in any activity.
Example: Since George has announced his resignation, we now hold all the aces. Our plan is certain to be adopted.
Show one’s hand
Literally, reveal all one’s cards, usually at the end of a game to see who has the winning hand.
Figuratively, intentionally or unintentionally reveal one’s secret plans or desires.
Example: If we flatter him enough, I think we can get George to show his hand.
Deal a bad hand; be dealt a bad hand; get a raw deal
Literally, to deal someone a set of cards of little or no value in the game; be dealt a set of cards of little of no value in the game.
Figuratively, to be put at a serious disadvantage, through circumstances beyond one’s control.
Example: Poor George, going from orphanage to orphanage. Life really dealt him a bad hand.
Raise the stakes; raise the ante; up the ante
Literally, to increase the size of one’s bet, often to try to frighten the other players into abandoning the hand, thus giving you the victory.
Figuratively, this expression has two meanings:
- Increase a bet (financial or otherwise) so that if you win, you will win more than with your current bet.
Example: When I was dealt a third ace, I decided to seriously raise the stakes.
- Attempt to elicit concessions from an opponent by increasing their potential loss if they lose.
Example: She said if he didn’t agree to a June wedding, there would be no wedding at all. She had raised the ante.
Follow suit
Literally, to play a card of the same suit as the last player before you.
Figuratively, do as others do, follow the same pattern.
Example: Jacques closed his eyes and clenched his teeth as the vaccination needled went into his arm. Impressed by his courage, the other boys followed suit.
Long suit
Literally, in certain games such as whist, to have five or more cards of the same suite.
Figuratively, a skill, strength, talent, or other type of advantage.
Example: Making quick, effective decisions is Jane’s long suit. Paying attention to details is not George’s long suit.
Double down
Literally, in certain games, notably blackjack (also known as 21), each player initially is dealt two cards. If the cards are identical, e.g. a pair of six, a pair of queens, etc., the player has the option of doubling down, i.e. using each card individually as if they had been dealt two separate hands.
Figuratively, to stubbornly reinforce one’s position or opinion.
Example: Rather than admitting he may have acted unwisely, George doubled down and rudely dismissed any analysis or criticism.
According to Hoyle
Literally, according to the rules of the game. Edmond Hoyle (1672–1769) was an English authority and writer on card games.
Figuratively, not totally honest or acceptable. Often used in the sense of a caution or reprimand.
Example: I don’t think that would be according to Hoyle.
Ace in the hole
Literally, in certain games, some cards are laid on the table face-up for everyone to see they are, while other cards are facedown so only the player knows what they are. The ace is usually a very valuable card, so a player who has an ace in the hole (i.e. face down) has a good chance to win the hand.
Figuratively, something important other people are not aware of that can be used at the right time to gain an advantage or win a contest.
Example: If Roberta didn’t receive the raise she felt she merited, she had an ace in the hole. She already had a job offer at another company that she was prepared to accept.
Above board; open and above board
Literally, in a card game, a player is supposed to keep their cards always in sight, never dropping hteir hand below the board (table) where they might do some cheating.
Figuratively, honest, open, not secretive.
Example: The salesman had gained a reputation of always being above board when dealing with people who were looking to buy a used car.
Deal (someone) in; deal me in
Literally, allow some to join a card game by dealing them a hand; to ask to join the game.
Figuratively, to include someone in any activity; to ask to be included in an activity.
Example: If you really think this plan can work, deal me in.
Call (someone’s) bluff
Literally, to bluff means to pretend one has a better hand than they actually have by making a very heavy bet. If the other players believe their opponent has such a good hand, they drop out (fold their hand), letting the bluffer win without showing the hand. However, if at least one player suspects a bluff, they can call the bluff by matching the bet, which requires the making a very heavy bet to show their hand.
Figuratively, to challenge or force someone to prove an apparently extravagant claim.
Example: My wife always said she didn’t want a pet dog, so I called her bluff by taking her to the animal shelter to see if she could really resist not taking one home with us. She couldn’t.
Ante up
Literally, in a card game, to make a preliminary bet before any cards are dealt just to get things going.
Figuratively, offer or pay a necessary sum of money to participate in a certain activity.
Example: Everyone ante up for Amy Johnson’s present; the minimum ante is $5.
Cash in one’s chips
Literally, in a betting game where chips (tokens) are used instead of actual money, to leave the game by asking that the value of one’s chips be redeemed in cash.
Figuratively, to leave any group activity before it is over, whether or not gambling is involved. Also, to die.
Example: James Dean, the legendary Hollywood star, cashed in his chips at the age of only 24 years old.
All bets are off (the table)
Literally, something has gone wrong during a betting game, so all bets on the table are cancelled until the game can resume again.
Figuratively, any activity that has gone unexpectedly wrong, so all engagements, financial or otherwise, are cancelled.
Example: The two teams appear to be so evenly matched, all bets are off as to who will win the trophy.
Come up trumps
Literally, in games such as bridge and whist, one of the four suits (clubs, diamonds, hearts, spades) is given a privileged status over the other three suits such that if you have a number of the privileged suit in your hand, you have an excellent chance of winning.
Figuratively, to complete something well or successfully, to produce a better performance or outcome than is expected.
Example: We entered the contest with little hope of success but our performance came up trumps, which was a big surprise to everyone, especially us.
Poker face
Literally, to maintain a passive facial expression in poker so as not to give other players any suggestion of the cards you hold.
Figuratively, to avoid giving others any hint as to what you are thinking or planning.
Example: When I told Amanda about the project, she put on a poker face, so I have no idea of what she thinks of it.
In spades
Literally, spades are the highest-ranking suit in certain card games such as bridge, so having a lot of spades is almost always a winning hand.
Figuratively, a great success of a superabundance of something.
Example: He asked, “Did your first date go well?” She replied, “In spades. I couldn’t have asked for anything better.”
Mathematical Magic
In the introduction to this blog, I promised you an intriguing card trick based on a mathematical formula. I came across this trick when I was a teenager. At that time I was in love with mathematics and intrigued by magic; this trick combined both.
Anyone can do the trick; it is only necessary to apply the formula. The difficulty was, I wanted to know why it works. As often as I tried, I just couldn’t figure it out. I didn’t become obsessed by it; however, every time I showed it to someone, I made another try at resolving the mystery. Eventually, I did solve the mystery and I will tell you how, but first the trick.
The Setup
Take an ordinary deck of 52 cards. Thoroughly shuffle them or let a spectator shuffle them. Then divide the deck as follows while telling the spectators exactly what you are doing.
Deal out the first card of the pack face up on a table. Starting from the value of that card, deal out more cards face up on top of it up to the value of 13. Example: You turn over a seven. For the next card you deal out, you say eight, then nine, then 10, then 11, then 12, then 13. Turn the pile face down. This is the first pile.
Now make a second pile the same way, i.e. from the cards left in your hand deal out a card face up. Starting from the value of this card, add cards until you get to 13. Turn this second pile face down. Continue making piles until the cards in your hand are exhausted.
Two caveats.
- When starting each new pile, if the card you turn over is a picture card, bury it somewhere in the deck. Start a pile only with values one (ace counts as one) through ten. Never start a pile with a picture card. When trying to make the last pile, if you don’t have enough cards left, just keep these cards in your hand; do not put them down on the table.
- After you have finished dividing the deck, you will probably have from four to seven facedown piles on the table, plus the cards remaining in your hand. While your back is turned, ask someone to move the piles around as much as he wishes so that you could not possibly know which pile is which.
Turn around and ask a spectator to remove all but three piles and give you the cards.
Finally, ask the spectator to turn over the top card of any two of the remaining three piles. You will apply the formula to predict the value of the top card of the third pile. Everyone will be amazed when you do.
The Formula
Here’s how you apply the formula.
First, from the cards in your hand, count out facedown on to the table the value of one of the visible cards on top of a pile, then count out the value of the second visible card.
Next, count out another 10 cards.
Finally, count out the number of cards you still have left in your hand. This number of cards will be the same as the value of the top card of the third pile.
As you deal out the cards, do all of this counting in your head, not aloud. You then announce the value of the third card. Just listen to the oohs and aahs when it is turned over and you are proved correct.
You can do this as many times as you want; it always works. But why? Think about it for a while.
Why it Works
This card trick is completely self-working. Anyone can do it; you just need to apply the formula. As mentioned earlier, as a teenager in love with mathematics, I wanted to know why the formula works, but I simply couldn’t figure it out. Only later in life did I realize that something about the instructions for doing the trick had led me astray.
Before reading on, see if you can figure out why this always works. If you have figured it out, congratulations. If not, here is the solution.
There is a red herring is the first caveat: “Never start a pile with a picture card.” The formula requires you to count out 10 additional cards no matter what the value of the two visible top cards of the three piles remaining on the table. I therefore naturally assumed, buttressed by the red herring caveat, that there had to be some kind of relationship between the numbered cards 1, 2, 3, 4 . . . 10 which did not apply to picture cards (Jack, Queen, King).
It took some 30 years before it finally occurred to me to investigate to see if there really was some intrinsic relationship between 10 numbered cards in a suit and the 10 in the formula. Instead of avoiding using picture cards to start a new pile, I counted the Jack as 11, the Queen as 12, and the King as 13. And the formula still worked. The number 10 has no significance. It is simply a necessary consequence of the derivation of the formula. It has absolutely nothing to do with the fact that there are 10 non-picture cards in each suit.
I presume the person who showed me the trick was not trying to be misleading. He probably said not to use picture cards because this would give piles that could possibly be identified since they would have so few cards, i.e. only one, two, or three.
How the Formula is Derived
Fundamentally, we know after dividing the cards into piles, H (number of cards in the hand) plus T (number of cards on the table) must equal 52, i.e. H + T = 52.
We also know how many cards are in each of the two piles where the first card has been turned face up. It is 14, the value of the first card. Example: If the faceup card is 8, then to make the pile we had to have counted 8, 9, 10, 11, 12, 13. So the number of cards in that pile will be 14 – 8 = 6.
Now we put these components together.
Let T1 be the value of the face-up card in the first pile, T2 the value of the faceup card in the second pile, and X the value of the still facedown card in the third pile. Then the number of cards on the table, T, must be must be (14 – T1) + (14 – T2) + (14 – X) = 42 – (T1 + T2 + X).
Now, because there are 52 cards in the deck, the number in hand, H, must be 52 – 42 + (T1 + T2 + X). Solving for X, we get X = H – T1 – T2 – 10.
In terms of the card trick, the formula for X tells us that from H (the cards in our hand), we must first subtract (count out) the value of the face-up card on one of the piles, then subtract (count out) the value of the face-up card on the second of the piles, then subtract (count out) another 10 cards. The number of the cards left in your hand will be X, the value of the facedown card atop the third pile.
Improbable Probability
Here is another one that takes considerably less time but is just as astonishing. In fact, it is so much quicker that you can do it over and over again, and each time the participants will be just as amazed. While not entirely self-working, it is extremely easy to do.
It might seem that if someone picks one of three numbers, you have just a 1/3 chance of correctly guessing their choice. This trick defies this logic.
Here’s what you do.
- After shuffling a standard deck of 52 cards, ask the participant to withdraw three cards at random and place them face up in a row on a table.
- Ask the participant to silently choose one of the three cards and to hold it firmly in mind.
- Turn your back and ask the participant to switch the positions of the two cards not chosen. Example: The three cards are A–B–C. The participant thinks of C. While your back is turned, the person switches the positions of A and B to give B–A–C.
- Tell the participant to turn the three cards face down.
- Turn around and tell the participant to slide the cards around on the table in any way desired for as long as desired.
- When done, ask the participant to turn the cards face up.
- You look at the three cards for a moment and then announce which card the participant thought of.
The participant may say, “Well, you were just lucky.” So you do it again, and again, and again. And never miss.
Here is how it works.
- In Step 1, when the three cards are laid out face-up on the table, you memorize the value of card in the middle—call it V.
- In Step 5, as the participant slides the cards around on the table, you watch carefully the card now in the middle—call it the M card—so that you know exactly where it winds up.
- In Step 6, after the cards once again been turned face up, you check to see if M (the card you have been following) = V (the card you memorized in Step 1).
If M = V, then this is the card the participant thought of. If not, then M cannot be the chosen card. And neither can it be V, the card now showing. So it must be the third card.
Here is a more detailed description of the logic:
- If the participant choses the middle card, it stays where it is during the switch in Step 3. Thus, it is the M card in Step 5. This is confirmed when you see M = V in Step 6.
- If the participant does not chose the V (middle) card, then the M card you follow around the table will not be the card you memorized because it has been switched there from another position. When you see that M ≠ V, you also know the erroneous M (middle) card cannot be the chosen card either because for it to have become the M card, it also must have been switched into the M position from somewhere else. Thus, the chosen card only be the remaining third card.
Playing Cards and Computers
I used to be an habitué of Las Vegas. Not because I was enamored of the place, although it is fascinating, but because my mother and sister lived there. Every two years I would make the long trek from Brussels across the Atlantic, then across the continent to visit them.
I am not a gambler but one thing I liked to do there was play video poker. If you aren’t familiar with them, video poker machines are like slot machines; however, instead of showing fruits, when you pressed the button (pulling a handle is long since passé), you would be shown a poker hand. Your job then was to evaluate the hand, decide how many cards to discard and new cards in order to achieve a winning hand. In short, unlike mind-dulling slot machines, video poker machines require you to do some actual thinking.
In the long term, I never won because the casino always had the advantage. You needed a pair of Jacks or higher in order to win anything; otherwise the house automatically took your bet. However, if you knew what you were doing, you could play for practically nothing. At that time (11 years ago), the minimum bet was only 1 cent, whereas for any of the live games in the casino, the minimum bet was at least 50 cents and often a full dollar.
Video poker is played on a computerized console similar in size to a slot machine. It first became commercially viable when it became economical to combine a TV-like monitor with a solid state CPU, which happened in the mid-1970s. Throughout the 1980s video poker became increasingly popular, not only because of its extremely low minimum bets, but because it was less intimidating than betting at live tables in the casino with other players.
If you start with the knowledge that eventually you will always lose, then the only wise bet is the minimum bet. This way, video poker can provide excellent entertain while doing little damage to your wallet. I remember one time I played video poker for nearly two hours for less than a dollar. Casinos hate people like me, because they count on people making more than the minimum bet, and therefore losing more than they have to for the same amount of entertainment.
Another point of interaction between computers and playing cards has been exploited by educators.
Tim Bell, a founder of CSUnplugged, made a set of cards with one dot on the first, two on the second, four on the third, eight on the fourth, and 16 on the fifth. He then handed the cards to five children and asked them to make numbers from their cards. For example, when he said “Make 13”, children 4, 3, and 1 held up their cards. They had discovered binary numbers without anyone teaching them about binary numbers! CSUnplugged uses playing cards to illustrate other concepts such as error correcting codes, sorting, and basic cryptography.
An even more significant interaction is the computational thinking that appears in mathematical card tricks such as the one described above. The formula employed in such tricks represents an algorithm the performer follows to get the cards to work their magic. In other words, the performer employs computational thinking to make the trick work without ever realizing he or she is engaging in computational thinking.
