Chivalry or Probability

Notice above that neither one of the two-eyed Jacks has a mustache.  Neither does the “Suicide King”.  Notice that the King of ‘Diamonds’ carries an axe.  The “Bedpost Queen” is the only queen that faces to her left.  These are hallmarks of Cartamundi’s Anglo-American or International classic pattern, the most prolific “classic” pattern being printed in the world today.

Now look for any notable religious symbology on the clothing of those face-cards.

  On face-cards, one might have expected to see multiple religious symbols tucked away in the fluff and folds of renaissance period dress, because of the real life longstanding historical association between European monarchies and the Roman Catholic Church.  But cards were predominantly about gambling and the church would grow to take a dim view of obtaining money in an easy or immoral way.  A deck of cards was a small and conveyable, precious and expensive hand made luxury that was prized by women and idle gentry alike.  There was no willful association between the Church and gambling cards – they were at odds.  Card printers usually avoided using religious symbols. 

If examining general religious symbols and semiotics briefly, one might recognize some familiar icons like the Egyptian ‘Eye of Horus‘, the Jewish ‘Star of David’, or the Taoist (Chinese) ‘Yin and Yang’ symbol.  In Christianity the cross becomes a symbol for the religion but an “ikon or icon” is generally not a statue or statuette but a sacred image or painting used in religious devotion.  A much younger religion like Islam though has intentionally avoided or prohibited the establishment of icons or symbols – calling such practice idolatry.

  By far the most prestigious and influential medieval Catholic military orders were the Knights Templar, Knights Hospitaller and Teutonic Knights.  Incorporating different artistic styles in the shape and color of their crucifixion cross symbols, they also wore unique color schemes in their garb to distinguish themselves and their orders.  There were many other similar brotherhoods to be established in the years following – but few as successful.

* One thousand years ago, believers being enthusiastically encouraged by the Church to make pilgrimages to the mid-eastern Holy Lands were being attacked, robbed and murdered with regularity.

  Between 1096 and 1271 several especially bloody religious wars for control over Jerusalem, ensued between Christianity and Islam. The major campaigns were called “Crusades”.  Old history books and encyclopedias usually cited only three proper Christian Crusades to the Holy Lands.  But nowadays newer (but farther removed) historians might enumerate more than a dozen conflicts in the middle-east,  to count as Crusades happening during that same period instead.  By re-defining Crusade to mean most any warlike Christian conflict of note up to the fall of Constantinople (1453), spiritual wars on the remote Spanish Iberian peninsula or even in the lands of present day Finland or Germany are now also included to their long list version of official religious Crusades.

  At the behest of the Roman Catholic church in the 11^th century, armed and logistically supplied, “military orders” were created and chartered to help protect and attend to those Christian pilgrims exercising their penance (in the form of pilgrimage) and to win back control of the Holy Lands from the Muslims.

* Just imagine how significant an event such a pilgrimage might have been during the primitive living conditions of the Middle Ages.  If a pilgrim departed from western Europe – say Paris for example, and walked to Jerusalem that would amount to 1,405 miles to Constantinople plus another 727 miles from there to Jerusalem, as the crow flies (over the mountains).  Taking that trip by car today over established and paved roads amounts to a more realistic one-way distance of 3,020 miles (4,871 km).  Then there is the return trip to consider, if you survive the first ordeal.  Of course the wealthier might have ridden on horseback or by wagon or have gone to Venice to make part of the trip by sea.

  After Jerusalem was won following the 1^st Crusade, the Knights Hospitaller in 1099 seem to have been the first important military order to have been chartered by the Catholic church.  Their mission was simply to care for and defend the sick, poor or injured pilgrims coming to the Holy Land.  Our English language gets the word “hospital” from them. 

  The Knights Templar were established two decades later in 1119.  But the founding members of the Templars were some of the very Romanized, Germantic-Franks that had had a big hand in the winning of the 1^st Crusade to begin with.  The Templars quickly rose to become the most prominent and powerful of the Catholic military orders, but 200 years later they would be unfairly destroyed by “Philip the Fair” and his puppet – the sitting Pope.

  The ‘Johnny-come-lately’ but honorable Teutonic Order of Knights were not established until after a century of time had passed following the 1^st Crusade.  The Teutonic order was also created at a time when the crusader state “Kingdom of Jerusalem” was in exile from Jerusalem (Jerusalem fell to Saladin in 1187).  But as time passed and the religious Crusades were abandoned or fizzled out so to speak, the Germanic Teutonic order would for the next several centuries, be a significant factor in the development of Eastern Europe.  Members of the Teutonic brotherhood still exist today in a small capacity as do members of some other orders.

  All told there were more than thirty Catholic military orders to be established, some older than others.   Sometimes the leaders or founders of these military institutions or brotherhoods were often wealthy, equestrian and aristocratic to begin with.  These brotherhoods were not private men’s clubs but were kindred in a sense with the companies or corporations of today.  These religious organizations provided gainful employment, food and shelter and upward mobility.  All during a primitive era when only the eldest sons in large families ever inherited any land or when the few alternative occupations amounted to becoming a monk or tilling the soil for someone else.

  So the notion of fairness, nobility, and chivalry – and the icons/symbols representing some of those notions began with the crusades and propagated through the Middle Ages.  Remnants and reminders of those fair ideas still appear as flags, on medallions or in churches.

  Above is a representative half portion of prominent Christian symbols, which also usually represent the execution apparatus that Jesus was crucified on.  No one knows for sure what the real instrument actually looked like.  It might have been shaped like a saltire (a “crux decussata“) or a Tau. 

*The Latin cross shape is a crux imissa, the common Greek cross shape is a crux quadrata and the crux comissia is shaped like the Greek capital letter “T” or Tau.  The crux ansata incorporating a circle is Coptic (African / Egyptian), and the limbs on a crux gamata have feet – swastikas and gammadion shapes which were also used in Christianity, can date back to previous Hinduism and Buddhism symbols.

  Christian military orders were predecessors of later “Chivalric Orders” and their accompanying symbols.  Chivalric social codes as developed from and for the institution of knighthood, began about the same time as the 1st Crusade.  The French word for a knight is “chevalier”; the French word for a single horse is “cheval” and plural is “chevaux”.  So the word “chivalry” stems from the French, as do probably many of the notions of how gentlemen should conduct themselves.  Consider the historic equine aspect too. Usually only the affluent in medieval Europe were able to maintain horses.

  Segar’s Roll is an English roll – of ‘coats of arms’ which dates back to about 1282.  This photo above of a 17^th century copy of the roll, shows only 20 examples, taken from 212.  Listing downward from the top left, the first seven are the names and arms of : Prester John, King of Jerusalem, Emperor of Constantinople, King of Greece, King of Germany, King of France and King of England.

• The whole list found on Segar’s Roll and a far more exhaustive display of English heraldry can be found here @: aspliogia.com.

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Below is a representative sample of European chivarlic or heraldic symbols.

Source: wikimedia.org : Heraldische Kreuze nach Ströhl (1909)

Naturally, several national flags in the world reflect or resemble some older symbols found in heraldry.

 

 

 

 

 

 

 

Getting back to Cards

The Classic Deck

  The secular, French-suited, modern International or “classic” playing-card pattern, represents a culmination of several centuries worth of periodic design development and improvement.  But there are many other old and/or alternate card patterns.  Actually there is an astounding array of variation to be found in alternative card patterns.

  The first cards might have been made in China.  Other cards were being used in Egypt long before they made their way into Europe by the 1370’s.  Soon many differing varieties of cards sprouted up across Europe. The Italians, Germans, Spanish, Russians and even the Swiss – each developed uniquely individual card decks with different characters, different suit-marks and sometimes a different total number of cards in the deck.

  At first there were no Queen face cards represented in decks, just males in a hierarchy. Something like a Knight or Bishop was used to occupy rank between the King and Jack/Knave/Page.  A 78 card Taro card deck used for gaming in one country might have been used for divination or foretelling the future in another country.

  The “Tarocco Piemontese” tarot card deck from northern Italy has a trump card called “the Fool”, which has no relationship to a joker.  The two “Jokers” usually found in a newly packaged deck of cards were originally an American addition, for optional use in the game of “Poker” – which also originated in America from the early 19^th century.

  Some collectors have literally gathered thousands of uniquely individual card decks. Vanderbilt University recently inherited one of the “most complete and scholarly collections”  to be found anywhere; consisting of over 1,000 unique card decks.  Columbia University’s Rare Book Library has over 6,000 individual decks.  According to Guinness World Records : “The record for the largest collection of playing cards belongs to Liu Fuchang (China), with 11,087 different sets of playing cards, as of 1 November 2007”.

  The above snapshots are taken from a personal computer that uses Microsoft Windows software.  The top set would be MS’s interpretation of a classic deck and the bottom set from a more fanciful or cartoonish alternative deck.  Notice that with the Windows classic deck that the Jack of Hearts now has two eyes.  The bedpost queen now looks to her right like all the other queens and has only one eye showing.  The suicide king (called so because the left hand of King of Hearts usually held a sword behind his head, in the act of swinging) is now holding up some sort of a wand with a jewel and has grown a mustache.  Compare the MS version with the more common Cartamundi version just below.

  Microsoft was certainly under no obligation to copy the little idiosyncrasies of Cartamundi’s pattern.  Perhaps they made changes to avoid copyright issues; who knows.

* Cartamundi Group is a Belgian printing company that was made by the merger of three much older Belgian printing companies, who fifty years ago were trying to stay afloat in a competitive business.  By specializing in board games, collectibles, playing cards and packaging the company has become huge.  They claim to be “the world’s largest manufacturer and distributor of playing cards and board games” and also that their experience with the printing of playing cards goes back to 1765.

  The standard 52-card classic (International or Anglo-American or English version of the French pattern) deck has become ubiquitous worldwide for very plain reasons.  Visually both its face cards and pip cards (the numbered cards) are quickly interpreted at a distance, at a glance or upside down.  More important historically, the pattern facilitated legible printing.

  Before 1440 or thereabouts, all playing cards had to be made by hand.  They were drawn, painted, trimmed and adorned by hand.  The arrival of the Gutenberg printing press not only facilitated the distribution of affordable bibles, but of playing cards too.  Once a carved woodblock had its ink pressed into the paper stock though, the other colors in face-cards still had to be added by hand.  By the 1480s, card printers in France were using brushes to apply colors through separate stencils, which laid over the card.  The reason for simple classic suit design is easily understood in light of the printing technology of the period.

  Playing cards utilized both 2D imagery and color.  Over the centuries, important technological advancements in printmaking were driven in part by the impetus to manufacture and sell playing cards, which were in high demand.  A much more thorough explanation of card printing and of card history in general can be found at the website of “The World Of Playing Cards”.

Printing

An etching, originally published in an 1851 German encyclopedia named: “The Iconographic Encyclopaedia of Science, Literature and Art”.

  As the carving done to woodblocks became more intricate, woodblock printing hit a roadblock.  A wood medium allowed the carver to cut only a limited amount of detail. Luckily the process of etching on metal sheets (plates) was developed in the early 16th century (1515).  Etching basically involves smearing a wax over a sheet of metal and then scratching a drawing through the wax with a bodkin (nail or pointed etching needle).  An acid is then used to eat away at the exposed metal scratches.  After the plate is cleaned and the ground (the wax) is removed, then ink can be applied and very carefully wiped off.  It is the small amount of ink trapped in the etched scratches and depressions – that will with the help of pressure, get transferred to the paper.  As with movable type or block printing both –  a reversed or mirrored image is produced.

  In the next three centuries to follow, improvements in etching and printing methods would occur that allowed more tonal control and contrast to printed pictures.  Mezzoprint (from 1642),  Aquatint (1772) and lithography (1796) are all fascinating subjects of discussion and were necessary developments before the first multi-color printing could occur, with chromolithography.  More on these subjects some other time.

Cards and Gambling tax

  From the Renaissance period onward, improved printing permitted cheaper, more easily obtained card decks to be available and that then allowed many new card games to evolve.  Those card games were first and foremost about gambling: the risk and recreational chance of easy money and by association, sex.  “Crucially, playing cards held more appeal for women, and associations between card play and seduction became widespread throughout European literature and painting”.

  Night life being what it was then (before electricity, Internet or Convid-19 virus), governments soon became jealous of the large sums of money changing hands from gambling.  To ‘get a piece of the action’ governments either taxed cards or printers directly, taxed indirectly the paper used or flatly seized all production of playing cards and then monopolized that printing for itself.  Woe to printers of counterfeit, unstamped cards.  To make income for his government the 17th century monarch French King Louis XIV turned his whole sprawling Palace of Versailles into one vast and profitable, card-playing casino.

* Most classic card decks have an ‘Ace of Spades‘ that displays a more ornate or elaborate center illustration, than do the other aces in the deck.  That’s a reminder that in years past that newly printed card decks were taxed by the government.  The Ace of Spades was stamped to legitimize the deck and show that the government’s tax had been duly paid.

* The infamous Stamp Act of 1765 passed by the British Parliament was unpopular enough to be instrumental in causing a revolution.  It was a direct tax imposed upon the America colonies for printed goods; like newspapers, almanacs, pamphlets, legal papers, cards and dice.  The Stamp Act “required that many printed materials in the colonies be produced on stamped paper produced in London, carrying an embossed revenue stamp”.

Probability

Gambling became important enough that people began to analyze and study the factors of chance.

  Probability is the usage of math to determine how likely an event is to occur.  The basic probability formula is very simple: probability = target outcomes / total outcomes.  Since the numerator is always smaller than the denominator in probability problems, dividing the fraction yields a decimal result that always ranges between 0 and 1.  To express probability as a percentage that decimal is multiplied by 100.

  A coin has only two sides.  Flip a coin in the air and when it lands it can come to rest one of two ways; heads up or tails up.  Here there are only two possible outcomes.  If (A) = “heads up” then the probability of that result happening is: P(A) = 1 / 2 (total number of possibilities) or 0.50 or 50%.

A basic probability formula is often written as:

P(A) = n(E)/n(S)

Where,

• P(A) is the probability of an event “A”
• n(E) is the number of favorable outcomes
• n(S) is the total number of events in the sample space

  If you were to toss a coin in the air 100 times and keep track of the way it landed each time, you might discover that it lands 49 times with heads up, or instead your count might show that the coin lands 52 times with heads up.  This discrepancy or variation is the “variance” to be expected in a real world (and if 49 and 52 were the real results of testing twice then you could write it as: 50% ±2%).

Dice

  The most common type of dice are cubes with 6 sides and each side is marked with a number of pips (dots or dimples).  Assuming that a single die can only come to rest in one of six ways then the possibility of any particular side ending face up, is 1/6 or P(1/6) or 0.1666… or 17% (rounding up).

Most games use two dice however.   If for example a player wishes to roll a total of four points from a pair of dice, what are his chances?  The answer is 8%.  You could safely predict that 92% of the time that the same player must roll any sum, other than 4.  How is this prediction derived ?

  It was already established that with one die the chance of rolling any particular side up is 1/6.   But when 2 dice are used, then the denominator of probability is compounded.  Here the probability of one event occurring is multiplied against the probability of another event happening also.  There are 36 ways to combine the faces of two dice and the probability of any varying combination of 2 dice = 1/36.  But since there are 3 ways to roll a sum of 4 with 2 dice (1|3, 2|2 or 3|1) the numerators are added.  P(A) = n(E)/n(S) becomes P(4) = 3/36; or 0.083 or 8%.

  Below the 36 different ways to roll a pair of dice are illustrated.  One can see that there are more ways to roll a total of 7 than of any other sum.  There are 5 combinations that will total 6 or 8, but only one combination (from 36 possibilities) that will yield either “Snake Eyes” or “Boxcars” (a sum of 2 or 12).  Such probability is well understood by the “Hazard” player or by the “Craps” player.  But the successful Craps player uses a different language and a different arithmetic.

Odds 

  From the chart – the likelihood of rolling a sum of 4; is 3/36.  In the game of Craps however this is expressed as “11 to 1 odds” (or written as 11:1).  To arrive at this position 3/36 is reduced to the fraction 1/12, and then the “odds” are figured as 11 rolls that won’t come out as 4, against 1 roll that will.  Without introducing more confusing examples of this convoluted mental arithmetic, the definition of the word ‘odds’ varies depending on whether “true odds” or “payback odds” are meant, or where the game is played (in the street, at the table or at which casino – because payback odds can differ).  If you need to roll a 7 on the next roll to win, the true odds are 5 to 1 against (instead of 3/36 probability).  But if you bet $1 and win the roll, the house (casino) pays back only $4.  Pay back odds ensure that the house makes a profit in the long run.

* Odds in the world of horse racing are not particularly straight forward either.  In parimutuel horse or greyhound racing, the money from all bets is “pooled”.  Until the race begins the odds that are posted on a running “tote board” change according to how people are placing bets on different animals.  A popular or favored horse is determined by him receiving more bets, the odds against him winning will drop and the payout if he wins will be lowered accordingly because the pot is being divided by more people.  Conversely, an unlikely horse will receive fewer bets, the odds against him winning will become high and if he does win the payout will also be high compared to the bet wagered.  After the race or event is concluded in parimutuel betting, the “house take” (or race organizer’s fee) and applicable taxes are deducted from the pool first; before the remainder is divided between the winning bettors.

* “Win, Place and Show” bets have separate pools.  If you place a bet on a horse to show, you win if he comes in 3rd, 2nd or 1st place.

Probability with Cards

(using standard 52 card deck)

* Bridge is one of the few games where the 4 suits have rank.  Any of the 13 cards in the suit of spades outrank their equivalents in diamonds, hearts or clubs.  “According to Hoyle” suits are ranked from high to low: spades, diamonds, hearts and finally clubs. Suits have no special value or meaning in games like poker.

The probability of pulling a red card from a deck is: P(red) = 26 / 52 = ½ = 0.5 = 50%.

The probability of drawing a Queen from a complete deck is: P(Queen) = 4 / 56 = 1/13 = 0.0769 = 8%.

The probability of drawing a face-card from a deck is: P(face-card) = 12/52 = 3 /13 = 0.23 = 23%.

The probability of drawing a non-face-card is: P(non-face-card) = 40 / 52 = 10/13 = 0.7692 = 77%.

The probability of drawing either a diamond or a 6 is: P(diamond or 6) = [13 + (4-1)] /52 = 16/52 = 31%.

Assuming that aces and face-cards are not numbered cards then:

The probability of drawing a heart or an even numbered card is: P(heart or even) = (13 + 15) / 52 = 28/52 = 7/13 = 0.538 = 54%.   [ there are 13 cards in the hearts suit; and 5 even numbered cards in each suit: #2, #4, #6, #8 #10. The five even numbered cards in the hearts deck were already counted once – so only the remaining 15 even numbered cards are added to 13 ].

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How many different ways can you draw 5 cards from a 52 card deck, in no order?

Answer: 2,598,960 ways.

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* Factorial – signified by the exclamation mark “!” means to multiply a given number by all of the proceeding numerals before itself.  For example 5! becomes ( 5 x 4 x 3 x 2 x 1 ) or 120.   There is a useful combinations and permutations calculator @ MATHCelebrity.com.

* When order is important then a permutation formula rather than a combination formula would be used.  In permutations where placement is a consideration (ABC, ACB, BAC, BCA, CAB and CBA) would all be considered unique and different.

  Understanding probability is a useful tool in developing a better strategy to win at games like Blackjack.   In a Blackjack game between individuals the deal should periodically rotate between players because dealers have the advantage in blackjack.  This inherent advantage is exploited at the Blackjack tables in casinos, where the house controls all the dealing.  Of course the casino pays itself a little dividend called the “house edge” with every hand dealt anyway.   Even if you win a hand, the table deducts a small cut (say 5%) from the winnings.

* In interpersonal Blackjack games the rules should be agreed to before the game begins.  Rules for instance that establish how the dealer should act if or when he draws “a 17” for himself, rules that establish whether or not the dealer wins in a “push” (tie) situation or rules that establish whether or not a player automatically wins when he draws 5 cards without busting.

* Normal Blackjack rules state that dealers should “stand” on counts of 17 but must “hit” any count that is less.  But rules for Blackjack vary from casino to casino, even sometimes from table to table in a casino.  The rules at one table a might oblige a dealer to hit his own hand if he draws a “soft 17” (meaning an ace and – a 10 or face-card / this situation actually improves the house edge a little).

  Probability comes into play when players try to improve their Blackjack betting by keeping track of the cards that have been played and then estimating what is left in a deck before the next deal.  There is a basic strategy to be used by a player, that lays out statistically wise actions to be used for certain situations.  Beyond that a good player might attempt a version of “card counting” where as an example: each type of card is assigned a value of -1, 0 or +1 and the player keeps a running total in his head.  That running total can give the player a useful probability tool which can be used to make profitable bets.  Books have been published on the topic.  Casinos realize this and change the deck (by piling 5 or 6 decks atop each other in the “shoe” / frustrating an accurate count) or will stop the game or remove the player if they believe that a player is counting cards.

“One armed bandits” or what passes for slot machines in this age of microprocessors and video screens, are notoriously bad gambling propositions from a statistical standpoint.  And yet casinos are filled predominately with these machines now.  Some people don’t mind being hoodwinked.  You can trust in the fact that casinos study human psychology every bit as much as they study statistical probability.  Gambling might be shunned by protestant churches because it brings out a weakness in some people and psychiatrists might classify such weakness as “addictive disorder”.  But designers of slot machines deliberately make their devices as psychologically addictive as is humanly possible.  (Many cell phone Apps are made that way too).

  Often these machines are complicated and sport “features that affect the payout of a spin: multiple symbols with different pay scales, wildcards, scatter symbols, free spins, jackpots” etc.  One of the major but subtle psychological factors at play is the reliably proven – irregular, or intermittent reward schedule at use.  The house edge might range from 1% to an atrocious 15% on identical slot machines in the same room.  But just as in some modern bars where liquor is digitally metered and delivered through a hose and spigot instead of being measured in an honest shot glass,  the volume or payoff can be adjusted up or down with a few simple keystrokes – when maintenance is preformed.

  By way of conclusion, when one studies a classic or International card deck, he or she might erroneously assume that there are hidden symbols of import in the suits and rank of court cards.  There are not.  Religious symbols abound though and the noble notions of chivalry, courtliness and manhood have long been associated with those old icons and symbols.  Cards instead, were mainly intended for gambling.  Governments funded themselves from gambling proceeds and from the printing of gambling cards.  Proficient gambling or the sponsoring of gambling events successfully, requires study and understanding of statistics and probability.