Tuesday, March 26, 2002

Arrays



By Linda

In New Spring, Siuan’s ability to assess information and analyse it for patterns is tested by a sequence of cards.

Siuan riffled through the pages too quickly for her to catch everything, but it seemed to be nothing but the names of playing cards, in no particular order she could see. The Ruler of Cups was followed by the Lord of Winds, the Ruler of Flames by the Lady of Rods, but then it was the Five of Coins followed by the Four of Cups.
"There's a game I've read about," Siuan said slowly, "a game wealthy women play with cards, called Arrays. You have to put the cards in descending order in one of a set of patterns, but only certain suits can be played on others. I think someone wrote down each card as it was played. In a winning game."

- New Spring, Entering Home

(See photo right of two of the sequences (Ruler of Flames (Swords) and Lady of Rods, Five of Coins and Four of Cups, Lo Scarabeo deck of cards).

Arrays is a pattern-making game and probably played solo (since only a solitary player could write out the order of cards as they are played without ruining the game). It is therefore derived from the real world group of patience or solitaire games. It may in fact be the Wheel of Time generic term for patience games as well as this particular game, just as the game of Patience (or Solitaire) lent its name to the whole group of single player games.


The Cards

Playing cards appeared in Europe in the 1370s. Early cards were individually hand-made and painted, which made them expensive to produce. Similarly, Mat tells us that aristocrats play cards while the common folk prefer their faster and simpler dice games. Siuan remarked that her family were too poor to afford playing cards. (They also couldn’t afford the time to play patience for hours on end, either).

Arrays is played with the Wheel of Time five suit deck: Cups, Winds, Flames, Rods and Coins - that we first saw in a Chop (‘Poker’) game in Tear in The Shadow Rising (see Chop article). The suits are similar to those in traditional Latin (Spanish and Italian) playing card decks and in tarot decks. In fact, three of the suits are exactly the same – Cups, Coins and Rods. The fourth suit in Latin and tarot decks is Swords. Flames is probably equivalent to Swords, since the ruler of Flames stabbed Mat with a sword when the bubble of evil hit and the sword image stayed. This would make Winds the extra suit. In the fifteenth century decks with five suits were common.

Below is a list of the Latin and Wheel of Time suits and their corresponding suits in international decks (from Wikipedia):

Latin/Wheel of Time.................International
Cups..................................................Hearts
Coins.................................................Diamonds
Rods (sometimes Batons)...................Clubs
Swords (Flames in WOT deck)............Spades

The Wheel of Time deck of course, has the Winds suit as well.

Siuan says that only certain suits can be played on others and from the way cards were grouped in the quotes it appears that Cups are placed on Coins, Winds on Cups, and Rods on Flames. Therefore probably Flames go on Winds and Coins on Rods.

From the quotes and what I know of real world patience games (and I play quite a few of them), the likely aim of the game is to construct runs of cards in rank order while following the restriction of the suit sequence described above.

Of the court cards, Ruler is highest and can be of either gender (we know this from Chop). The next rank appears to be Lord and Lady. Some suits have one, some the other. This would fit in with Jordan’s theme of balance between the sexes. Since the Four and Five are mentioned, the suit ranks probably run from Ruler, Lord/Lady (perhaps with one or more other court card ranks) right down to One (Ace).

Arrays is an appropriate name. In patience games cards are laid out or arrayed, in decorative patterns and in certain sequences (an array in mathematical terms).

Many patience games have some restriction on suits, usually requiring runs to be in all the same suit or in alternating colour. There is only one real world patience game which has the restriction of a descending run in a particular order of suits: Following. This suit order is Heart, Club, Diamond, Spade: meaning that only a Club can be placed on a Heart, a Diamond on a Club, a Spade on a Diamond and a Heart on a Spade. As shown above, Hearts are equivalent to Cups, Clubs to Rods, Diamonds to Coins and Spades to Flames with Winds the extra suit, so the suit order of Following is not exactly the same as for Arrays. This is not surprising since Arrays has an extra suit. The method and principle of the games are the same, however.


Following

Following uses a four suit pack of thirteen ranks (52 cards). To start, six cards are laid out in a row face up to form the tableau. Any of these cards that is the following suit of an exposed card in the tableau and one rank lower, is placed on that card in the tableau to commence a column of descending cards. Cards are turned over singly from the stock, that is the remaining cards in the player’s hand, and built on the descending columns (following the suit pattern in descending order) for first preference or filled on any empty spaces in the tableau. Cards from stock unable to be used go into the waste pile.

As the Aces occur they are placed above the tableau in the foundation row and are built on in the same suit rotation but in ascending order. This ascending sequence can be built on from the exposed cards on the tableau or the waste pile or the stock and the aim of the game is to completely build the foundation row. The photo right shows a game in progress using Latin suits. Sequences can be transferred from one column to another in the tableau provided the join follows the rule of the suit and rank order. Any vacant place in the tableau may be filled from stock, waste or tableau. Only one run through the waste pile is allowed.


Arrays

While Siuan said the aim of the game of Arrays was to form descending columns in a particular suit order, this may not be the ultimate goal. Many people would say that the aim of the real world game called Solitaire/Patience is to form descending columns in alternating suits, and this is certainly essential to winning, but not the full story. These columns are formed in Solitaire in order to make ascending sequences of all one suit in the foundation row above the descending columns. The game is won when these are made. Likewise, the successful completion of the descending columns in the proper suit order means that the game of Following is effectively won, because they ensure that the ascending columns of the foundation row can be made correctly (so long as the player doesn’t make a mistake). We don’t know if Arrays is exactly same as Following but it would be very similar.

A five suit deck of thirteen ranks has 65 cards and would start with either a seven or eight card tableau. After some experimentation, I found that as the mathematics would predict, using a tableau of seven cards the game was less likely to be won than the four suit version of the game (which uses a six card tableau). With a tableau of eight cards the odds were in favour of winning the game and it was much less challenging. My preference is for the seven card tableau.

If there are fewer ranks in the suits, then the tableau would be decreased accordingly. A twelve rank suit (60 cards) would use a seven card tableau and a ten rank suit (50 cards) would use a six card tableau. While Chop would be an interesting game with seven to nine ranks in the five suits (35 to 45 cards), Arrays would not be. Therefore I consider 50 cards the minimum size of the Arrays deck. It is quite possible, even likely, that Chop and Arrays use different size decks, just as happens with different real world card games.

The photo to the right shows a late-stage game of Arrays in progress with a seven card tableau which will be won. (Lovers of Terry Pratchett’s Discworld books might be interested to know that the deck I used is the eight suit Fat Pack designed to play Cripple Mr Onion.) I chose Roses as the extra suit and used all thirteen ranks (sixty five cards).

So there it is: those wealthy women that Siuan had only read of were playing a patience game.

2 comments:

Tim said...

In the Chop article you say "There are not likely to be 13 ranks per suit as in most real-word decks, since that would be 65 cards in a five suit deck, which is unwieldy and the probability of high ranking hands would be low. The most likely range is 7 to 10 ranks in the five suits, making a deck of 35 to 50 cards." Why in this article do you simply assume that there are 13 ranks and a 65 card deck? I find it much more likely that there are around 10, as you said, to make the deck more managable.

Linda said...

When I wrote that, I was not planning on writing an article on Arrays, and so I was referring to the Chop deck size only. I'll add a section to this article discussing the size of the Arrays deck.

If the two games used the same deck it would be one of 50 cards. It's quite possible though, that as so often happens in real world card games, the two games use different size decks.

A 65 card deck would make for a very boring Chop game, but it is quite good for an Arrays game.