Eeyore and Tigger Read the Cards: The Statistics of Optimism

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Every Day Oracle (La Vera Sibilla): Malinconia and L’allegria (Lo Scarabeo); with A. A. Milne’s Eeyore and Tigger (E. H. Shepard, illustrator)

Have you ever caught yourself subconsciously picking which of your friends to confide in? When you’re bursting with exuberant feelings about that hot new date, you’re not rushing to Facetime your good buddy Eeyore. And when you have vague unsettling suspicions about how your boss is treating you, trying to get Tigger to stop bouncing and listen is a fruitless task.*

But there are times you want neither Eeyore nor Tigger’s one-dimensional world view. Because…tell me the truth! Is the world basically a happy place or a difficult one? Is the cup really more than half-full, or less than half-empty? Sometimes you want a friend who will give it to you straight, both the good and the bad–whatever that means.

“Good” and “bad” is a big can of philosophical worms. Buddhists think people are good, with clouds veiling their goodness, but the world is a bad place of suffering. Christians think people are bad (original sin and all) but the world is good since God created it (plus we have dominion over it, making it doubly good). Then there’s non-dualism, where everything is neither good nor bad, it just is. These are vast oversimplifications, so I’ll stop here before offending even more readers, but you get the picture. It’s not like we all agree on what’s good or bad, though we think in those categories all the time. (And you thought this post was just about reading cards.)

Many traditional systems of cartomancy assign a pretty definite good, bad, or neutral to each card.  And when were these traditional cartomantic systems used? More likely when you had a problem than when things were going okay. I always imagine life was–not easier–but more straightforward back then. Today’s problems are nebulous, speculative. If I am a workman in 18th century Italy and I lose my leg, that’s pretty clearly “bad.” Less clear is the impact on global warming of my food choices. My world seems to take place in a more mental sphere (using “mental” in both the American and British senses) where good and bad get more malleable. Confusing.

I got curious about the distribution of “good” and “bad” cards in the traditional, 52-card Italian Sibilla (La Vera Sibilla). Is it an Eeyore friend, a Tigger, or in between? So I did some simple number-crunching.

In the system I am working with, cards are read upright or reversed. Generally, the court cards are good when upright, bad when reversed (Spades being an exception), so that’s mostly a wash. This leaves 40 cards with upright or reversed indications, giving 80 designations. I used the designations on Matt Sybil‘s site to categorize them as positive or negative. Here are the data:

sibilla statistics

Upright meanings are somewhat more positive than negative: 13 to 9. Adding positive and positive/neutral categories gives 24; likewise with the negatives give 13. So the positive/negative ratio is 24 to 13, or almost 2 to 1. The cup is 2/3 full. The uprights have a Tigger vibe.

With the reversed meanings, only four cards are positive, compared to a whopping 25 negative. Grouping categories as before makes the overall ratio 6 positive to 33 negative. I guess you could say reversed cards are not so good. There’s only an 18% chance that reversed card you just turned over is any kind of positive. Definite Eeyore feeling here.

Since this is an integrated system, it isn’t really fair to cherry-pick–in other words, to use only the upright meanings and simply discard the reversed meanings. Using just the upright meanings give a far rosier picture of the world than the system as a whole. Unless you want totally-Tigger Sibilla–or as close as Sibilla gets, as there’s still only a 2/3 chance your upright cards will play nice.

Taking the whole group of 80 upright and reversed meanings gives 30 positive, 46 negative, and just four neutral meanings. Including court cards (with spades negative either up or down), the ratio is 39 positive to 61 negative. The cup is 2/3 empty.  Sibilla veers toward Eeyore. The preponderance of negative cards in La Vera Sibilla makes it tough to get happy news.

Now, the whole premise of cartomancy is that cards don’t obey the laws of statistics. Those “laws” are really expressions of the behavior of large numbers of trials. If you toss a coin and get heads, you can get heads next time, though the probability of heads is but 0.5. In fact, there’s a calculable statistical probability of getting quite a long string of heads, though it rapidly gets smaller the longer the string. So even if you (or a disbelieving friend) think the cards you pulled are just following random chance, it’s possible to pull all negative cards from a “happy” deck, or vice versa. Just not likely. And no one knows why, on that particular day, you got 15 heads in a string of coin tosses anyway. Or all positive cards in a 9-card string. A statistician would shrug, uninterested.

Recently, Amore appeared repeatedly in my daily three-card draw. It showed up three days out of five, a statistical probability of  0.181%, or less than a 1 in 500 chance. The next day it showed up again–four days out of six. Now the probability dropped to 0.0147%–i.e., 3 chances in 20,000.** Yes, it could happen, but it isn’t all that likely based on the assumption of meaningless chance.

If you contend that you get the string of cards you were supposed to get (via synchronicity, etc.), then you don’t care about statistics anyway. Low statistical probability doesn’t stand in the way of it was meant to be. Let’s say you were meant to receive super-happy news. In that case, getting the only three “good” cards in a deck of 1000, say, would be unremarkable–you were “supposed” to get them, so you did.

Now let’s think about cards as a language. A language expresses a world-view, a way of valuation, underlying its expression of direct content. Think about the old question: “How many Eskimo words are there for snow?” The latest scholarship pegs that number at 53 in one Inuit dialect, with 73 terms for ice in another Inuit dialect, and 180 terms for snow and ice among the Sami people of far-northern Europe. Likewise, medical encyclopedias of mental conditions have relatively few entries to parse “quiet contentment” from “an inward smile,” but lots to distinguish one negative condition from another. Major concerns get close attention, with fine distinctions of meaning articulated. Phenomena of little interest don’t get the same attention, nor are they rewarded with the same number of distinct words. Moreover, there’s feedback in the loop. The thinking of a language’s users is colored by the language itself. We tend to notice what we have words for.

If a card system is a language, then its vocabulary tells us something about the world-view of the culture that uses it. Even though the Italian Sibilla is a somewhat patched-together system, with some near-duplicate cards, it has survived, with all its dour “synonyms.” Is this due to tradition, habit? A gloomy, Eeyore world-view? To reinforce the message? Or a need to make subtle distinctions–one alarm, two alarm, or three alarm fire? Predicting happy outcomes satisfies my curiosity and longing, but alerting me to danger can save me. We are hard-wired to notice trouble. Attention helps us survive.

From a statistical perspective, you’re more likely to get “bad” news from the Sibilla than good. But from a linguistic perspective, the percentages suggest that the cards simply describe more nuances of unhappiness than of happiness. This is not so strange, after all. Good news is a tad featureless. Who hasn’t been attracted by the intricately lurid details of some on-going crisis (current politics comes to mind)? On the other hand, who hasn’t been bored within 10 seconds by a new parent gushing about the latest variety of coo their genius baby has produced? (I speak as one who collared perfect strangers with this type of information when my own kids were young.) “They lived happily ever after” is quite enough to satisfy, after a thrilling tale of combating hideous ogres and other evils.

Let’s return to the slippery nature of good and bad. Old-time Italian cartomancers were practical folk who would easily have understood the following old story (variously attributed to the Sufis or the Buddhist masters, and universal in its wisdom):

A man’s horse ran away. His neighbors all said, “Oh, what bad luck!” but the man just said, “We’ll see.” Looking for the lost horse, he came upon a herd of wild horses, thus vastly increasing his wealth in horses. The neighbors all said “Oh, what good luck!” but the man just said, “We’ll see.” Soon after, his son was thrown as he was breaking in one of the horses, becoming permanently lamed. The neighbors all said, “Oh, bad luck!” but the old man just said, “We’ll see.” Shortly afterward, the army conscripted all the young men in the region–but the son was not taken, being lame. The neighbors all said “Oh, what good luck!” but the man just said, “We’ll see.”

That’s the end of the story as I know it, but of course it could–and does–go on forever. “Good” and “bad” were malleable in the old days, too, and their mixture tells a story as complicated as real life. “He’s gonna cheat on you–but you’ll be thanking him, cause you’re gonna wind up with a real prince.” “Cheating” is a bad card–till it’s not.

Here’s a practical conclusion based on my ponderings. With such an extensive vocabulary for describing nuances, laying more cards seems better. Are three cards too cryptic for the Sibilla? Five, seven, nine, and 13 card strings are traditional, as well as various other, more elaborate spreads. We like to be efficient, with our bullet lists and sound-bites and Twitter feeds, but long ago people took time. Time to lay a string of cards down, add more cards, do a Grand Tableau or maybe three.  That friend who goes all around the block before getting to the point doesn’t do so well in 140 characters, but his long-winded stories make the point colorfully and well.

I’m glad I took the time to do the numbers on this deck. I wanted to know if it had a bias and how to take that into account in reading with it. It does have a bias–it wants me to know the full story on bad news. I’d like to think it’s being helpful rather than just pessimistic. But in the end, I only know what feels good–who knows what is good? The waning of a friendship, the loss of a job, the new lover…Good? Bad? Both or neither? Just another wave in the endless flow of “This too shall pass.”


*  For readers unfamiliar with Eeyore and Tigger, they are friends of the famous Winnie-the-Pooh, beloved by English-speaking children. Their Sibilla counterparts are Melancolia and L’Allegria, respectively. I highly recommend getting to know these archetypal figures through the works of their creator, A. A. Milne, rather than through their Disney doppelgangers.

**  I calculated the probabilities like this: I used this expression for the probability of k occurrences out of n: Pr = (n choose k) (p*k)(1-p)*(n-k).  I assumed I had 3 chances out of 52 of getting Amore in my three-card draw, thus 49 chances out of 52 of not.  So p = 3/52 and (1-p) = 49/52.  k = 3 and n = 5 for the first calculation; k = 4 and n =6 for the second. My statistics is plenty rusty, and I used this source to refresh it, but please let me know if these calculations need correction.

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