Statistics! Tarot! Yay!

Ladies and gentlemen, the results are finally in. This summer, I announced that I would be performing a statistical analysis on my daily draws, conducted over the course of a hundred consecutive days, to look for patterns in Tarot that deviate from a random distribution of the cards. And now, a hundred days later, my experiment has come to an end.

This depressing XKCD comic is what comes up when you Google “math party” and limit yourself to results labelled for noncommercial reuse.

I embarked on this journey out of simple curiosity. So many people in the Tarot community talk about near-mystical experiences where they conduct readings and exactly the right cards come up to describe a querent’s situation. Many (if not most) Tarot readers believe that there is some underlying principle, be it the collective unconscious, a guardian angel, or active volition on the part of the cards, that consistently results in astounding synchronicities.

For myself, I’ve certainly experienced those jaw-dropping coincidences, in readings for myself as well as for others. But I’ve also had a hell of a lot of readings where the cards that came up were really rather blah, and only related to the querent’s life through my ability to interpret them and to work with the querent in understanding themes they might represent. And there have been other cases where the cards really and truly could only have meant one thing,* and that thing turned out not to be the case. Or I’ve had readings where I offered an interpretation for the cards, and found that my interpretation was off-base, but could find absolutely no way to connect the reality of my querent’s situation back to the cards I had drawn. In my experience, every instance of awe-inspiring synchronicity is matched by three or four other instances where there was no objective significance to the cards, or where the significance was derived from my skill as a reader and not from the cards themselves.

So, being scientifically minded, I decided to put this idea to the test. Do the cards that come up in Tarot reading actually deviate from a random deviation? Are there demonstrable patterns that point to some outside force guiding Tarot reading? Are the cards that show up the “right” cards, or are they just randomly selected?

Over the course of 100 days, I drew a card for myself each day. In between draws, I shuffled my deck at least eight times (which, mathematically speaking, is the number necessary to completely randomize a 78-card deck). And each day, I recorded my draw based on three variables: number, suit, and reversal (or lack thereof). I determined that at the end of my hundred days, I would perform a chi-square analysis on each of these variables to see if there were any discrepancies that might point to some kind of supernatural element in Tarot beyond simple randomness.

Depending on what you’re hoping for, these results are going to be either very pleasing or very disappointing.

Looking at a hundred daily draws, the distribution is almost exactly what would be expected from simple randomness. Exactly half of the cards I drew were reversed. Seventeen were Cups, and nineteen were Swords (out of an expected 18 for each suit). The median number of times I drew a card of a given number from the Minor Arcana (e.g. a Four or a Knight) was 4.5, compared with an expected 4.78.

In short, Tarot looks random. Absolutely nothing in the distribution of the cards even hints of an outside force that selects the cards that are “right” for a given day. Instead, it looks like I randomly drew 100 cards from a 78-card deck, reshuffling after each draw; the results look the same as they would if I had drawn all of the cards in one fell swoop, not asking the Tarot any questions or thinking about the draws as Tarot readings.

The closest thing to an anomaly that I found was that I only drew 11 Pentacles out of an expected 18; but there, using the chi-square test, we get a chi-square value of 2.69 for that amount of deviation. In order for there to be even a 25% chance that this deviation was not the result of chance,** we would need a chi-square greater than 11.14. Even if, at a casual glance, drawing eleven instead of eighteen seems somehow significant, from a mathematical perspective it’s really not.

To those who do believe in some metaphysical principle that guides Tarot, allow me to make myself perfectly clear. I am not saying I have “disproved” your beliefs. I am not saying that I, with my one flimsy experiment, have thoroughly and irrefutably shown that there is nothing supernatural or metaphysical about Tarot. To claim that would be ridiculous.

However, I think I have shown that Tarot–whatever you believe it is and however you believe it works–is functionally very similar to randomness. And if you do believe that something guides the cards or chooses certain cards based on a querent’s needs, it might be useful to think about the results of my experiment and find a way to reconcile them with your beliefs. Maybe Tarot encompasses the totality of the human experience so perfectly that all of its different components are represented in equal measure when you use it to examine an individual’s life. Maybe it’s unfair of me to look only at objective variables like suit and number, rather than the deeper “meanings” of each card as they connect to each other. Maybe the cards picked up on my über-rationalistic energy and spat out randomness at me because of it.

For myself, I’ve always been inclined to think that the turnup of the cards is just random, and this experience has reinforced that opinion. It seems like the simplest explanation to me. And the thing is, that doesn’t in any way abase the Tarot or make it less useful for me to work with it. To me, the value of Tarot is not in some supernatural belief about it “working” or about the cards knowing my problems or predicting their solutions. I see value in Tarot as an interpretive process. I see the deck as chock-full of universal themes that I can relate to my life, and reading for me is not about finding guidance from some external source, but rather about reflecting on those themes and how they fit into my world. And for that, it really doesn’t matter whether the “right” cards show up in a reading or not. What matters is that I find a way to make those cards relevant. (For more on this, feel free to check out my “How I Use Tarot” tag.)

Now, all that aside, here are a few things I noticed in the overall spread of cards. They aren’t statistically significant, but in the process of reading and interpreting the hundred cards together, I found them noteworthy. They’re part of that process of meaning-making for me, of taking something random and finding patterns in it that can help me think about my life in new and interesting ways.

fool-juggler

The three most commonly recurring cards were the Fool, the Two of Wands, and the Sun, each of which appeared four times. The Sun was upright all four times, as was the Fool three out of four. So I would say that these cards are tone-setters for these hundred days as a whole. (Not a bad hundred days, if I do say so myself.)

The King of Swords appeared three times, and all three times he was in reverse. I identify very strongly with the suit of swords (which must be shocking to you after reading this whole long post about how I think Tarot is completely random and I did a statistical analysis to prove it), so it was interesting for me to note this. Although the number of Swords I drew on the whole was pretty much exactly what should have been expected, seeing the inverted King pop up multiple times makes me think about setting my rabid rationalism aside and focusing more on creative and artistic endeavors. It also makes me think about limiting the scope of my view and focusing on the short term rather than the big picture. (Both of these interpretations are, incidentally, in line with the Fool as a tone-setter, although the latter doesn’t fully jibe with the Two of Wands.)

It’s also interesting to note that I drew every card from the suit of Cups except for the Seven. The run of Cups, and the exception of this specific card, suggests that the past hundred days have been very much about expanding on emotional awareness and cutting away false views or unhealthy expectations. Similar notable absences include the Six and Nine of Wands.

There’s more that could be interpreted, but that’s the general gist of it. And hopefully, in looking at this analysis, you can see a bit of what I mean when I say that the randomness of the cards doesn’t deter me from interpreting or finding value in them. Do I believe that some external force (or my own subconscious, or the manifest will of the universe, or…) prevented the Six of Wands from showing up in my daily draws for the past three months? Certainly not. I think that card is as likely to have shown up (or not) as any other. But knowing that it didn’t show up, and knowing the meaning ascribed to it, I can sit and reflect and think about some way that card fits into my life.

I would be really interested to see what other people make of my results after these past hundred days, especially those of you who take a more mystical approach to Tarot. How do you interpret my findings? How would you respond to what I’ve said here? Have you ever conducted a similar experiment of your own, just to see? Leave a comment, make a reply post, put a video on YouTube, hire a skywriter to fly above New York with your response. I’ll read ’em all. (Or, you know, watch, in the case of the YouTube video.)


*Blah, blah, blah, multiple ways to interpret each card, blah, blah, subjectivity, and so on. But you know what I mean. I had a reading not too long ago where the cards positively screamed that my querent’s marriage was falling apart. Yes, if I’d really searched, I could have found another interpretation, but sometimes a certain narrative fits together more easily than others.

**The 25% mark is actually exceptionally lax. In the scientific community, it’s common to test at or below the 5% mark. So you see, I really did try to give the non-random argument a fair go.

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6 thoughts on “Statistics! Tarot! Yay!

  1. I acktually read this weekend from The Tarot of Spirit by Pamela Eakins that non mystics explain why cards tell you just what you need to know is because every card gives you a certain perspective to see your problem/the world through. So no matter what card you pull it will always apply in one way or another. I tend to believe that… but I also believe in synchronisity. Magic is all around us and I choose to believe that along with mathematical theories and scientific evidence, the magic and mysteries of life are right there beside them.

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  2. Very nice article. I think there’s plenty of magic to be had in making one’s own meaning of a random draw, and you explain that very clearly here. Thanks.

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  3. Good work doing the 100-day study. I can relate to your finding trends in card/suit occurrences during that time and creating a new perspective out of those. That is similar to how I think when I look over my frequency charts of 28 years of reading.

    About the Tarot and synchronicity, I would say that life itself has synchronicity, but we don’t stop and focus on every moment or every conversation snippet or song on the radio or type of bird flying over our car to piece together meaning, the way we do when we sit at a Tarot reading. We are also not educated in a way to understand synchronicity as it relates to the events that occur in our physical bodies, which should be huge antennas of perception for us to use to experience more than the physical world. Therefore, I ask my clients why the clarity they are seeking over the issues and circumstances of their lives would not be racing towards them as fast as they are racing towards it. In other words, if they are sincerely open to input about whatever they are processing, why do they think that input would not be surrounding them. It doesn’t mean that the input would be an “answer,” it just means that what they need to support them and move them further along would be there. At that particular moment, it could be in the form of a Tarot reading.

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  4. Also, about the Tarot and randomness, this reminds me of my experience owning my Thoth Tarot deck for 28 years. This deck belongs to me, and I choose to treat it like a magical object. I tend to keeping the deck clear of foggy energies that might gravitate towards a magical object. I build relationship with it. I invoke it before a reading, respect what it offers me, thank it after the reading, and store it in a dignified way. We have an understanding that I will not come to it in a state of insincerity, and it will not spew out card combinations that do not yield timely, relevant, powerful meanings to me. All this means to say that the cards are sensitive to the thought processes of their owners. If an owner places a lot of value on conformity to the theory of randomness, the cards can conform and still be a meaningful tool.

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  5. This is an interesting experiment, but I think the inherent problem is: you came to a conclusion that cards are random, and yet they made sense to you, in context of your own life. So are they random, then? 😉 True randomness would be something that does not have meaning, IMO.

    I don’t believe that simply receiving the same card or the same suit would prove tarot correct (or the opposite, incorrect). After all, if tarot reflects something, it’s our inner states and emotions. How likely it is that you experience exactly the same emotion days in a row?

    Would you only believe you’re in love if you receive a row of Ace of Cups, whereas real love fluctuates from joy of life to passion to insecurity to bliss to jealousy to obsession, and myriad of shades between? Where I’m going is: life, or our emotions are inner states, are not in a stasis. How could tarot be, then, if it’s supposed to mirror what’s inside or on some higher/spiritual/intuitive level?

    I’m much more interested in whether the card *really* fits into the querent’s life, or is it superimposed by our hopes that it fits? And that’s the difficult part to prove, either way. But thanks for a well-written article, I’ll run this same experiment myself!

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  6. Although I do understand the reversals of the King of Swords I’m actually very happy to see someone apply their analytical mind and knowledge of science to Tarot without completely discarding it’s authenticity.
    Thank you for dedicating this attention to tarot and I hope to see more of your experiments in the future.

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