Tarot Math

If you’re like me, you have no doubt looked at what seems to be a wildly notable pattern of cards having something dramatically in common in a spread, and wondered, “what’s the odds of that?” We’ll start with a simple example. In a three card spread, what are the odds of getting three Eights? I’ll tell you. The odds are 19,019 to 1. If you see some cards and know they had odds against them all appearing together of nineteen thousand to one, you’re going to pay attention. And in fact, the 19th and early 20th century experts took note of these patterns. You’ll find that Waite, in The Pictorial Key to the Tarot, has an entire section on "The Recurrence of Cards in Dealing." He even provides additional meanings for these patterns. For example, in the case of those three upright Eights, Waite writes that it signifies marriage. Waite most likely was looking at a layout of ten cards. Given seven additional opportunities to draw an Eight in a ten card layout, the odds drop all the way down to 175 to 1. But more than just numeric patterns, we can also ask what the odds are for getting all the cards associated with Capricorn. Or if we see four of the six cards associated with Venus, we can look up the odds of that. Fortunately modern spreadsheets provide something called a hypergeometric function which allows us to answer questions like these. And you’ll be able to download a spreadsheet in which you can plug your own numbers.

Given a fair-sized spread—say ten cards—we sometimes might say to ourselves, “hmmm… that’s a lot of swords there…” or “gee, not a single court card…” Those insights can and do affect the “bottom line” of a reading. Knowing, for example, that in the spread you just laid out for your client, Mars is very heavily represented can provide a rather important insight. Though deck designers often try to give us clues, it might be easy to miss something like that. Some decks even print the zodiac, planetary and/or qabalistic symbols on each card, specifically for this reason. This post isn’t going to give you any startling revelations. It’s just an odd, longish table I drew up to calculate, using standard deviation functions, the minimum-maximum numbers of the types of cards we should expect, in layouts between 1 and 16 cards in size. You’ll find breakouts for the classical elements, the Zodiac signs, the planets, the major and minors, the court cards, and, last but not least, reversals. If you find it helpful, great. If not, no worries… we’ll get back to those deep analysis type posts soon enough; this is just my way of takin’ a break. 😉