# The math behind the card game "Spot It"

Originally published at: The math behind the card game "Spot It" | Boing Boing

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I forget where I’d heard about someone calling the company to complain about the two missing cards, and being told, the piece of paper we cut them out of is slightly too smaller. Junior Spot It! has the full 5^2+5+1 cards.

As the article explains, it’s based on the fact that two lines in the plane intersect in exactly one point – as long as you include the “line at infinity”, which itself has one point for each slope.

This suggests two new ways to play with a Spot It! deck. One is based on the fact that two points determine a line. Lay out all the cards, name two symbols, and race to find the unique card that bears both symbols. After half an hour of desperate boredom give up, deciding that you hit the 2 in 57 chance that the card you’re looking for is missing.

In the other, pick a symbol and decide that the 7+1 cards bearing that symbol are on the line at infinity. Then lay out the remaining 7^2 (well, missing two) cards in a 7x7 grid, subject to the condition that in each row, each column, each diagonal, even each diagonal of slope 2, or 3 or 4 or 5 or 6, there must be a common symbol. You can start by picking three arbitrary cards to go in positions (0,0), (1,0), (1,1), so long as they don’t all three have a symbol in common. After that there will be a unique way to proceed!

At one point I was thinking about an extension pack for Spot It!. Instead of lines in the projective plane (i.e. equations of the form Ax+By+Cz=0 up to rescaling), let’s throw in irreducible conics as well (equations of the form Ax^2 + Bxy + Cy^2 + Dxz + Eyz + Fz^2 = 0 that don’t factor; think ellipses). The tricky bit is that we now need to go back to the original cards and label them not only with the “real” points that had before, but also with the “complex conjugate pairs”. I imagined some difference like inanimate / living, for the symbols. Maybe give the new cards a yellow border or something. If you pick two old cards, find the inanimate symbol they share. If old and new, find the animate. If new and new, look for two animate — but every now and then your ellipses will be tangent. This would probably get too big for p=7 but I should really make it for p=3 someday.

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This is the type of game that Mrs Peas is so good at, it’s really not fun to play her. I end up so far behind within a few card flips that there is zero chance of catching up.

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I know this game as Dobble. It’s our train journey standard

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# that no two shall walk twice abreast.

That’s easy for a sailor.

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People who are good at these real-time pattern recognition games (I had to look this up on Boardgane Geek, otherwise I just call them reaction games) are simultaneously amazing and frustrating. I love how they can analyze and process the visual data that quickly and act on it. But at the same time, it quickly saps games of their fun because there’s just no way for the rest of us to catch up or even realistically train to get better.

I’ve a friend who bought a game like that for me so that we could play it on game nights. It quickly got hidden away because we’re all convinced she bought it for the purpose of embarrassing us at it on a regular basis.

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I thought the post was going to be this video, which is incredible, features meta-dobble, and the 10.3k icon version insanity.

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Spot It is in our regular rotation for game night starter-uppers. I knew there was some crazy math involved, but myself just a little too thick for that kind of sorcery. Learning its history is really neat, tho.

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