Comments on: Set!

Set!

brevator — Mon, 04 Feb 2008 09:40:18 -0800

Set! Set! Set! (now @ NYTimes!) Learn to play. Get a deck! I love set!

Yeah, this was once posted back in 2000, but now you can start a group game on NYT, so I figured this was worth a repost.

By: ORthey

ORthey — Mon, 04 Feb 2008 09:42:27 -0800

Man, I used to love set, but being colorblind made it so damn frustrating.

By: grimmelm

grimmelm — Mon, 04 Feb 2008 09:43:27 -0800

And for everyone who loves Set but thinks it's just too . . . simple, check out Ordered Triplet.

By: Afroblanco

Afroblanco — Mon, 04 Feb 2008 09:43:40 -0800

I've tried this game before. Unfortunately, I'm smart enough to play it, but not smart enough to enjoy it.

By: brevator

brevator — Mon, 04 Feb 2008 09:43:45 -0800

Supposedly 25% of the male population is color blind.

By: DU

DU — Mon, 04 Feb 2008 09:45:53 -0800

My son's teacher introduced him to it and he introduced me. (Making your own deck from index cards to cheap and super simple.) It's a good game for adults to play with kids since it's a pattern recognition thing, not a strategic/knowledge thing. Assuming the child has the attention span for a 15 minute or so game.

By: not_on_display

not_on_display — Mon, 04 Feb 2008 09:58:54 -0800

I'm getting a headache, but I like it.

By: agregoli

agregoli — Mon, 04 Feb 2008 09:59:27 -0800

I LOVED this game. If that's true about many men being color-blind, it would explain why whenever we taught it to new people in college, the men were almost always slower to learn it than the women.

By: PhiBetaKappa

PhiBetaKappa — Mon, 04 Feb 2008 10:00:25 -0800

That's a great game to play with anyone (for reasons DU notes above). It's very good for exercising your ability to use intense focus for short bursts. I've often found that the mentally "out of shape" take an instant dislike to this game.... I've also found I need to be easy with people learning the game...it takes most a few rounds to get up to speed and it would be a snap to really smoke 'em and discourage them. If I take my time and let them build the skills needed to see the patterns, most pick it up quickly and some give me a tough challenge...which makes it really fun. Even moreso if you add in a "Loser has to ___________" or "Winner gets _________" bet.

By: Dr-Baa

Dr-Baa — Mon, 04 Feb 2008 10:01:51 -0800

Oh dear, and I thought I'd get some work done today. Set is new to me, and I like it.

By: pravit

pravit — Mon, 04 Feb 2008 10:02:54 -0800

I remember playing this back in elementary school when they had this special group for smart kids (AEP I think?) and then they'd take us out of class and we'd play Set and make Indian dreamweavers while the other kids had to do actual work. Good times, although I never liked Set.

By: cortex

cortex — Mon, 04 Feb 2008 10:07:27 -0800

My family got a copy of Set when I was a kid. We played a bunch of it for a while; it was interesting to find something that was both abstract enough that it appealed to everybody at least somewhat, and simple enough that it wasn't a turnoff to anyone who didn't want to bother with a bunch of rules to learn a new game. I remember being pretty damned good at it.

By: butterstick

butterstick — Mon, 04 Feb 2008 10:09:30 -0800

I've gone through at least 3 SET decks. THEY ARE NOT BEER PROOF.

By: 23skidoo

23skidoo — Mon, 04 Feb 2008 10:10:47 -0800

Oh wow, I used to play Set with my afterschool kids like 8 years ago. I picked up like 3 copies in a dollar store, because they were a dollar. Only about 3 kids had the brain power to even find the game interesting, and only one kid could actually play the game without just picking random cards and then asking me if it was a set.

By: milarepa

milarepa — Mon, 04 Feb 2008 10:12:18 -0800

I played the daily puzzle at the first link every morning for 3 years. Nice to see it expanding in popularity.

By: Miko

Miko — Mon, 04 Feb 2008 10:14:17 -0800

It's a good game for adults to play with kids since it's a pattern recognition thing, not a strategic/knowledge thing. Totally true. I used to teach kindergarten and we played the game with the kids. A 5-yuear-old can be a formidable contender against an adult, which really displays minds at work. Fascinating. Fun, quick game, too, that you can carry with you and play anywhere in just a few minutes, and explain to anyone right quick.

By: not_on_display

not_on_display — Mon, 04 Feb 2008 10:18:31 -0800

Can someone point me to rules on how to play multi-player set? Is it competitive (who gets all the sets first or in a certain amount of time) or is it collaborative (let's all try to find the sets)?

By: cortex

cortex — Mon, 04 Feb 2008 10:22:12 -0800

not_on_display, I don't know if my family played by canonical rules, but what we'd do is gather around a table and deal out a 3-by-3 tableaux; whoever could call a set first would do so, point it out, take the cards, and deal out three more to replace it. A set was a point, and we'd go until the deck ran out. Kind of like play slapjack except with moderately less slapping.

By: shoesandships

shoesandships — Mon, 04 Feb 2008 10:31:53 -0800

grimmelm, Do you have anything else on ordered triplet? It seemed interesting, but most of the links on the site are broken.

By: Wolfdog

Wolfdog — Mon, 04 Feb 2008 10:37:17 -0800

Set is intended to be competitive, though of course you can play it however. There was a group of us that sort of played in grad school; I say "sort of" because there was one girl who was so blindingly fast that no-one else ever got a point. Cards were put out, she said set, and took it. Done. You still played, though, because you never knew - maybe. Someday.

By: billtron

billtron — Mon, 04 Feb 2008 10:44:11 -0800

I played this the same way cortex described above. My mother, a junior high art teacher, now uses it with her students after they finish their projects. This game has fewer parts than Puerto Rico.

By: billtron

billtron — Mon, 04 Feb 2008 10:44:40 -0800

That's Puerto Rico the game, not the country.

By: DevilsAdvocate

DevilsAdvocate — Mon, 04 Feb 2008 10:48:24 -0800

Supposedly 25% of the male population is color blind. More like 7%, at least among males in the U.S. Still enough to be an issue which affects not just Set, but many tabletop games. It comes up fairly frequently at boardgamegeek.com.

By: alexei

alexei — Mon, 04 Feb 2008 10:51:43 -0800

Canonically, I believe, it's a 4 x 3 grid that you lay out, with three more if there are no sets to be found. One of my faves.

By: marginaliana

marginaliana — Mon, 04 Feb 2008 10:58:48 -0800

Awesome. I learned to play the way cortex describes from a friend in high school, and I have a homemade deck around here somewhere. Great to know I can play online.

By: goodnewsfortheinsane

goodnewsfortheinsane — Mon, 04 Feb 2008 11:04:15 -0800

OMG you guys did you know that Englimos have ~~119~~ 120 meanings for "set"??!

By: aspo

aspo — Mon, 04 Feb 2008 11:10:25 -0800

Brush with set fame: I know the man whose mother invented Set. I've never actually seen him play, but I've been made to understand that he is not allowed to play with mere mortals.

By: Wolfdog

Wolfdog — Mon, 04 Feb 2008 11:15:22 -0800

'course whenever Isis comes over we try and don't bring up Set, otherwise it's all "dismembered this" and "gouged out that", lord she does go on about a thing.

By: naoko

naoko — Mon, 04 Feb 2008 11:28:13 -0800

My roomie and I were total Set maniacs in college. You think it's hard now, try playing stoned.

By: milarepa

milarepa — Mon, 04 Feb 2008 11:34:46 -0800

56 seconds. Still got it. *blows on fingernails*

By: tits mcgee

tits mcgee — Mon, 04 Feb 2008 11:37:38 -0800

Squee!!! I love Set and play it with my high school math students.

By: Skorgu

Skorgu — Mon, 04 Feb 2008 11:53:58 -0800

Heh, just goes to show (something). I found the first 5 in about a minute and literally spent the next 3 minutes trying to find the one I was missing. Which was, of course, blindingly obvious once I'd found it. Wonderful game, I need to get myself a new deck, god knows where the last one went to.

By: agregoli

agregoli — Mon, 04 Feb 2008 11:57:45 -0800

More like 7%, at least among males in the U.S. Ah. I'm going to go back to feeling superior.

By: rouftop

rouftop — Mon, 04 Feb 2008 12:06:16 -0800

I was a fantastic Set player in college. Except that there was one woman who beat the pants off of me almost every game. Interestingly, though I'm really competitive I don't remember hating her guts for it. It was just so impressive to watch her focus.

By: escabeche

escabeche — Mon, 04 Feb 2008 12:25:07 -0800

The largest collection of cards you can have without a Set is 20. This is a surprisingly hard fact to prove, and I don't actually know of a proof that doesn't require a bunch of painful casework or computer search. Now suppose you consider "n-dimensional set" in which you have n characteristics, and 3^n cards (so that usual set is the 4-dimensional case.) What's the largest collection of cards containing no set? When n=3, the answer is 9 (not hard to prove), when n=4 it's 20, as I mentioned, when n=5, if I remember correctly, it's 45, and when n=6, I think it's 112. And the answer isn't known for any larger n. In fact, understanding the behavior of this number as n grows is a beautiful and hard old problem in combinatorics. Fields Medalist Terry Tao discusses the problem, which he calls his "favorite open question," on his blog. The problem has a beautiful geometric formulation -- it turns out that if you think of the Set cards as points in 4-dimensional space over the field of three elements, then three cards form a Set if and only if they are collinear.

By: rouftop

rouftop — Mon, 04 Feb 2008 12:40:14 -0800

Oh, another comment: I spent a good year where I played the Set puzzle (from the first link) every day. After each game, I would write a haiku in the comments section asking if I could kindly be awarded the prize this week. I figured they went into some database somewhere and were rarely reviewed, and thought I'd be giving some DBA a laugh or two. After a full year of not winning (and a few untimely visits from the boss when I should have been working), I wrote a final haiku saying that I was through playing since they never awarded me a prize. I received the following email in response.

love your haikus -- please continue. unfortunately I do not have any control over who wins. Marsha J Falco President Set Enterprises, Inc.

After that I was too embarrassed to actually write another one...

By: artifarce

artifarce — Mon, 04 Feb 2008 12:42:06 -0800

Never seen a whole thread where everyone agreed with each other. Set is magic (and I do like it too).

By: cortex

cortex — Mon, 04 Feb 2008 13:01:11 -0800

That's a great link, escabeche, if pushing to the heady limits of what I can nod along to. One subproblem of the cap set question, pushing over to probability, that seems interesting (if a bit silly) in the context of actually playing Set: the likelihood of a non-set-bearing tableaux of cards where the size of the tableaux is some number m, the size of the cap set is n, and (m < n). What does the distribution of probabilities look like for various values of m? I'm having trouble figuring out if this is a harder related subproblem, an easier related subproblem or actually a mathematically unrelated problem. And I have kind of a headache now. But the key thing is, yay math. And yay Set. The problem has a beautiful geometric formulation Before I saw your comment, I had been thinking about the idea of visualizing a one-fewer-dimension version of the game as a sectioned cube, where each card occupied a single slot, and how a proper set would "look" different, land in one of a few specific spacial configurations that would correspond only to sets. Wackiness.

By: klangklangston

klangklangston — Mon, 04 Feb 2008 13:01:52 -0800

Man, I liked this game a lot in high school, and I was usually one of the better players, but now my girlfriend just smokes me so bad that I don't even want to play it with her.

By: futrelle

futrelle — Mon, 04 Feb 2008 13:04:31 -0800

Hmmm. Anyone know if there's a Palm OS version of the game?

By: roll truck roll

roll truck roll — Mon, 04 Feb 2008 13:06:07 -0800

Thanks for linking to Tao's blog, escabeche. In college, I saw a lecture by someone (I can't remember the guy's name) who had (I think) published the paper showing that there's no polynomial formula for finding the minimum number of cards for x number of characteristics. It was a really fascinating, entertaining talk. Also, a friend of mine has a handmade Set deck, beautifully printed with potato stamps. Someday I'm going to kill her and steal it.

By: Wolfdog

Wolfdog — Mon, 04 Feb 2008 13:16:47 -0800

What does the distribution of probabilities look like for various values of m? For the standard game, apparently, monotone decreasing from 78/79 when m=3 (three randomly chosen cards almost certainly won't form a set) down to 0 when m=20. The monotone decreasing down to the 0 at the cap is obvious for any generalization. A related (and interesting) question would be, if you deal out cards one at a time, on average how many do you deal out until a set is formed? Sometimes, oddly enough, you can answer expected value questions like that without knowing all the details about individual probabilities.

By: escabeche

escabeche — Mon, 04 Feb 2008 13:37:46 -0800

Here's another question I don't know the answer to, which I think is much less studied than the "cap set" question. Call a collection of cards "maximal Set-free" if it contains no Set, and if no card can be added to the collection without creating a Set. How small can a maximal Set-free collection be? I think I once narrowed this down to two possibilities -- maybe 13 and 14? but I don't have my notes on this with me right now.

By: yeti

yeti — Mon, 04 Feb 2008 13:51:49 -0800

When I as in high school I made up rules for a turn-based variation. There was a field of eight cards or so, a single shared "bonus" card on top of the deck worth double points, and a card in each player's "hand" (or something like that). So while the turn-taking would slow the game down, having all the extra cards to find a single set sped things up. And while it took me a while to perfect the balance and speed of the two-player variation, I only actually played against a real opponent twice. I love my mom.

By: cortex

cortex — Mon, 04 Feb 2008 13:53:56 -0800

How small can a maximal Set-free collection be? One thing that I don't recall about Set is whether there were duplicate cards, which could change the answer. But yeah, regardless, that's an interesting puzzler.

By: jmd82

jmd82 — Mon, 04 Feb 2008 13:59:52 -0800

I saw a lecture by someone (I can't remember the guy's name) who had (I think) published the paper showing that there's no polynomial formula for finding the minimum number of cards for x number of characteristics. It was a really fascinating, entertaining talk. Wow, y'all are dorks. Huge dorks. And I love it.

By: cortex

cortex — Mon, 04 Feb 2008 14:12:12 -0800

Assuming I didn't bork my napkin experiment, the maximal Set-free collection for a 3-dimensional 3-set version without replacement (so essential Set cards with shapes, ordinalities, and shading but no color dimenion, 27 cards without duplicates) can be done in at most 8 cards. Whether there's a method to reduce that, I don't know. I also don't have any theory to back it up, yet, though it seems like generalizing it wouldn't be nasty. This is just the sort of thing that could eat a whole afternoon for fiddling.

By: OverlappingElvis

OverlappingElvis — Mon, 04 Feb 2008 14:22:45 -0800

I hate this game. My friends always used to try to make me play it and every time they'd convince me it would be fun, it wasn't.

By: escabeche

escabeche — Mon, 04 Feb 2008 14:33:39 -0800

Assuming I didn't bork my napkin experiment, the maximal Set-free collection for a 3-dimensional 3-set version without replacement (so essential Set cards with shapes, ordinalities, and shading but no color dimenion, 27 cards without duplicates) can be done in at most 8 cards. Nope, cortex, you can do with with 9! I leave it as a puzzle to find this configuration. (If you're doing it with actual Set cards, one way to "reduce the dimension" is to restrict to the 27 red cards.) For the math lovers, this 9-card configuration, considered as a subset of F_3^3, is the set of rational points on the paraboloid x^2 + y^2 = z.

By: harhailla.harhaluuossa

harhailla.harhaluuossa — Mon, 04 Feb 2008 14:37:01 -0800

How many cards must be dealt to guarantee a set? The elegant geometric representation mentioned by escabeche is on page 3.

By: cortex

cortex — Mon, 04 Feb 2008 14:40:16 -0800

Nope, cortex, you can do with with 9! Wait, are we trying to minimize the maximal Set-free collection? Or maximize it? Or both?

By: escabeche

escabeche — Mon, 04 Feb 2008 14:49:42 -0800

Oh, sorry, cortex, I didn't realize which question you were answering! Yes, I think a maximal Set-free collection in dimension 3 has size at least 8. The largest Set-free collection has size 9.

By: eritain

eritain — Mon, 04 Feb 2008 14:53:27 -0800

I hate this game. Shun the non-believer!

By: escabeche

escabeche — Mon, 04 Feb 2008 14:54:14 -0800

The paper linked to by harhailla.harhaluuossa is terrific, by the way, and contradicts my earlier assertion that there isn't a nice clean proof for the "no Set-free configuration with more than 20 cards" theorem.

By: mecran01

mecran01 — Mon, 04 Feb 2008 15:01:28 -0800

What I like about this game, which I found at a thrift store, is that it is portable and great for camping, the kids play it, and after you have played for a while you start looking at the world around you differently. It reprograms your head, briefly. The game's page at Boardgamegeek with many links, discussion, etc.

By: cortex

cortex — Mon, 04 Feb 2008 15:09:51 -0800

When I mentioned the visualization of sets or cards as occupants of a cube, something was tickling the back of my brain, and it was this: a post I made close to a year ago linking mainly to some spatial-puzzle games where the goal was to put small cubes into a large sectioned cube to produce three specific planar views from the three sides of the cube. Part of the (unstated?) challenge there was in accomplishing the task with a miximum or a minimum number of blocks. So in a sense, when we're talking about minimal or maximal solutions to these problems in Set, it's isomorphic to a specialized version of that: specific constraints on what the three plane views can be that limit (to what, that's the fun question) how many or how few blocks in the cube can meet the requirments. Or, in the case of some of what we're on about here, how many blocks can manage to not meet those requirements. I wish I had an easy way to visualize some of this stuff.

By: peep

peep — Mon, 04 Feb 2008 15:29:32 -0800

I am SO bad at this. Especially the "different in every category" sets. I can't stop playing. Will this eventually make me smarter?

By: artifarce

artifarce — Mon, 04 Feb 2008 15:33:31 -0800

Will this eventually make me smarter? No, but it'll help you avoid Alzheimer's.

By: Eideteker

Eideteker — Mon, 04 Feb 2008 15:52:19 -0800

I play the daily game (and now the NYT version as well) every day at lunch, to improve my mental mind.

By: lester the unlikely

lester the unlikely — Mon, 04 Feb 2008 16:08:28 -0800

I'm always on the lookout for 'antipatterns', or whatever you call that thing peep was describing: For a while I had a strategy for getting the "different in every category" sets by focusing on a card that was unique among the others (the only card with two shapes or only card with a green shape or...you get the idea) and then would quickly build from that since antipatterns typically require these types of cards....I think this helped since sets with multiple matching characteristics seem less common and are easy to spot when they show up. But then again I dig Grassman numbers and bank shots, so maybe I'm just weird.

By: rmless

rmless — Mon, 04 Feb 2008 16:16:46 -0800

I love this game. I can always find the "anti-patterns"-- the3 that have nothing in common-- the most easily. I wonder if this says something about me.

By: roll truck roll

roll truck roll — Mon, 04 Feb 2008 16:34:11 -0800

Playing the NYT version, it suddenly hits me that this would be a completely badass Facebook app.

By: brevator

brevator — Mon, 04 Feb 2008 16:34:34 -0800

I'm really excited about this.

By: roll truck roll

roll truck roll — Mon, 04 Feb 2008 16:42:00 -0800

harhailla.harhaluuossa typed "How many cards must be dealt to guarantee a set? The elegant geometric representation mentioned by escabeche is on page 3." If anyone's curious, this is definitely the guy I was talking about here. [whistful sigh] I went to the wrong sort of graduate school.

By: princelyfox

princelyfox — Mon, 04 Feb 2008 17:31:51 -0800

This is great. Thanks.

By: kimyo

kimyo — Mon, 04 Feb 2008 18:14:34 -0800

i postulate (i'm a boy) that girls are just inherently better at this game. does that make me sexist? regardless, it's just an observation that has been repeated time and again over the years i've been playing. thanks brevator for all the links.

By: hurdy gurdy girl

hurdy gurdy girl — Mon, 04 Feb 2008 18:52:37 -0800

I had never heard of this game before. I like it! I can see how it could become addictive. Thanks for posting this.

By: brevator

brevator — Mon, 04 Feb 2008 19:53:37 -0800

you're quite welcome. i'm really glad that so many mefites dig set.

By: Ambrosia Voyeur

Ambrosia Voyeur — Mon, 04 Feb 2008 21:11:04 -0800

I've got my set skills, I've got my skill set. I've got the board cleared and you ain't blinked yet. Man, if I ever meet someone who poses anything like a challenge to me in Set, I will be ever so delighted. Driking Set. It's the only way to get it in hand.