Talk:Set (card game)

Image

I'd like to get a picture of some Set cards here. I'm not well-versed in the copyright issues (with respect to Set Enterprises, or whoever holds the copyright, if any, on the cards' design) or in trademark issues (if, again, there's a trademark on the cards' design). Perhaps someone else, who has experience with pictures on Wikipedia (I have none) can deal with this. (Oh, how I love passing the buck.) —msh210 20:38, 23 Nov 2004 (UTC)

See, e.g., Image:RiskInPlay.jpg. This is a photo of a board game. The photographer released it under GFDL, but isn't the manufacturer's copyright an issue? Or its trademark? —msh210 20:49, 23 Nov 2004 (UTC)

Very good pictures for this article are [1] and [2], but those also require copyright permission from the image-maker, I guess, no? Although, if we already must ask permission for using a picture of the cards, we may as well just ask for permission for using that picture of the cards. (Or just implicitly include both requests: "may we put on Wikipedia a copy of your /images/card.gif?". Hm?) —msh210 20:58, 23 Nov 2004 (UTC)

Why not just take a screenshot of the computer game version, and add the picture to the article under fair use? Use the screenshot template, like so:

{{screenshot}}

I went ahead and added an image as per Wikipedia:Requested images before I noticed this talk page. The image is my own creation though it uses the Set designs, so I think it falls acceptably under fair use. —Miles (Talk) 00:48, Apr 24, 2005 (UTC)

next step on the image is to add perhaps 1-4 other variations of sets. the one pictured is a "good one" in set parlance, but to best communicate the notion of the game/article, we could perhaps add some more. e.g. three green solid triangles; 1/2/3 purple hollow/lined/shaded all-squigleys; 3/3/3 solid r/g/b. need at least 3 and better yet 6-12 types of examples to best convey the notion. -:)Ozzyslovechild 04:18, 20 June 2006 (UTC)

Variations

I have heard of (and played) other variations of Set, but if they were merely inventions of my friends (or me), are they notable? For example, the memory variation mentioned in the article gave birth to a "Go Fish" game using Set cards: players fish for sets rather than pairs, and may ask other players for cards as specifically or as generally as they wish ("do you have any diamonds?" and "do you have any green solid diamonds?" are both legal requests). My guess is that Wikipedia is descriptive, not prescriptive, and unless it can be demonstrated that enough people play this variation to make it notable, it stays out of the article. Your advice is appreciated . -- Mitchell k dwyer 23:25, 26 January 2006 (UTC)

I think the Go Fish version sounds pretty interesting. Do you know whether or not the other variations listed are that common? I had never heard of any of those. None of those are even listed at the setgame.com Other Rules site. I don't see why the Go Fish variation shouldn't be added to the article. --Paulie Peña 16:39, 21 May 2006 (UTC) P.S. For Memory Set, do you lay down all 81 cards or just 12? It seems like it would be hard to know when there are no more sets, if only three cards are turned up at a time.

Basic Combinatorics Error?

There are 1080 sets. Clearly each card is used in the same number of sets and each set using three cards, so each cards is used in 1080*3/81=40 sets. (Alternatively that can be seen be realizing that once we pick a single card, for each possible second card there is a unique third card to add to make a set. So once we've picked our card, the other 80 cards form 40 pairs to make sets with).

Now I question the next fact. Suppose we move the three red diamond cards with all three shadings into a separate pile. This fact states we only lose 3*2/2=3 sets (sets that require crossing between our piles of 78 and 3 cards). Now how many sets involve those triple reds? Each is involved in 40, but that counts the set of them all three times. So there are unique 3*40-2=118 sets involving them, and only one is still in existence. So we lose 117 sets, not 3. If someone can clarify this fact to me (with a link to a proof) we can keep it. Also, just to further the inconsistency, if we made a pile of 78 and 3 cards, but the 3 cards DIDN'T form a set, those three cards would be a part of 3*40-3=117 sets (the -3 is for each set involving two of them we double counted), and we would lose all of them. So maybe there IS a formula, but -n*(n-1)/3 isn't it. —Preceding unsigned comment added by 207.237.246.79 (talk • contribs)

Are you questioning the formula that arrived at the number 1080? I think the answer is like this: $\sum _{n=1}^{4}{{4 \choose n}27\times 2^{n-1}}=1080$. I arrived at this through induction: First, I'm going to look for how many sets I can make with 3 of the qualities being the same and one being different, for example all colors, fillings, and shapes being the same and the number being different (there are no sets where all the qualities are the same, because all of the cards are unique). I can make 27 sets like that $\left({\frac {81}{3}}\right)$. That is then multiplied by four, because of each of the four qualities (meaning, keep 3 the same and 1 different). Next: I keep two qualities the same and 2 different (for example, color and fill the same, number and shape different). How many can I make like that? 27, right? Wrong! Continuing with color and fill being the same, number and shape being different, what about the following situation: I have the card with 1 solid blue diamond. How many sets can I make with that? I can have 2 solid blue oval, and 3 solid blue squiggles, OR I can have 2 solid blue squiggles and 3 solid blue ovals. Before when only one thing was different, I had no room for this. Now, I have to multiply my answer by 2 to get the real number, so I take 27 and multiply by two. And how many combinations of two qualities being different and two being the same can I get? ${4 \choose 2}=6$. So I multiply 27 * 6 * 2. Next, how many sets can I make in which 1 quality remains constant and 3 qualities must be different? Lets say filling remains different, then I can make 27 sets. Now account for each of the four being the "different" one, i have 27 * 4. But wait! what about that multiplication by 2 that I did before? Now, I multiply by 2*2 because there are 3 qualities that are different. Lastly, for the case where all four of the qualities are different, I have my 27 base, times 2*2*2 because of the 4 that are different. That leads me to my formula from above, $\sum _{n=1}^{4}{{4 \choose n}27\times 2^{n-1}}=1080$. I hope that makes sense to somebody! If anybody feels the that the formula deserves a spot on the article page (I do, but I don't know if it really belongs) then lets put it on (at least the formula, because the inductive proof might make sense only to me ;) ). Max613 (talk) 20:46, 21 June 2008 (UTC)

Actually, there's a simpler way to arrive at the 1080 figure. Start with the premise that for any two cards in the deck, there is one other card that completes a set. There are ${81 \choose 2}=3240$ ways to choose two cards from the deck. But each set can be arrived at 3 different ways, depending which two of the three cards were chosen. Thus there are 3240/3 = 1080 possible sets. --Mwalimu59 (talk) 00:35, 22 June 2008 (UTC)

Or note that there are ${81 \choose 3}$ triples in the deck of 81 cards, and the probability for a random triple being a set is $79^{-1}$ (because only one of the reamining 79 cards supplements two cards into a set), so the number of sets is ${81 \choose 3}79^{-1}=1080$, and the number of non-sets is ${81 \choose 3}(1-79^{-1})=84240$. There are ${12 \choose 3}=220$ possible triples in 12 cards. The mean number of sets in 12 cards is ${12 \choose 3}79^{-1}\approx 2.78481$ because the mean number of sets in one triple is $79^{-1}$. But what is the standard deviation? I do not know the exact answer to that question. The event that one triple being a set is dependent on the event of another triple being a set. This dependency does not influence the mean value, but it does influence the standard deviation. The approximation that the number of sets has a hypergeometric distribution, (take 220 triples from 1080 sets and 84240 non-sets,) gives $\sigma ^{2}\mu ^{-1}\approx 0.98480$. The further approximation that the number of sets has a binomial distribution, (220 experiments each with success probability $79^{-1}$) gives $\sigma ^{2}\mu ^{-1}=1-79^{-1}\approx 0.987342$. The still further approximation that the number of sets has a poisson distribution (with mean value $220^{1}79^{-1}$) gives $\sigma ^{2}\mu ^{-1}=1$. But a Monte Carlo simulation, counting the number of sets in 10000 random 12-card samples from the 81-card deck, gives $\sigma ^{2}\mu ^{-1}\approx 0.68$, which is much less than that of the above approximate distributions. The total number of 12-samples from the 81-deck, ${81 \choose 12}=70724320184700$, is beyond the reach of my computer, so I cannot make an exact calculation of the standard deviation. Can you?. Bo Jacoby (talk) 12:32, 26 March 2017 (UTC).

Is it worth linking to pSet on Sourceforge?

Is it worth linking to pSet on Sourceforge? There is no software availiable for download, and there is no indication there ever was, or ever will be. --Logomachist 04:00, 14 July 2007 (UTC)

No Cards Left if Played Rigth is incorrect

The part in the main story that says: "When a game of Set is played correctly (i.e., no one accidentally takes a false Set) with a complete deck of 81 cards, it is impossible to end up with only 3 cards that are not a Set. Put another way, if a complete deck of 81 Set cards is partitioned into 27 piles of three cards, and 26 of the piles form Sets, the remaining pile must also form a Set." is just wrong. The person who wrote it has obviously never played the game. If three cards made a a SET and only THAT SET, it would be true. But a single card, and any other card, will connect with a third, specific, card to form a SET. When dealt out 12 at a time, players cannot predict, and control, the taking of the cards in such a way as to use them all up. I'm no mathematician, so I can't explain it, but you do end up with cards most times, and it's not because someone "accidentally takes a false Set". —Preceding unsigned comment added by 72.25.82.43 (talk) 19:43, 15 October 2007 (UTC)

It is possible (and common) to end up with 6, 9, 12, maybe more cards without having any sets left, but if all the sets taken during the game were correct, valid sets, it is impossible to finish with exactly 3 cards left that are not a set. --Mwalimu59 03:47, 22 October 2007 (UTC)

Probability of a setless deal?

What the combinatorics subsection needs is: what is the chance that a deal of 12 cards has no set? When you play this game, and you're all staring at the cards without seeing anything (this happens to me because I am dumb and perhaps my friends are too), you keep asking this question. Llajwa 01:11, 22 October 2007 (UTC)

That would be a good question for a general discussion forum about the game. I'm not sure how much of that sort of detail we would want to go into in the Wikipedia article about the game, but if you know of a website where game discussions can take place, that would be a candidate for adding to the article too, subject to WP:LINK. --Mwalimu59 21:51, 22 October 2007 (UTC) (edited earlier comment)

I think that the chance of any 12 cards having at 0 valid set are as follows: $\left({\frac {78}{79}}\right)^{12 \choose 3}\approx .0607$ or 6%. I arrived at that based on the assertion on the main page that the "probability of producing a Set from 3 randomly drawn cards is 1/79". So, the chance that any 3 cards not form a set is 78/79. Now I multiply that by itself for each group of three cards on the table (12 choose 3). Conversely, the chance of having at least 1 valid set is $1-\left({\frac {78}{79}}\right)^{12 \choose 3}\approx .9393$ or 94%. The chance of having at least 1 valid set with 15 cards on the table is about 99.7%. If I'm wrong about this, please correct me. I'm fairly sure, but not sure enough to put his on the article page. If somebody can verify this, please let me know or put this in the main article. Max613 (talk) 21:01, 21 June 2008 (UTC)

I'm not sure the results that gives are entirely accurate. If nothing else, one could get a definitive answer by examining all ${81 \choose 12}$ possible deals to see how many have no sets. Maybe a constructive approach would work - as you add each card, figure out how many cards still in the deck would not complete a set, but that gets complicated once you have to handle the fact that the number of set-completing cards still in the deck is not constant depending on which cards have already been dealt.

A while back I wrote a computer simulation that produced 6,000,000 random 12-card deals, and of those, there were 193272, or 3.22%, that had no sets. I modified the same program to produce 5,000,000 random 15-card deals, which produced 1754 (0.035%) that had no sets, and 4,000,000 18-card deals, and it didn't produce a single occurence of a no-set deal. --Mwalimu59 (talk) 19:16, 23 June 2008 (UTC)

We know it's possible to have 18 cards with no sets, but evidently the odds of it happening on a random deal are very slim. I wrote another simulation and played 30,000,000 games with it (the same 10,000,000 shuffles but using three different methods of choosing which set to remove from a deal). Of that number, there were only 11 games that went to 21 cards on the table. --Mwalimu59 (talk) 19:16, 23 June 2008 (UTC)

Logical statement

I don't pretend to have the least understanding of what Set is. But aren't these statements logically equivalent? 1: "Two are ... and one is not if and only if it is not a set." and 2: "Two are ... and one is if and only if it is a set."? If so, the latter is more direct and thus preferable. 128.95.217.229 00:35, 24 October 2007 (UTC)

As applied to the game of Set and interpreted in that context, no, they are not equivalent. --Mwalimu59 06:00, 24 October 2007 (UTC)

More formally, that statement would be: "A group of three cards is not a Set if and only if there exists a characteristic (red, green, blue, single, double, triple, oval, diamond, squiggle, clear, shaded, or solid) such that the number of cards in the group having that characteristic is 2." DropZone (talk) 18:30, 21 February 2008 (UTC)

External links are promotional and/or not notable

To bring this article in line with linking guidelines, I suggest we pare down the external links, many of which appear to be spam. Quaternion (talk) 18:02, 24 March 2008 (UTC)

I went ahead and pared down the links, although I left the board game geek link. If I've removed a link that's important to the article, please discuss that here. Please keep in mind that a wikipedia article is not a web directory. Thanks. Quaternion (talk) 13:58, 26 March 2008 (UTC)

I wish you'd stop leaving ads to the card game up, while removing links with content. The versions that you can actually play are probably the best links up there. Specifically, the JavaScript iPhone one is simple, elegant, and a good resource for anyone interested in Set. —Preceding unsigned comment added by 140.247.133.82 (talk) 03:22, 14 April 2008 (UTC)

I have not previously removed links from this article. Nonetheless, the game of Set is directly attributable to Set Enterprises (with whom I have no relation). In the same way that Monopoly provides a link to Hasbro, this article should provide a link to the game's creator. (That said the external links of the Monopoly page are also turning into a web directory.) I removed the long list of external links to play the game of Set, as they do not meet linking guidelines. Links to play the game can still be found by following the link to the BoardGameGeek website. I think this is more in line with Wikipedia's recommendations for dealing with long lists of links (ie. to link to one directory of links, rather than duplicate those links on the article page.) Quaternion (talk) 14:36, 14 April 2008 (UTC)

Erroneous caption

There is an illustration showing three cards that form a "set". But the caption reads:

Three cards from a Set deck. These cards each have a unique number, symbol, shading, and color, and are thus a "set."

which does not at all accurately describe why the three cards form a set! Of course each card has a unique number, symbol, shading, and color -- this applies to every one of the 81 cards in a Set game. But it utterly fails to describe why these particular cards happen to form a "set".

In fact, this group of three cards includes all three numbers, all three shapes, all three colors, and -- if one interprets the middle card as striped -- all three shadings (but the middle card does not appear at all striped to me).Daqu (talk) 10:54, 1 April 2008 (UTC)

poker variant

Myself and some friends created this poker variation of set. we play it as a hold'em poker game but it can be converted to any style. each player is dealt three cards in the hole, flop is three cards, turn is two cards and river is one card. normal hold'em betting rules and strategies apply.

A hand consists of 6 cards. hands with 1 set beat those with no sets, and hands with two sets beat hands without two sets. Each card can only be used for one set. Sets and cards are also ranked. Sets with 3 similar attributes are the best, followed by sets with 2 similar attributes, then 1 then zero. Within each attribute, the values are ranked (e.g. diamonds are better than ovals which are better than squiggles) but shape, fill, color and number are given equal weight. When two hands are equal in sets (e.g. neither one has a set or they have two equal sets) they are ranked according to the highest card in the hand which wasn't used in a set.

these rules provide the closest possible simulation of standard poker games using Set, and the game is highly entertaining for groups which are familiar with both poker and Set. —Preceding unsigned comment added by 209.6.170.96 (talk) 01:48, 13 August 2008 (UTC)

Set simulations subsection

Does anyone object to removing the Set simulations subsection of the article? The results of a computer simulation, while interesting, strike me as being rather arcane for an encyclopedic article. --Mwalimu59 (talk) 04:00, 28 November 2008 (UTC)

Since no one objected, it's been removed. It also appeared to be original research. --mwalimu59 (talk) 19:44, 5 December 2008 (UTC)

Removing that section as OR was correct. Also, the stuff was incomplete as the simulations must make a choice whenever two or more sets are present - and it is not stated how that was done. It's hard to tell how different choices might affect the results.

But (as stated a couple of sections above this one in the talk) it would be nice to have something (well sourced) in the aricle about the probability of having no set when n cards are picked at random, for different n. (The chance of having no set with n cards later in the game is different, and must depend on player behaviour.)

Here are my simulation results, based on 5 000 000 shuffles:

Cards P(no set) (source)

0 1.0000000 (theoretical)

1 1.0000000 (theoretical)

2 1.0000000 (theoretical)

3 0.9874056 (simulated), 0.987342 (theoretical)

4 0.9493922 (simulated), 0.949368 (theoretical)

5 0.8758650 (simulated)

6 0.7629274 (simulated)

7 0.6167740 (simulated)

8 0.4535472 (simulated)

9 0.2970616 (simulated)

10 0.1694184 (simulated)

11 0.0817136 (simulated)

12 0.0323554 (simulated), 1/34 = 0.029 (rules)

13 0.0100106 (simulated)

14 0.0023046 (simulated)

15 0.0003598 (simulated), 1/2501 = 0.00040 (rules)

16 0.0000360 (simulated)

17 0.0000002 (simulated)

18 0.0000000 (simulated)

19 0.0000000 (simulated)

20 0.0000000 (simulated)

21 0.0000000 (theoretical)

The rules inlaid in my copy of the game give the odds "~1:33" and "~1:2500" for the two cases indicated above. I trust my simulations to be more accurate!!!

I suspect working out these values theoretically gets very difficult as n gets large, so perhaps only simulations are available.

But are there any reliable citable sources???--Noe (talk) 18:03, 6 October 2009 (UTC)

exclusion?

The largest group of cards you can put together without creating a set is 20. ...

If 26 Sets are drawn from a collection of 81 cards, the remaining 3 cards form a Set too.

Is it possible to take 21, 22, 23, 24 or 25 sets leaving 18, 15, 12, 9 or 6 cards that do not include a set? —Tamfang (talk) 07:51, 1 February 2014 (UTC)

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The odds of getting at least one Set when dealing three consecutive cards

I don't think that this is true. --Jobu0101 (talk) 13:58, 10 January 2019 (UTC)

Okay, maybe it's true. I did a simulation with 100,000,000 games and had 63,924,014 with three consecutive cards as set. --Jobu0101 (talk) 22:39, 10 January 2019 (UTC)

The odds to have at least one Set in 3 consecutive cards are 1 - (78/79)^78 = 0.6344612683342776, which means your experiment had an accuracy of 99%. This assumes you lay down the cards of a random/shuffled deck. Bcurfs (talk) 10:46, 11 November 2020 (UTC)

FunSearch

Various sources e.g. [3], [4] and [5] have reported a breakthrough using large language models to optimise solution bounds, specifically on cap sets of the Set game with 8 dimensions.

Perhaps this article should mention it. Cheers, cmɢʟee⎆τaʟκ 00:34, 29 December 2023 (UTC)