(edit) Compatibility card game
Oct. 20th, 2008 02:45 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackI can't remember the name (edit: thank you Woodpijn) but at alextfish and woodpijn's we played a card game where the point was to select from a deck of cards with pictures on, the ones someone else would choose, corresponding to a certain word, and you score according to how identical the two selections are.
Specifically, there's a deck of cards with words (although you could choose random words in another way) and one is turned up. Each player has an identical deck and chooses 5 cards from it (in fact, 5 varies in a proprietary way as your avatars move along a scoring track).
It's quite fun guessing surprising interpretations or amusing choices of picture -- it's surprising how often people _do_ agree on them -- or any special knowledge of the person matching against.
The rules as given describe either being in a team and trying to match each other more than the opposing team members match each other, or a free-style each taking it in turns to be a designated "judge" each other player must match.
The rules give (iirc) a traditional mastermind-style matching score. Give five (or however many) cards in order and score 3pts for same-card-same-place as the matchee, and 1 pt for same-card-different-place. That works reasonably well. But the question is, what ought the rules to be?
* At first, I thought the idea of a rotating judge was odd, since it seemed just an arbitrary contrivance of the rule system. It still offends my aesthetics that you can't just match against all the other players. But OTOH, if you were omniscient and knew what everyone were going to play, you ought to get a perfect score, and you couldn't if two people were going to play different things and you couldn't match both of them. Is there are compromise?
* The three/one point match is acceptable, but I don't think it quite describes matching. Suppose the word were "black" and I played pictures crow, sloe, fishing boat, night, black dog, and someone else played another card in first place, followed by my four first place cards -- that feels like they matched me except for one datum, but the old scoring system would only give four points. Is there a better algorithm, maybe something that (in a simple way) includes a information theory metric of distance?
Specifically, there's a deck of cards with words (although you could choose random words in another way) and one is turned up. Each player has an identical deck and chooses 5 cards from it (in fact, 5 varies in a proprietary way as your avatars move along a scoring track).
It's quite fun guessing surprising interpretations or amusing choices of picture -- it's surprising how often people _do_ agree on them -- or any special knowledge of the person matching against.
The rules as given describe either being in a team and trying to match each other more than the opposing team members match each other, or a free-style each taking it in turns to be a designated "judge" each other player must match.
The rules give (iirc) a traditional mastermind-style matching score. Give five (or however many) cards in order and score 3pts for same-card-same-place as the matchee, and 1 pt for same-card-different-place. That works reasonably well. But the question is, what ought the rules to be?
* At first, I thought the idea of a rotating judge was odd, since it seemed just an arbitrary contrivance of the rule system. It still offends my aesthetics that you can't just match against all the other players. But OTOH, if you were omniscient and knew what everyone were going to play, you ought to get a perfect score, and you couldn't if two people were going to play different things and you couldn't match both of them. Is there are compromise?
* The three/one point match is acceptable, but I don't think it quite describes matching. Suppose the word were "black" and I played pictures crow, sloe, fishing boat, night, black dog, and someone else played another card in first place, followed by my four first place cards -- that feels like they matched me except for one datum, but the old scoring system would only give four points. Is there a better algorithm, maybe something that (in a simple way) includes a information theory metric of distance?
no subject
Date: 2008-10-20 02:07 pm (UTC)no subject
Date: 2008-10-20 02:08 pm (UTC)no subject
Date: 2008-10-20 02:49 pm (UTC)no subject
Date: 2008-10-20 06:52 pm (UTC)no subject
Date: 2008-10-20 02:12 pm (UTC)no subject
Date: 2008-10-20 02:14 pm (UTC)no subject
Date: 2008-10-20 02:24 pm (UTC)no subject
Date: 2008-10-20 02:27 pm (UTC)no subject
Date: 2008-10-20 02:15 pm (UTC)I think it's actually 3 points for an exact match and 2 points for same-card-different-place. Which makes position less important than in your version, but still not completely unimportant.
no subject
Date: 2008-10-20 02:29 pm (UTC)no subject
Date: 2008-10-20 02:52 pm (UTC)Mmm. Fiddly one. You kind of want to find the set of shared cards between the two hands, and then look just within those shared cards to see whether they're all in the same order. That sorts out your example of ABCDE vs XABCD. But then the question is what you do if the shared set aren't in the right order; again, you want to score ABCDE vs EABCD by treating the E as a single out-of-place element rather than by considering absolutely everything to be undifferentiatedly "in the wrong place" as Mastermind would.
One obvious thing is to look at all the pairs of cards among that set, and score a point for each pair that's in the same order as in the other hand (or inflict a penalty point for each pair that isn't, depending on how you want to combine this score with the one for completely different cards). That has the nice feature that ABCDE vs ACBDE only scores one demerit, but ABCDE vs EABCD scores four, representing the fact that E was more significantly misplaced. On the other hand, it's a bit inconvenient that it's a scoring system with a quadratic cap – you then have to scale it in some annoying way in order to combine it with the basically linear score for elements not in the other list at all.
(This ties slightly in to a thing I was thinking about some years ago, which was how you determine the interestingness of an anagram. If you process a large computerised word list by sorting the letters of each word into alphabetical order and then sorting the whole list using those transformed versions as a key, you bring together every set of words that are mutually anagrams and can then go through and list them very easily. But how do you extract the most interesting anagrams from that list? Many of the obvious metrics for how much jumbling has taken place, such as the one I describe above, turn out to have the undesirable property in this application of giving a disproportionately high score to the operation of moving one or two letters from the start to the end, so that your list-of-interesting-anagrams is topped by lots of tedious things like REINTERPRET / INTERPRETER. Eventually Gareth came up with a neat metric which avoided this problem and which is still the best thing I've seen so far, although it seems clear that for today's application it's not what's required.)
eta Oh yes. The other thing I was thinking about was to work the scoring in terms of the longest common subsequence between the two lists, which seamlessly handles both the ABCDE/XABCD and ABCDE/EABCD cases without having to give fundamentally different treatment to replacement of an element as opposed to movement. Unfortunately, that approach gives identical scores to ABCDE/XYABC and ABCDE/DEABC, and it seems pretty clear to me that I'd want those to be scored differently!
no subject
Date: 2008-10-20 04:02 pm (UTC)- Find the longest common subsequence of the two lists. Suppose it has length n.
- Score n-1 + n/k points, where k is the actual length of the lists (i.e. the longest the common subsequence could possibly have been).
- Delete from both lists all the elements of that longest common subsequence.
- Repeat (with appropriately reduced k), adding up the individual scores as you go, until the residues you are left with have no common elements at all. Then you have finished.
This system has the nice properties that:- scoring is essentially linear: a perfect score is the length of the list
- a full point is lost per element which is not in the other list at all
- within lists that are anagrams (i.e. contain all the same elements), more points are scored in general by having long subsequences in common, i.e. tending to rank things in the same order
- more points are scored for few long common subsequences than for many short ones
- importantly, a long and a short common subsequence together score higher than two of equal length, even if they have the same combined length. For example, ABCDEF/DEFABC scores 5 1/2, whereas ABCDEF/FABCDE scores 5 5/6.
Downsides include:- it's fiddly to calculate; you really need a computer implementation
- it's not clear to me that it imposes enough penalty on list misorderings, though that might be easily enough tweaked
- most worryingly, I don't like its iterative nature. I instinctively distrust iterative methods like this; I want the answer to be expressible in some nice fashion that shows a property of the entire pair of lists as a whole, and I want any discussion of iterative faffing with LCS algorithms to be relegated to the "implementation considerations" section rather than being a necessary component of even describing the scoring policy.
But it's the best I've thought of so far.no subject
Date: 2008-10-20 04:22 pm (UTC)Perhaps I'll stop replying to myself now, and wait to see if anyone else is interested in this subthread at all before I try again :-)
no subject
Date: 2008-10-20 04:36 pm (UTC)My best guess was some metric based on "fewest moves of some sorts", including some sort of simple moves and replacements, but I don't know what would be appropriate if anything.
no subject
Date: 2008-10-20 04:47 pm (UTC)I'd be inclined to arrange that y is proportional to x/(n-1) as n varies, so that no matter what the length of the list you'd score the same fraction of full marks for getting exactly the right list in exactly the wrong order. Then it's just a matter of adjusting the remaining constant factor between x and y, and scaling so that full marks is some sort of nice round number (either a constant or n, as you please).
eta: oh no, I'm wrong again! In fact, my formula above is not quite right, because of the possibility that a single massively misordered element might be more cheaply dealt with as a deletion and insertion than as lots of interchanges to move it to the right place. This only comes into play if the constant factor is such that 2x can ever be less than (n-1)y, but if that's the case then working out the minimum edit distance might get fairly hairy. Perhaps it would be better to treat this as a sanity constraint on the constant factor :-)
no subject
Date: 2008-10-20 04:11 pm (UTC)no subject
Date: 2008-10-20 06:39 pm (UTC)no subject
Date: 2008-10-20 06:50 pm (UTC)For some reason Joe was bad at Hive Mind. No, bad is incorrect. He was abysmal. For some reason he just didn't have the gene that allowed him to group think. Yet, Joe constantly played the game because he wanted to show that he could pick up the skill. But the more he played, the more everyone realized it was hopeless. Which leads us to the last game of Hive Mind I remember playing with Joe.
The topic was Name Three Famous Dwarves (see, I told you this was on topic). Everyone wrote down their answers. Joe was smiling. Finally, he was convinced that he found the topic that was going to turn everything around for him. This topic, he had it. This was the game where he wasn't going to stand out. This time he was going to just be one of the crowd. Joe was so excited that he asked if he could read his answers first.
Once again, the topic was Name Three Dwarves. And the goal was to match the answers of all the other players. Joe pulled out his list. He even cracked his knuckles in a show of bravado. "Okay," he started, "Who's got Gimli?"
(As a quick postscript – the correct answers turned out to be: Dopey, Grumpy, Doc in that order.)
That might well be the best expression of the sort of game. (I think having a set definitely adds some value -- restriction breeding creativity, etc, a lot of fun in deciding between cards or finding unusual interpretations -- but that doesn't mean the original and simplest isn't more fun overall, even if you want to try other variants too.) I wonder if the german game mentioned is the one Darcy mentioned?
I see "What were you thinking?" isn't in print, but I wonder to what extent you could duplicate it without any equipment? (Obviously game manufacturers have a vested interest in selling as if extra arbitrary rules are useful, hence the board, etc.)
no subject
Date: 2008-10-21 08:09 am (UTC)Wouldn't be very hard to have very similar game if you just made up the questions. (either beforehand or as you went along)
no subject
Date: 2008-10-21 10:36 am (UTC)I thought the story was all in good fun, I didn't think anyone was actually upset.
Wouldn't be very hard to have very similar game if you just made up the questions. (either beforehand or as you went along)
Yeah, I should make up some defaults.
no subject
Date: 2008-10-24 11:08 am (UTC)Minimum edit distance (aka Levenshtein distance).