(edit) Compatibility card game

[jack]

I 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?

Comments

[andrewducker]

apples to apples?

[woodpijn.livejournal.com]

It's called Compatibility.

[woodpijn.livejournal.com]

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. ... The three/one point match is acceptable, but I don't think it quite describes matching.
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.

[simont]

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?

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!

[darcydodo]

There's also a German game with sheep that's a similar principle. (Somewhere between this and Apples to Apples, I think.) Can't remember the name either, though.

[ravingglory.livejournal.com]

I still think "What where you thinking?" is the best of this style of game. Too bad it's never likely to be in print again. In that you score points equal to the number of people who put down the same thing. So the more people you match the better. (Also you get to make up your answers rather then having a set)

[gareth-rees.livejournal.com]

Is there a better algorithm, maybe something that (in a simple way) includes a information theory metric of distance?

Minimum edit distance (aka Levenshtein distance).