The question on everyone's mind...
Alex on 2014/10/22 01:09
of Lightswitch
Having played through our game, no doubt the question everyone is asking is: What, exactly, is the best possible word to open with? "Millisecond" is a strong contender, checking for a bunch of individual letters and for a double letter. "Doll" is also up there, along with "firewall"... and surely it can't be "aardvark"...
This turned out to be a reasonably interesting problem: complicated enough structurally that there was no simple direct solution (well, that I could find, anyway :), large enough at 58 rules that it can't easily be brute-forced, but not so large that it's obviously out of reach. And indeed, after a bit of tinkering and solving some sub-problems, and then throwing 30 odd cpu hours at it, the answer is:
*drumroll* (that's for effect, the answer is not "drumroll")
Freeze!
The is solving for the minimum average number of words needed to determine which rule is in play (and that minimum average is ~6.79066667), using only the 1616 words we have pictures for. An interesting variation would be to solve for the minimum average number of words needed to get 5 points, though I'm not sure that's computationally feasible.
Anyway, full solution available here.
And now back to rating all the other games. :)
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Comments
Alex on
2014/10/22 20:29:
Indeed. :) The starts-with ones are definitely annoying. I don't think changing the frequencies is the solution, though (and yeah, it takes them into account). I think the problem is that once you're left with only starts-with rules, there's no finesse or cleverness or anything left: You just have to plow through the alphabet, trying one word for each letter.
I think what we should do instead is replace the starts-with rules with something with more interesting structure, that allows you to try one word and have multiple accepting _and_ rejecting rules! A simple approach would be to have "starts with one of ...", maybe stuff like "hard consonant" vs "soft consonant", or "a letter than can appear in a roman numeral", or "a letter with only straight lines"...
cyhawk on
2014/10/22 10:52:
Awesome! The decision tree also highlights which rule is the most annoying :). Maybe the frequency of the "starts with X" rules should be changed to be proportional to the number of words starting with X, so that at least you can guess at the higher probabilities first.(You took into account the relative frequencies of the different rules, right?)