Every day, I play the puzzle game Collections. It starts out kinda like the game show Wheel of Fortune: You're looking at three sets of blanks. You ask about some letters. The game shows you where those letters are in the blanks. When you have some idea what words you're looking at, you figure out what collection (category) they all belong to. Guess the collection correctly to win.
To ask about a letter, you spend points. You want to spend as few points as possible to win. From that description, you might think "Obviously the best strategy is to ask about E first, it's the most common letter." But wait: The game designer thought about that. You spend 10 points for E, but only 1 point for Q. If you start by asking for E, your best score will only ever be 90. If you start by asking for rare, "cheap" letters, maybe you can do better. Which letters should you pick? I guesse hypothesized I should start with the cheap letters, but wasn't too sure. So I wrote a computer program. I tell the program what I've guessed so far, which letters are in which blanks. The program knows the phraser word list and knows how much letters cost in this game. Based on that, it recommends which letter to pick next.
Here are the letters it recommended for several recent Collections games. Here, the line zJxqkyFvwhGBdlNcS means in one puzzle, start with Z, then J, then X…. One line per puzzle. The program pretty consistently suggests starting with the cheapest letters: Z, J, X, and Q. Then prrrrobably the next cheapest: K, Y, V, F, and W. Yay, I will stick with my hypothesis with more confidence now.
zJxqkyFvwhGBdlNcS zjxqkyfvwhGBdMpu zjxqkyFvwHgBMDCPlUn zjxqkYfvwhgBMDSpU ZjxqkYvfWhBgmdPNu zJxqkyvfwHbGMDuAp zjxqKYvfwHbGMPdLN zjxqkyvfWhGBdMLNp zjxqKYvFwHGbdmlnR zjxqkyvfWHgbdSmPn zjxqkyVfwHgbdSpMA zJxqkyvfwHgbMApd zjxqkYvfWhGbmdPL zjxqkyvfwHgBmdSlN zjxqKyvfwhgBmdSP zjxqkyvfwHGbmDsPL zjXQkyvfwHGbmdSpN zjxqkyVfwHgbmSdA zjxqKyVfwHgbpDmluC zjxqkYvFWhGbPlDU zjXqkyvfwHGmdPlN
While I'm content with this result, some more rigorous thinkers will note problems:
№1 The program chooses a letter trying to narrow down the number of word possibilities overall. In general, that's a fine strategy. But suppose you're looking at _____, __YX, _____. That middle word is onyx, Styx, or oryx; if you knew which, you could probably figure out the collection right away, even if you don't know anything about the other words. But the program doesn't think narrowing three choices down to one as being very useful; instead, it will mostly try to narrow down the thousands of possibilities for those _____ all-blank words.
№2 The phraser word list is just what I had handy. It was created as a general word list, not necessarily words that you'd expect to see in Collections puzzles. For example, the phraser word list thinks that "eagle" and "helped" are roughly equally awesome. But I bet "eagle" shows up in lots more Collections puzzles. Maybe the category is Birds. Maybe it's golf scores. Maybe it's things on the Mexican flag. When I try to think of categories I'd clue with "helped," I think of… Uh. Hmm. I think of… Yyyyeah. Ideally, my word list would have "eagle" but not "helped".
Not the most important thing going on these days, but a topic on which I can provide expertise, so here ya go.
