While playing Word with Friends, I became curious. What word would actually cause the score meter's graph to actually hit its peak? Intuitively, it seemed the graph was non-linear -- playing a word that was just short of the maximum might still leave a lot of points on the table. Was I just not seeing the best play or was the best play always some out-of-the-ordinary word, like kabeljou[1].
By the way, playing the highest scoring word on every turn is not necessarily the best way to win a game. It's apt to leave easy openings for your opponent to use multiplers to good effect. That said, it works pretty well against Zynga's computer players.
[1] an Afrikaans-derived name for a fish, known in Britain as the meagre.
Install sbt, a la brew install sbt.
In the main directory, run:
$ sbt "run -wwf -board=empty.wwf -hand=xypdqab -interactive"
This will load a board from the file empty.wwf (which, as you'd expect, is an empty board) and produces a list of plays for the given hand and some options.
Drop the -interactive flag to just get a list of the top 25 plays.
You can specify a blank tile by passing an asterisk (*) in the hand.
When loading the board, the program removes played letters from a list of available tiles (a.k.a. the tile bag). An invalid board (e.g., one where more E tiles have been played than exist in the game) will cause the program to abort with an exception. Similarly, if you simulate playing a hand that contains tiles that cannot still be in a rack, you'll get an error.
In interactive mode, you'll be presented with the top 10 plays. You can step through more plays by entering N for next or P for previous. You can filter for plays that have a tile on a particular row/column with F=r,c (rows and columns are indexed from zero). You can see what the play looks like on the board with D=n (where n is one of the enumerated plays). Finally, if you just choose a play by entering its number the board file will be re-written with your play.
The board file is trivial. Each line is a row, and each character in the row is a column. Underscores represent unplayed squares. Upper case letters represent played letters. Lower case letters represent blank tiles that have been played and are now fixed as the given letter.
The algorithm started as an exhaustive, recursive search of the possible placements of tiles: compute the places a tile may be placed on the board, try every rack tile in each place. For each tile placed, compute a new set of playable locations and try every remaining tile. As each tile is placed, determine if the play is valid (all newly formed words are in the dictionary) and remember the valid plays.
The rules of the game allow some optimizations. During the recursion, once a second tile has been placed, all subsequent tiles must be placed in line with the first two, either horizontally or vertically. I call this the direction of play. One optimization is that if any word formed perpendicular to the direction of play is not in the dictionary, the algorithm can short-circuit. Further, once a particular perpendicular word has been validated it need not be checked again.
Another optimization involved adding a bloom filter containing every fragment of every word in the dictionary. The bloom filter takes the current word (in the direction of play) and tells us whether, through the addition of more letters (suffixes and/or prefixes) we can ever produce a valid word.
Once all the valid plays are computed, they are scored and sorted.
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