Valett

Valett is an open source software tool for calculating fair values for letters in word games, developed by Joshua Lewis and announced on his blog in late 2012.

Here are some mostly technical thoughts about Valett, by John Chew.

Catastrophic Outrage: A Reply to Joshua Lewis’ “Rethinking the value of Scrabble tiles”

On his blog, Joshua Lewis announced the publication of his open source software, Valett, a tool for calculating ideal letter values for word games, inspired by his experiences as a SCRABBLE enthusiast. While Lewis’ intentions are clearly good, he has stirred up a lot of public attention by suggesting that the SCRABBLE game would be better if it used tile values computed by his program instead of the traditional values. I disagree, and have some issues with his methodology as well.

As I understand it, Valett takes a word list and an estimate of the distribution of word lengths that will be played in a game, and creates a list of letter values based on how difficult it estimates that it will be to play each letter in the game. It estimates this difficulty based on how many words each letter appears in, and which other letters each letter appears beside. The Q is hard to play not only because it only appears in 1.4% (2576/178691) of the playable words, but also because in all but 42 of those words it is followed by a U.

This kind of thinking is more advanced than what Alfred Butts did with the words that appeared on the front page of the New York Times to create the initial version of the tile values that eventually became enshrined in the SCRABBLE rules, but significantly behind the times in modern SCRABBLE strategy theory. Quackle, the free SCRABBLE artificial intelligence that has earned a 2224 Elo rating against human opponents, keeps track of how playable every possible combination of one to six tiles is, based on extensive simulation of game play. For example, it finds that a single “I” left on your rack after a play will lower your average final score by two points: as SCRABBLE players put it, an “I” has an equity value of -2. Given that the “I” currently has a face value of 1, if you wanted to create a “fair” SCRABBLE game that didn’t penalize players for drawing an “I”, you’d want to increase the face value by 2 points to 3. Likewise, you’d want your blanks to be worth -26 points. Yes, negative twenty-six: sure, you can often make a seven-tile “bingo” play if you draw the blank, but it wouldn’t help you much if it cost you 26 points every time you did.

If you did this, you’d reduce a little bit of the luck of the draw, but at the same time you’d be reducing the skill involved in recognizing which tiles are good or bad and playing accordingly. You’d end up with a game that was a little closer to just rolling a die to determine the winner. It’s worse, though, because as Quackle knows, equity values are not additive, and are not strongly correlated with adjacent tiles, as assumed by Valett. Two “I”s on your rack have an equity value of -12, and three “I”s -21. Even if those “I”s were now worth three points, you’d still be gnashing your teeth at your bad luck if you drew more than one of them at a time. There would always be lucky and unlucky tiles in the bag.

As an aside, this points out a smaller failing of Valett: it doesn’t prescribe a distribution of tiles. There are nine “I”s in a SCRABBLE set, and it’s generally understood that the “I” is a bad tile not only because multiple “I”s go poorly together in words, but because there are too many “I”s in the bag to begin with. There would be a lot more support for removing an “I” from the standard tile distribution than there would be for changing the value of an “I”.

The particular tile distribution also affects the playability of tiles. While there is a “Q” in 1.4% of words, we can’t have 1.4% of the tiles in the game be a “Q”, so we round down to one tile, making it slightly easier to play. For one thing, there’s no chance of drawing a second “Q” from a regular bag.

Valett’s requirement that you specify the rates at which words of each length are played is also problematic for a few reasons. The author finds in his own experience that he tends to play words of 2, 3, 7 or 8 letters more often than words of 4, 5 or 6 letters. This is typical for players who have done a little SCRABBLE word study, concentrating their efforts on where it pays off the most: 7- and 8-letter words to get that 50-point bingo bonus, and the 2- and 3-letter words that you need to know in order to find ways to fit those bingoes onto the board. It’s not typical of high-level or computer play, but who then is right? Should you play with different values against a weak opponent than against a strong opponent? Who should get to choose?

Finally, there’s the question of why the values should be changed at all. It would certainly cost the consumer a lot of money and lead to endless confusion about what version of the game was being played.

The design of the SCRABBLE game carefully balances skill and luck, and its enduring popularity is a consequence of this balance. The game has enough skill that a winner can take pride in his abilities, and if he hones his skills further, can win more often; the game has enough luck that a loser can tell himself that he could have won had he drawn better tiles. People often suggest to me ways in which this balance could be tipped, and given that the people who talk to me are usually skilled players, not surprisingly, the suggestions are almost always to remove a little luck from the game in favour of skill. The game doesn’t need this: it’s always had an intentional imbalance between the face and equity values of the tiles, and a deeper understanding of this tension can increase one’s enjoyment of the game.