Summing up to Scrabble

These are easy questions for the mathematically minded players who dominate national and international Scrabble tournaments. For the less mathematically inclined, the answers are 12 and otarine — meaning “relating to a sea lion” — respectively.

“Scrabble and math definitely use some of the same parts of my brain,” said Adam Logan ’95, a Scrabble champion and mathematics professor at the University of Waterloo in Canada.

This past Monday, his combined mathematical and verbal skills propelled Logan to win his third Canadian National Scrabble Championship, defeating a computer programmer in the final round by using the word “parities,” for which he received two triple-word bonuses and a total of 113 points.

Logan, a native of Canada, received his A.B. in mathematics from Princeton and started playing competitive tournament Scrabble at age 9. He has won numerous Canadian Championship titles, as well as the 1996 National Scrabble Championship and the 2005 World Scrabble Championship. When he’s not playing Scrabble, he researches algebraic number theory and elliptic curves.

While the game does not involve advanced or formal mathematics, many players like Logan recognize that subjects like probability and geometry, as well as basic arithmetic, play a huge role in Scrabble.

In his article “Newbie’s First Scrabble Lesson,” 2002 National Scrabble Champion Joel Sherman advises players to “accept the idea that Scrabble is a math game just as much as it is a word game.” Sherman goes on to explain that the strategy of the game is rooted in statistical analysis and probability, as well as spatial relationships on the board.

When Logan plays Scrabble, he uses his score sheet to keep track of exactly which letters have been played and which tiles are left. This enables him to track the probability of drawing certain tiles and judge the strength of his opponent’s letters and potential plays. The blank tiles, which can be used as any letter, are particularly important to monitor, Logan said.

“If I know that neither of the blanks have been played, then I might play more tiles so I would be able to draw more and maybe get [the blank tiles],” Logan said. “Also, I might restrict the ways my opponent could use all seven of his tiles, in case he has a blank one.”

Rapid tile turnover is often touted by mathematically minded players as a key to competitive Scrabble playing. There are only 100 total tiles in the game, and whichever player manages to use more of them in each turn gets to draw more, potentially higher-value, tiles.

The close relationship between math, computer science and Scrabble has also led to a number of computer programs that can help competitive Scrabble players train, Logan said. He uses one called Zyzzyva — named for a type of American weevil and the last word in the Scrabble dictionary — which allows users to practice by finding all words possible given a certain set of letters.

Logan does not, however, actually do any math when he plays Scrabble, except for adding up scores.

“It’s much more intuitive than calculated,” he said. “I wouldn’t compute any probabilities in the middle of a game. I like doing math, and I like playing Scrabble, but it’s difficult to concentrate on both at once.”