Carnegie Mellon University

# The Piper

## CMU Community News

February 03, 2012

# Lucky Letters

## Statistics Scores Big With Scrabble

By Shilo Rea

In Scrabble and the online game Words With Friends, the letter "Q" has a high 10-point value, but it's really more like a five-point penalty.

According to new research from Andrew C. Thomas, visiting assistant professor of statistics and Scrabble aficionado, "Q" is the worst tile to have because you will end up scoring less. The best letters to have are S, Z and X.

Thomas' findings come from simulating roughly 10 million Scrabble games using an open-source artificial intelligence crossword game called "Quackle." Thomas conducted the research to determine how to better design a tournament to make the variable of drawing tiles as small as possible.

"I also wanted to find out how much of the variance in score comes from the tile order and board," he said.

Thomas lined the tiles up in a row instead of putting them in a bag.  Each player (not seeing the line of tiles) drew from one end. The alteration allowed for the same pattern to be replicated over multiple games, so that a player's result could be better compared against others.

He found that when you draw a tile during the course of a game makes a difference; there is a 30-point swing for having a blank tile at the beginning of a game versus the end.

Thomas calculated each tile's worth as it affected final scores. "S," the best letter to have, adds approximately 10 points. "Z" and "X" are also good letters to have. "V" and "U" are not tiles you want to draw very often.

Other findings include:

• The blank is worth about 30 points to a good player, each "S" about 10.
• "Q" is a burden to whichever player receives it, effectively serving as a five-point penalty.
• "J" is essentially neutral point wise.

Thomas' research and results also correlate to the popular online game Words With Friends. The only main difference in tile values between the two games is with "J." Words With Friends values a "J" at 10 points; its Scrabble value is eight. Drawing a "J" in a Words With Friends game positively affects your score - in Scrabble, it doesn't really make a difference.

"What's interesting about this research is that it used actual statistics - it wasn't just about having fun with Scrabble," Thomas said. "The simulations used data-mining and large-scale applications to tell us more about the game then we've ever known."