… And Scrabble Proved PSPACE-Complete
Having been invented in the US in the mid-20th century, Scrabble is now available in dozens of languages and sells in numbers measured in hundreds of millions. That makes it one of the most popular games in the world.

That has naturally piqued the interest of game theorists. “Since Scrabble is such a successful game, it becomes a natural question to determine the computational complexity of finding an optimal play,” say Michael Lampis at the KTH Royal Institute of Technology in Sweden and a few pals.
The same question has been successfully asked of many board games, such as chess, Go and Othello, which tend to be PSPACE or EXPTIME-complete. But Scrabble is trickier because players do not know the order in which the tiles will be drawn meaning that chance plays a greater role.
The question that Lampis and co attempt to answer is this: given a Scrabble position how hard is it to determine the best playing strategy?
They point out that in any given round, a Scrabble player is confronted with two tasks: deciding which word to form and deciding where to place it on the board. These tasks are related because the words that can be formed depend on the position of letters on the board.
But which of these task is it that makes Scrabble hard? What Lampis and co show is that both are hard and give a proofs of each to back up their claim. That’s impressive because it allow us to ‘see’ why Scrabble is hard.
“We establish that during the course of a game, Scrabble players need to perform not one, but two computationally hard tasks, which is probably the reason why Scrabble is so much fun to play,” they write.
That’s not to say computational complexity theorists are done and dusted with Scrabble. Their next task is to discover whether there is a polynomial-time algorithm to determine the move that would maximize the score achieved in this round.
Now that would be handy!
Ref: arxiv.org/abs/1201.5298: Scrabble is PSPACE-Complete
Keep Reading
Most Popular
Geoffrey Hinton tells us why he’s now scared of the tech he helped build
“I have suddenly switched my views on whether these things are going to be more intelligent than us.”
ChatGPT is going to change education, not destroy it
The narrative around cheating students doesn’t tell the whole story. Meet the teachers who think generative AI could actually make learning better.
Meet the people who use Notion to plan their whole lives
The workplace tool’s appeal extends far beyond organizing work projects. Many users find it’s just as useful for managing their free time.
Learning to code isn’t enough
Historically, learn-to-code efforts have provided opportunities for the few, but new efforts are aiming to be inclusive.
Stay connected
Get the latest updates from
MIT Technology Review
Discover special offers, top stories, upcoming events, and more.