MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The rules for "all words valid" scrabble are exactly the same as ordinary scrabble, except that every single combination of letters is in the dictionary. To make the game deterministic, we will also assume that every letter is worth the same amount of points (though it may be interesting to remove this restriction somehow)--so essentially it is just a game of placing tiles. Is there a winning strategy for either player?

share|cite|improve this question
Do you have the same arrangement of double/triple letter/word score panels? – S. Carnahan Sep 23 '10 at 5:26
In the absence of bonus panels, the locally score-maximizing strategy seems to involve playing 15 letter words in adjacent rows or columns. In this case, the first player wins, 1065 to 945. Under these assumptions, it seems to be against the second player's interest to fill in the next-to-last row or column, so I suspect the endgame (and perhaps the rest of the game) is nontrivial. – S. Carnahan Sep 23 '10 at 7:18

'Pass' is a valid move in Scrabble. This means that a game can last for ever, so you need some criterion for ending the game after each player has passed. It also means that the game is either a win for the first player, or a draw (because if the starting position is losing, the first player can pass).
If you don't allow passes, then I can't see a way of calculating who wins. It looks more complicated than Draughts, which succumbed to rigorous evaluation only after years of dedicated effort -- see
I have some experience in these matters -- a Scrabble program I co-wrote won a Computer Olympiad gold medal many years ago.

share|cite|improve this answer
Very interesting! Is your program publicly available? If not, can you, please, give some details or a link where it is described? – Victor Protsak Sep 23 '10 at 7:12
It was so long ago, I don't have source or executable any more. It gets a mention (Quetzal) on this compilation page: – TonyK Sep 23 '10 at 22:03

I'll try to kick things off...

Are there still double/triple letter/word score squares? I imagine the strategy would focus on putting down all your letters while aiming for these bonus squares while trying not to open up the board (to restrict your opponent's access to them)?

share|cite|improve this answer

I did indeed mean for the arrangement of of triple letter scores, triple word scores, etc to remain intact. I hadn't thought about the passing issue. I guess "no passes" would be the reasonable thing to do, though I believe TonyK when he says this will make the problem too difficult!

share|cite|improve this answer
This should have been left as a comment, rather than an answer... – Yemon Choi Sep 27 '10 at 2:58
I don't see how to do this...sorry I'm new to math overflow. – Phil Sep 27 '10 at 3:22
Yemon, people with reputations less than 50 cannot leave comments, so if they want to say something, they are forced to say it through an answer. – Todd Trimble Oct 27 '11 at 2:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.