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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?

flag	asked Sep 23 2010 at 3:01 Phil 61●1

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Do you have the same arrangement of double/triple letter/word score panels? – S. Carnahan♦ Sep 23 2010 at 5:26

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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 2010 at 7:18

Pengo · Answer 1 · 2010-09-23 05:26:21Z UTC

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)?

TonyK · Answer 2 · 2010-09-23 07:06:16Z UTC

'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 http://www.sciencemag.org/cgi/content/abstract/1144079v1.
I have some experience in these matters -- a Scrabble program I co-wrote won a Computer Olympiad gold medal many years ago.

Phil · Answer 3 · 2010-09-26 14:24:37Z UTC

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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!

answered Sep 26 2010 at 14:24

Phil
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	This should have been left as a comment, rather than an answer... – Yemon Choi Sep 27 2010 at 2:58
	I don't see how to do this...sorry I'm new to math overflow. – Phil Sep 27 2010 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 2011 at 2:05

What is the strategy for “all words valid” scrabble?

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